Microfluidic system, apparatus and method for particle focusing and separation

Abstract

According to a first aspect of the present inventive concept there is provided a system for sheathless focusing of nanoparticles, comprising a substrate with at least one straight microchannel, a viscoelastic fluid containing nanoparticles, a pumping mechanism to drive laminar flow, wherein the fluid, channel geometry, and flow conditions generate elasto-inertial forces that focus nanoparticles as small as 10 nm, overcoming Brownian motion through optimized viscoelastic stress profiles. According to a second aspect there is provided an arrangement for sheatless focusing of nanoparticles contained in a viscoelastic fluid wherein the microchannel's geometry is configured to together with the visco-elastic fluid's composition generate elasto-inertial forces on the nanoparticles to separate the nanoparticles on different levels in the laminar flow, such that the nanoparticles are focused based on the size of the nanoparticles.

Description

[0001] MICROFLUIDIC SYSTEM, APPARATUS AND METHOD FOR PARTICLE FOCUSING AND SEPARATION

[0002] Technical field

[0003] The present disclosure relates to microfluidic systems and methods for the high-resolution focusing and separation of nanoparticles. More specifically, it involves a sheathless elasto-inertial microfluidic system capable of manipulating nanoparticles as small as 10 nm for biomedical diagnostics, nanomedicine development, and environmental monitoring.

[0004] Further, the disclosure relates to microfluidic devices and methods for the separation and concentration of particles in non-Newtonian fluid. The devices utilize hydrodynamic and elasto-inertial effects to achieve high resolution and high-throughput separation of particles based on size.

[0005] Background

[0006] Microfluidics has been used in a wide range of research areas, such as biotechnology, medicine, chemistry, and environment as it allows control and manipulation of fluids in microchannels with high precision. Therefore, this technology has been attractive for focusing, mixing, sorting, and separating particles suspended in various mediums. If the particle manipulation is achieved using an external field such as electric, magnetic, or acoustic, it is referred to as active microfluidics. On the other hand, a system only relying on features such as the channel geometry, fluid flow, particle size, and density is defined as passive microfluidics. Deterministic lateral displacement (DLD), pinched flow fractionation (PFF), and inertial focusing are the examples of such systems. Among active and passive microfluidic techniques, inertial microfluidics presents itself as a robust, reliable, label- free, and high-throughput technique.

[0007] Inertial focusing indicates the migration of randomly distributed particles toward equilibrium positions as they flow in microfluidic channels. The focusing phenomenon was initially observed in 1961 by Segre and Silberberg. According to their observation, randomly distributed spherical particles at the inlet of a cylindrical pipe migrated and formed an annular ring that was located 0.6 times of pipe radius between the centerline and pipe wall at the outlet. Over the past two decades, other cross-sections such as rectangle, square and triangle have been studied as microfluidic channels, and unique equilibrium positions have been found. These studies have shown that the balance between shear-induced (FS) and wall-induced lift forces (FW) in Newtonian fluids defines the final equilibrium positions of the particles. In addition to the microchannel cross-section, the Reynolds number (Re), which is a dimensionless number defined as the ratio of inertial over viscous time scales, plays a key role for the particle migration. Unlike general microfluidic applications, where fluid inertia is negligible (Re~0), inertial focusing occurs when fluid inertia is not negligible (Re>1 ). Although interesting from a physics perspective, inertial focusing in straight channels with Newtonian fluids results in multiple equilibrium positions, thereby limiting its application. Single equilibrium positions can be achieved by adding curvature to the systems, but such systems work in a narrow bandwidth of conditions, require high pressures when targeting micron and sub-micron particles, and are more cumbersome to parallelize to increase the throughput than straight systems. On the other hand, using non-Newtonian fluid, i.e. resorting to elasto-inertial microfluidics can easily achieve single stream focusing of particles in straight microfluidic channels.

[0008] While inertial microfluidics is based on the finite flow of Newtonian fluids, elasto-inertial microfluidics requires non-Newtonian fluids (viscoelastic fluids). The combination of elastic and inertial forces dictates the particle migration in microchannels.

[0009] Studies have shown that when inertial microfluidics is used in a rectangular microchannel, two focusing positions appear at the middle of the longer side of the channel. On the other hand, using the same cross-sectional channel with a viscoelastic fluid results in a single focusing position at the center of the microchannel. This single focusing stream arises due to the particle migration toward the region of lowest first normal stress difference, located at the middle of the microchannel. While relatively large particles can be focused into a single streamline in these systems described above, there is currently a challenge has remained as a challenge due to the increasing complexity of the particle manipulation as the particle size becomes significantly smaller than the characteristic channel dimension ( blockage number defined as particle size divided by characteristics channel dimension, B<0.07).

[0010] The ability to manipulate nanoparticles is crucial for many fields ranging from disease diagnostics to drug delivery. Nanoscale bioparticles in the body play an indispensable role in health and their dysregulation causes many diseases. For example, lipoproteins, such as high-density lipoprotein (HDL) and low-density lipoprotein (LDL), transfer lipids through the body. Their imbalance, as well as their deviation from canonical physical properties such as size, is a marker of dyslipidemia and metabolic diseases. Moreover, certain types of lipoproteins are associated with neurodegenerative diseases such as Alzheimer’s. Extracellular Vesicles (EVs) enable intercellular communication in the body, and certain types of EVs are associated with diseases like cancer. Current methods to sort biological nanoparticles, such as size exclusion chromatography (SEC), asymmetrical flow field-fractionation (AF4) or centrifugal techniques8 are cumbersome, expensive, and rarely result in pure fractions. Therefore, developing advanced methods to sort and study particles based on their physical properties, such as size, is crucial. In addition to biomedical applications involving biological nanoparticles, environmental nanoparticles are also relevant for human health. For example, microplastics in water pose a significant threat to human health. The toxicity and environmental impact of these contaminants is highly affected by particle size and properties. Therefore, size-based enrichment of nanoparticles is critical for downstream analysis in environmental studies towards determining the toxicities of these particles in solution.

[0011] Existing nanoparticle focusing technologies, such as size exclusion chromatography (SEC) and asymmetrical flow field-fractionation (AF4), are limited by low throughput, complex setups, and limited resolution for particles below 100 nm. Prior microfluidic systems require external fields (magnetic, acoustic, electric) or complex channel designs to manipulate nanoscale particles, often resulting in high operational costs and limited scalability. There remains a critical need for a cost-effective, high-throughput, and scalable method to focus and separate nanoparticles without relying on external forces.

[0012] Although there is considerable interest in the field of elasto-inertial microfluidics owing to its potential applications, research on particle focusing has been mostly limited to low Reynolds numbers (Re<1 ), especially in flow through straight rectangular cross-section channels, and particle migration towards equilibrium positions is not well studied. In addition, the particle separation applications in the previous studies using straight channels all considered two inlets where one inlet carries the sample flow and the second inlet carries a sheath flow. The utilization of the sheath flow decreases the overall throughput.

[0013] Summary

[0014] An objective of the present disclosure is to provides a system, method, and apparatus for the sheathless focusing and separation of nanoparticles using elasto-inertial microfluidics.

[0015] To overcome these issues, we present a high aspect ratio (AR, height>width) microfluidic channel with a single inlet, which initially focuses all particles and then separates them by size exploiting the difference in their migration speed.

[0016] This disclosure addresses the aforementioned challenges by introducing an optimized elasto-inertial microfluidic design that operates efficiently under practical conditions.

[0017] According to a first aspect, there is provided a system for sheathless focusing of nanoparticles. The system comprises a substrate with at least one straight microchannel, a viscoelastic fluid containing nanoparticles, a pumping mechanism to drive laminar flow, wherein the fluid, channel geometry, and flow conditions generate elasto-inertial forces that focus nanoparticles as small as 10 nm, overcoming Brownian motion through optimized viscoelastic stress profiles.

[0018] By sheathless it is here meant that the system utilizes only a single flow, wherein the particles to be separated are distributed in that single flow.

[0019] The microchannel has a geometry configured to cause the viscoelastic fluid to generate elasto-inertial forces that separate the nano particles within the fluid.

[0020] Advantageously, the system achieves focusing of nanoparticles as small as 10 nm without the need for external sheath flows by utilizing the elasto-inertial forces generated by the flow of the visco-elastic fluid within the straight channel comprising a specific geometry.

[0021] Thanks to the system being sheathless, the overall throughput of the system is increased, as compared to prior art. There is thus provided a high through-put system.

[0022] Furthermore, by providing a passive system that does not rely on external forces a cost-effective, high-throughput, and scalable method to focus and separate nanoparticles is provided.

[0023] According to a second aspect, there is provided an arrangement for sheathless focusing of nanoparticles contained in a viscoelastic fluid. The arrangement comprises a substantially straight microchannel, a pumping mechanism configured to drive the viscoelastic fluid as a laminar flow through the microchannel, wherein the microchannel’s geometry is configured to together with the visco-elastic fluid’s composition generate elasto-inertial forces on the nanoparticles to separate the nanoparticles on different levels in the laminar flow, such that the nanoparticles are focused based on the size of the nanoparticles.

[0024] This second aspect may generally present the same or corresponding advantages as the first aspects.

[0025] According to an embodiment, the microchannel may be designed as a dual-section microchannel, with a focusing section upstream and a separation section downstream, the focusing section having a smaller cross-section than the separation section, where the focusing section’s cross-section has a width, w of 1-30 pm and a height, h of 10-200 pm, preferably with the width about 5 pm and a height of about 60 pm, wherein the microchannel is split into two or more subchannels downstream the focusing section towards the separation section. As the microchannel is split into two or more subchannels after the focusing section, pre-focused nanoparticles leaving the focusing section start to migrate from the inner walls towards the center of the subchannels of the separation section.

[0026] According to an embodiment, an aspect ratio, AR, where AR=h / w is between 20 and 2 for the focusing section, and between 10 and 2 for the separation section, preferably AR for the focusing section is about 12, and AR for the separation section is about 6.

[0027] According to an embodiment, the nanoparticles in the viscoelastic fluid are in a range between 10 nm and 1000 nm, preferably between 20 nm and 500 nm, and more preferably between 50 nm and 200 nm.

[0028] According to an embodiment, the viscoelastic fluid comprises at least one elasticity enhancer from a group comprising: polyethylene oxide, PEO, polyacrylamide, xanthan gum, and hyaluronic acid.

[0029] According to an embodiment, the viscoelastic fluid has a concentration in a range from about 50 ppm to about 80000 ppm.

[0030] According to an embodiment, the pumping mechanism is configured to provide the laminar flow in a range from about 0.5 pl / min to about 200 pl / min.

[0031] According to an embodiment, the microchannel is arranged on a substrate, where the substrate is designed as a plastic chip, an elastomerbased chip, a silicon-based chip, a Polydimethylsiloxane (PDMS), based chip, a thermoplastic chip, a glass-based substrate, or a glass-silicon-based substrate.

[0032] According to an embodiment, the focusing section extends between 2 and 4 mm, preferably about 3 mm, and wherein the total length of the microchannel, including the focusing section and the separation section is between 5 and 10 mm, preferably about 6 mm.

[0033] According to a third aspect there is provided a method for sheathless focusing of nanoparticles contained in a viscoelastic fluid. The method comprises arranging an arrangement according to any of claims 1 to 10, and pumping the viscoelastic fluid comprising the nanoparticles as a laminar flow through the microchannel of the arrangement, to generate elasto-inertial forces on the nanoparticles to separate the nanoparticles on different levels in the laminar flow, such that the nanoparticles are focused based on the size of the nanoparticles.

[0034] This third aspect may generally present the same or corresponding advantages as the former aspects.

[0035] According to an embodiment, the method may further comprise the nanoparticles in the viscoelastic fluid comprises a sample comprising lipid nanoparticles, LNPs, the sample having been introduced in the microchannel, the LNPs are aligned and separated by the elasto-inertial forces along a streamline in the microchannel, wherein the method further comprises simultaneously when aligning and separating the LNPs, exchanging a solvent or a buffer phase of the viscoelastic fluid by co-flowing the viscoelastic fluid with a second fluid through the microchannel.

[0036] According to an embodiment, the method may further comprise focusing the nanoparticles and exchanging a solvent or a buffer phase using at least one of tangential flow filtration (TFF), dialysis, or diafi Itration.

[0037] According to an embodiment, the method may further comprise encapsulating, within the LNPs, therapeutic nucleic acids from at least one of mRNA, siRNA, or plasmid DNA.

[0038] The system, method and apparatus disclosed in the present disclosure provides at least the following advantages.

[0039] Sheathless Focusing: Achieves focusing of nanoparticles as small as 10 nm without the need for external sheath flows.

[0040] Dual-Section Microchannel Design: A high-aspect-ratio focusing segment followed by a low-resistance separation section maintains particle alignment while minimizing pressure drops.

[0041] High-Throughput and Low-Pressure Operation: Optimized fluid dynamics allow for flow rates exceeding 1 mL / min without excessive pressure requirements. Broad Size Range: Capable of focusing particles from 10 nm to 1 pm with high size resolution.

[0042] Viscoelastic Force Optimization: Incorporates viscoelastic forces in flows through high aspect ration microchannels to counteract Brownian motion, enabling stable nanoparticle focusing even at the nanoscale.

[0043] Versatile Applications: Applicable to biomedical diagnostics (lipoproteins, extracellular vesicles) and environmental monitoring (nanoplastics).

[0044] In one embodiment, a system for focusing micro- and / or nanoparticles in a fluid is provided. The system may include a substrate and at least one straight microchannel with an inlet and an outlet. The system may further include a fluid moving through the channel in a laminar flow with suspended nanoparticles and a pumping element driving the flow. The fluid, channel, and pumping element may be configured to cause elasto-inertial forces to act on the micro- and nanoparticles, focusing them into localized stream lines at the channel center.

[0045] In another embodiment, a method for focusing nanoparticles in a moving viscoelastic fluid includes providing micro- and nanoparticles suspended in a fluid into a channel and flowing the fluid through the channel under conditions such that elasto-inertial forces acting on the particles result in their localization into one or more stream lines at the channel center.

[0046] In a further embodiment, an apparatus for focusing micro- and / or nanoparticles of a predetermined size suspended in a moving fluid into one or more localized stream lines is provided. The apparatus may include a substrate and at least one straight microchannel with an inlet and an outlet. Moving the fluid suspension from the inlet to the outlet in a laminar flow focuses the nanoparticles of a predetermined size into one or more localized stream lines.

[0047] In another embodiment, a system for sorting nanoparticles from a mixture suspended in a fluid is provided. The system may include a substrate with at least one straight microchannel having an inlet and an outlet. Moving the fluid suspension through the channel in a laminar flow focuses the nanoparticles into one or more localized stream lines. The outlet may have multiple branches for separating the nanoparticles based on size.

[0048] In yet another embodiment, a method for separating target microparticles and / or nanoparticles from a population of particles includes providing a population of particles in a fluid suspension and flowing the suspension through a channel under conditions that cause the particles to form localized stream lines at the channel center. The method may further include dividing an output from the channel into multiple branches, where one branch is enriched in target particles.

[0049] In yet another embodiment, a method for pre-focusing the microparticles to form localized stream lines at the channel center followed by splitting the channel into two parallel channels to force the particles to migrate towheads the channel center for size based separation.

[0050] In yet another embodiment, a method for pre-focusing the nanoparticles to form localized stream lines at the channel center followed by splitting the channel into two parallel channels to force the particles to migrate towards the channel centre for size based separation.

[0051] In yet another embodiment, a system for focusing nanoparticles in a fluid, may comprise a substrate; at least one straight microchannel provided on the substrate, the microchannel having an inlet and an outlet; a fluid moving along the channel in a laminar flow, the fluid having suspended nanoparticles; and a pumping element driving the laminar flow of the fluid, wherein the fluid, channel, and pumping element are configured to cause elasto-inertial forces to act on the nanoparticles, focusing them into one or more localized stream lines.

[0052] In another embodiment, the system may comprise a microchannel having a width between about 2 pm and about 500 pm and a height between about 10 pm and about 200 pm. The nanoparticles may range in size from about 20 nm to about 1000 nm The viscoelastic fluid comprises an elasticity enhancer selected from the group consisting of polyethylene oxide (PEO), polyacrylamide, xanthan gum, and hyaluronic acid. In addition, the viscoelastic fluid may have a concentration ranging from about 10 ppm to about 10000 ppm.

[0053] In another embodiment, an apparatus for focusing nanoparticles of a predetermined size suspended in a moving fluid into one or more localized stream lines, comprising: a substrate; at least one straight microchannel provided on the substrate, the microchannel having an inlet and an outlet; and means for moving the fluid suspension from the inlet to the outlet in a laminar flow, wherein the fluid, channel, and moving means focus the nanoparticles of a predetermined size into one or more localized stream lines. The apparatus wherein the microchannel has a width between about 2 pm and about 500 pm and a height between about 10 pm and about 200 pm. The apparatus, wherein the nanoparticles range in size from about 20 nm to about 1000 nm and the viscoelastic fluid comprises an elasticity enhancer selected from the group consisting of polyethylene oxide (PEO), polyacrylamide, xanthan gum, and hyaluronic acid. The apparatus wherein the viscoelastic fluid has a concentration ranging from about 50 ppm to about 10000 ppm is envisioned.

[0054] Finally, a system for sorting microparticles and nanoparticles from a mixture suspended in a fluid, comprising: a substrate; at least one straight microchannel provided on the substrate, the microchannel having an inlet and an outlet; means for moving the fluid suspension through the channel in a laminar flow, wherein the fluid, channel, and moving means focus the nanoparticles into one or more localized stream lines; an outlet with multiple branches for separating the nanoparticles based on size. The system has the microchannel has a width between about 2 pm and about 500 pm and a height between about 10 pm and about 200 pm. The system of claim 16, wherein the nanoparticles range in size from about 20 nm to about 1000 nm. The system of claim 16, wherein the viscoelastic fluid comprises an elasticity enhancer selected from the group consisting of polyethylene oxide (PEO), polyacrylamide, xanthan gum, and hyaluronic acid. The system wherein the viscoelastic fluid has a concentration ranging from about 50 ppm to about 10000 ppm. A method for separating target nanoparticles from a population of nanoparticles, comprising: providing a population of nanoparticles in a fluid suspension; flowing the suspension through a channel under conditions that cause the nanoparticles to form localized stream lines; and dividing an output from the channel into multiple branches, where one branch is enriched in target nanoparticles. The method wherein the channel has a width between about 2 pm and about 500 pm and a height between about 10 pm and about 200 pm. The method wherein the nanoparticles range in size from about 20 nm to about 1000 nm. The method of wherein the viscoelastic fluid comprises an elasticity enhancer selected from the group consisting of polyethylene oxide (PEO), polyacrylamide, xanthan gum, and hyaluronic acid. The method, wherein the viscoelastic fluid has a concentration ranging from about 50 ppm to about 10000 ppm.

[0055] In certain embodiments, the disclosed elasto-inertial microfluidic system enables precise, sheathless focusing of lipid nanoparticles (LNPs) and may be used either in conjunction with or as a replacement for conventional buffer exchange methods such as tangential flow filtration (TFF), dialysis, or diafiltration.

[0056] When integrated upstream or downstream of these modules, the system enriches for LNPs within a defined size distribution, improves removal of unencapsulated payloads or aggregates, and enhances the efficiency of buffer exchange by presenting a more uniform particle population.

[0057] In another embodiment, the system functions as a standalone purification and buffer exchange platform, eliminating the need for conventional TFF altogether. In this mode, the device simultaneously performs nanoparticle alignment, size selection, and flow-mediated buffer replacement by continuous or staged co-flow with desired formulation buffers. This continuous, pressure-controlled process enables low-shear, high- resolution purification of LNPs, minimizing shear-induced structural damage and improving process scalability for clinical and industrial applications.

[0058] The method is particularly suited for formulation of LNPs encapsulating nucleic acid cargo such as mRNA, siRNA, or plasmids, where precise control over particle size and buffer conditions is critical to therapeutic efficacy and stability.

[0059] Brief description of the drawings

[0060] The above, as well as additional objects, features, and advantages of the present description, will be better understood through the following illustrative and non-limiting detailed description, with reference to the appended drawings. In the drawings like reference numerals will be used for like elements unless stated otherwise.

[0061] Figure 1 a is a schematic illustration of the microfluidic design, including the cross-sectional view showing the forces governing particle focusing in inertial and elasto-inertial microfluidics. Figure 1 b is an experimental comparison of inertial and elasto-inertial focusing in a high-aspect-ratio microchannel (h = 60 pm, w = 5 pm) at a flow rate of 3 pL / min. Scale bar: 50 pm.

[0062] Figure 2 is a schematic illustration of the microfluidic system meticulously engineered with high-aspect-ratio microchannels that facilitate the sheathless focusing and size-based separation of nanoparticles. The key design elements and dimensions are illustrated in the provided schematics (a-d), reflecting progressive optimizations for improved focusing efficiency, differential migration, and separation.

[0063] Figure 3 is a schematic illustration of a design of the microfluidic chip, a Focusing section - the inlet is followed by a straight focusing section, b Migration section - the main channel is split in two parallel channels where bottom channel has slightly higher resistance as highlighted in the box. This resistance causes particles to follow upper channel that allows to observe migration.

[0064] Figure 4 is a schematic illustration of the effect of particle size on focusing at different flow rates. Fluorescence intensity graphs of 3, 5 and 10 pm particles in microchannel (h=60 pm, w=40 pm) at PEO concentration of 4000 ppm for a 25 pL / min, b 50 pL / min, c 100 pL / min and d 250 pL / min.

[0065] Focusing qualities of particles in each case are shown in the boxes.

[0066] Figure 5 is a schematic illustration of the effect of channel geometry on particle focusing. Cross-sections of each case are shown on the left side, a Effect of channel width- Focusing quality of 5 pm particles in microchannels with two different width (w=20,40 pm, h=60 pm) b Effect of channel height- Fluorescence intensity graphs and focusing quality of 5 pm particles in microchannels (h=90,60 pm, w=20 pm).

[0067] Figure 6 is a schematic illustration of the effect of PEO concentration on focusing, a Experimental data of focusing of 10 pm particles at different PEO concentrations (Flow rate=50 pL / min). The fluorescence signals were recorded at the end of the focusing section. Dashed lines are the channel walls. Scale bar: 100 pm b Focusing bandwidths (FWHM) over normalized channel width of 10 pm particles for four different PEO concentrations from 5 to 150 pL / min. Increasing the PEO concentration improves focusing quality more significantly at higher flow rates.

[0068] Figure 7 is a schematic illustration of a numerical study of particle migration, a The first normal stress difference (N1 ) across the cross-section of the channel. The particle attains its equilibrium position at the center of the channel where / V1 = 0. b Migration of 7.5 and 10 pm particles from two different positions near the wall toward the channel centerline. Dashed lines represent the starting positions and solid lines represent the final measured positions, c Particle spanwise position. Two different starting positions (0.15 W and 0.3 W) are shown, d Particle migration velocity, e Particle stream-wise velocity, f Particle angular velocity.

[0069] Figure 8 is a schematic illustration of particle migration trajectories, a Schematic of microfluidic chip with focusing and migration section. Highlighted boxes (left, w=20 pm and right, w=40 pm) show representative experimental results of particle migration from position 1 to 9 at a PEO concentration of 4000 ppm. White dashed lines are the channel walls. Scale bars: 100 pm. b-c Trajectories of 3 pm and 5 pm particles at PEO concentration of b 2000 ppm and c 4000 ppm at flow rates of 1 pL / min and 2.5 pL / min. The channel AR=3 (w=20 pm), d-e Trajectories of 5 pm and 10 pm particles at PEO concentrations of 2000 and 4000 ppm at flow rate of d 2.5 pL / min and e 50 pL / min. The channel AR=1.5 (w=40 pm).

[0070] Figure 9 is a schematic illustration of particle trajectories from position 1 to 6 with experimental image of 5 (cyan), 7 (red), and 10 (green) pm particles at position 6. Separation of 5, 7, and 10 pm particles at fixed PEO Concentration (1000 ppm) is shown at flow rates a 50 pL / min, b 100 pL / min and c 150 pL / min. (w=40 pm, h=120 pm) Dashed lines are the channel walls. Scale bars: 100 pm.

[0071] Figure 10 is a schematic illustration of the focusing of 25 nm particles. Experimental data of particle focusing from 0.5 to 2 pL / min a high aspect ratio microchannel (h=60 m, w=10pm). Scale bar is 50 pm.

[0072] Figure 11 is a schematic illustration of the effect of the channel width. The fluorescence intensity as a function of normalized spanwise position. Experimental data and the fluorescence intensity of the 50 nm particles in two channel widths from 0.5 pL / min to 3 pL / min. Scale bar is 50 pm.

[0073] Figure 12 is a schematic illustration of the effect of PEO concentration. Experimental images and normalized fluorescence intensity graphs as a function of spanwise position of 25 nm and 100 nm particles for four PEO concentrations. Scale bar is 50 pm.

[0074] Figure 13 is a schematic illustration of the effect of particle size. Experimental data and the fluorescence intensity of the particle focusing at fixed PEO concentration (2000 ppm) and flow rate (1 pL / min). Scale bar is 50 pm.

[0075] Figure 14 is a schematic illustration of the effect of flow rate, a) Experimental data and fluorescence intensity graphs. Scale bar is 50 pm. b) Heat map. Figure 15 is a schematic illustration of a numerical analysis of particle focusing and migration, a) The first normal stress difference (Ni) across the channel cross-section. The particle reaches its equilibrium position at the center of the channel where Ni=0. b) Particle spanwise position for AR=12 and the particles with diameters of 1 .6 pm, 1 pm and 750 nm over time.

[0076] Figure 16 is a schematic illustration of migration of particles, a) Microfluidic device to observe migration and experimental results of migration of 500 nm and 1 pm particles. Scale bar: 50 pm b) The fluorescence intensity results of both particles. Pink line indicates the center of the channel c) The trajectories of both particles based on average intensity points.

[0077] Figure 17 is a schematic illustration of focusing of nanobioparticles at 1000 ppm of PEO and 1 pL / min of flow rate, a) HDL (10 nm), b) LDL (25 nm), c) Liposome (90 nm), d) EVs (100 nm). Scale bar is 50 pm.

[0078] Figure 18 is a schematic illustration of the effect of particle size on focusing for various conditions, a 3-5 pm particles in microchannel (h=60 pm, w=20 pm) at 10 pL / min and 500 ppm of PEO b 5-10 pm particles in microchannel (h=60 pm, w=40 pm) at 10 pL / min and 500 ppm of PEO c 5-10 pm particles in microchannel (h=60 pm, w=40 pm) at 10 pL / min and 2000 ppm of PEO d 5-10 pm particles in microchannel (h=60 pm, w=40 pm) at 100 pL / min and 2000 ppm of PEO. Scale bars: 100 pm.

[0079] Figure 19 is a schematic illustration of particles in the corner. 5 pm and 10 pm particles flowing through the channel, where some of the 5 pm particles are trapped in the corner of the channel while 10 pm particles are focused in the channel center under the same experimental conditions. Scale bar: 100 pm.

[0080] Figure 20 is a schematic illustration of the effect of channel height. Fluorescence intensity graph and focusing quality of 10 pm particles in microchannels (h=60, 120 pm, w=40 pm). At flow rate 50 pL / min (1000 ppm) and at 100 pL / min (500 ppm). Figure 21 is a schematic illustration of the effect of channel height. Fluorescence intensity graph and focusing quality of 10 pm particles in microchannels (h=60, 120 pm, w=40 pm) at three different Reynolds numbers.

[0081] Figure 22 is a schematic illustration of the effect of PEO concentration on focusing of 5 pm particles.

[0082] Figure 23 is a schematic illustration of lateral particle focusing positions at the channel outlet (position 9). a Cross-sectional intensity summarizing all the experimental conditions for 3-5-10 pm particles, b Schematic of secondary flow streamlines in high aspect ratio microchannels, c Final position of 3-5-10 pm particles at different PEO concentrations (from 500 ppm to 4000 ppm) and flow rates (5, 10, 25, 50, 100 and 150 pL / min).

[0083] Figure 24 is a schematic illustration of shear viscosities of solutions at different PEO concentrations.

[0084] Figure 25 is a schematic illustration of three-dimensional view of the computational domain. N1 and U represent the first normal stress difference and stream-wise velocity in their corresponding planes. The aspect ratio of the channel is 3 and the ratio of the channel height to the particle diameter is 12. The particle has reached an equilibrium position in the middle of the domain.

[0085] Figure 26 is a schematic illustration of the angular velocity of the particle relative to the x axis normalized by the shear rate is calculated across different Weissenberg numbers. The blue circles denote the numerical results, the black squares the experiments of Snijkers et al.12, and the purple symbols are from the numerical code in Goyal & Derksen13.

[0086] Table S1 Rheological properties of solutions containing PEO of MW=2x106 g / mol. Figure 27 is a schematic illustration of the microfluidic design, including the cross-sectional view showing the forces governing particle focusing in inertial and elasto-inertial microfluidics.

[0087] Figure 28 is a schematic illustration of a method according to an aspect of the present disclosure.

[0088] Detailed description

[0089] The present disclosure is based, at least in part, on the discovery that if one carefully controls the geometries and dimensions of microfluidic devices in flow through non-Newtonian fluids, it is possible to focus particles at blockage ratio beyond the theoretical and practical limit in flow through microfluidic channels. For example, careful control of the geometries, concentration of viscoelastic fluid, and flow rate can be used to focus particles into a narrow fluid streamline. Furthermore, by splitting the channel in the middle into two channels the pre-focused particles can be forced to go through a strict sizebased migration for separating the particles. The migration velocity can enable to sort particles by size, and to design devices with desired throughput and reasonable dimensions. Here, particles are first focused, and then the channel split into two to allow particle migration from the side wall toward the centre based in size. By controlling the channel aspect ratio, it is possible to focus nanoparticles without the need of sheath flow which significantly reduce complexity and increase throughput of the system.

[0090] Different microfluidic channels with different widths and heights may be designed fabricated. The microfluidic channels may contain a first section aiming at focusing particles in the middle which is followed by a second section where the already-focused particles are quickly displaced toward the inner channel wall and observed as they migrate back to the center. In the second section, the trajectories can be observed, and their dependencies on the particle size, channel width, flow rate, and concentration of elasticity can be used to optimize particle separation. The first section is a straight microchannel and in the second section, the channel splits into two branches, which receive 1 :1 ratio of the fluid of the fluid and / or arbitrary ratio depending on the channel resistance designed. Pre-focused particles enter the second section very close to the wall of the channel receiving the portion of the flow and start migrating toward the center of the new channel. The splitting can be repeated several times to increase the purity of particles migrating.

[0091] Elasto-inertial particle focusing is complex and the relationship between the forces affecting the particle migration towards the equilibrium position. For example, particles pre-focused near the channel wall will with increase of the flow rate experience stronger inertial and elastic forces, and thus enhances the secondary cross-flow induced by the second normal stress difference. Secondary flow streamlines for the high aspect ratio corresponds to a specific region will cause a second equilibrium position, in addition to midplane. This is yet another differentiating parameter that occurs at relatively high flow rates in viscoelastic flows. These observations suggest a role of the N2-induced secondary flow at high flow rates when inertia becomes important. Here, some region where flow streamlines are assumed to be stronger, acts as a barrier. If the forces that move the particles overcome this barrier, particles are likely to be in the channel center. As the forces strongly depend on the particle sizes, larger particles are able to pass this barrier and focus in the center easier than smaller particles. Similar results are obtained for different PEO concentrations: most of the particles are found before and after the barrier. For example, three different particle sizes are observed in Region before the barrier, when the PEO concentration is lowest (500 ppm). Increasing the PEO concentration to 4000 ppm reduces the number of particles found in Region before barrier and increases the number of particles found in Region at the channel center. Moreover, this change is more significant for the largest particle. Hence, while complex, manipulating several parameters that have an impact on particle focusing, such as particle size, channel dimensions, concentration of viscoelastic fluid, and flow rate it is possible to first pre-focus particles into a narrow stream in. a focusing section of straight high aspect ration microchannel and follow this by splitting the channels to allow particles migrate from the channel wall towards the center based on size. By optimizing the flow conditions, particles can be allowed to pass a barrier of secondary rotational forces to reach the channel center while other smaller particles are restricted to reach the channel center and may be separated.

[0092] This paper reports elasto-inertial focusing of nanoparticles, down to 50 nm, for the first time using straight high aspect ratio (AR=height / width) microchannels in a sheath-less flow. Moreover, the presented work provides a comprehensive study of parameters affecting nanoparticle focusing in elasto-inertial flow, dominated by the elasticity and it covers the Reynolds number from 0.03-1.22, Weissenberg number from 48-1110, and Elasticity number from 63-5955. These experimental findings have a great potential to be the initial steps for the applications that require high-resolution particle separation and manipulation in various fields.

[0093] Previously, the blockage ratio defined as the ratio of particle size over characteristic dimension of the channel (a / L) to determine the focusing of the particles in a microfluidic channel was suggested 0.06 for the elasto-inertial flow. In this disclosure, using a high AR microfluidic channel, we describe particle focusing at least down to 50 nm in size. Our approach benefit from the high AR geometry of the microchannels, where the smaller dimension of the channel (width) determines the focusing. We show the elasto-inertial focusing of 50 nm particles at the blockage ratio of 0.005. We also investigated the focusing of larger particles, and as expected the focusing improves as the particle size gets larger, and the increasing the viscoelasticity of the fluid allows focusing the particles at the lower flow rates. Furthermore, we show the complete focusing of all the particle sizes at the channel center for the optimized PEO concentration and flow rate. Our results show that the elasto-inertial focusing of nanoparticles is possible in a sheathless flow and the limitations of the blockage ratio can be reduced using high AR microchannels. Furthermore, the ability to focus nanoparticles in a simple and small footprint microfluidic channel has a potential to increase the throughput by the parallelization of the microchannels. Therefore, the presented method can lead to many applications in the field of biomedicine that high-throughput and high-resolution particle separation are needed, such as separation of cells, bacteria, exosomes in diagnostic applications and other industrial applications.

[0094] Below follows a description of a plurality of examples od use of the system, method and apparatus of the present disclosure.

[0095] Bacteria separation is combination of selective cell lysis with elasto- inertial enrichment of bacteria for sepsis application. Blood cells in the sample is exposed to selective lysis mixture of sodium cholate hydrate and saponin (Russom et al, patent pending), which completely disrupt blood cells while intact viable bacteria and debris are remaining. By adding elasticity enhancer, such as PEO to the cocktail of blood and lysis buffer one can selectively separate bacteria from remaining blood debris.

[0096] Exosome separation is_nanoparticle separation of exosome from other extra cellular vesicles for size based fractionation of exosomes.

[0097] According to a first example of focusing and separation of microparticles, there is provided particle focusing at dynamic range of flow rates and particle migration and separation using single inlet high aspect ratio straight microchannels. The present disclosure covers a wide range of dimensionless numbers (0.05 < Reynolds number < 85, 1.5 < Weissenberg number < 3800, 5 < Elasticity number < 470) and show that particle size plays a dominant role, and by tuning the parameters, particle focusing can be achieved at Reynolds number ranging from 0.2 - 85. As a proof of principle, there is demonstrated separation of 5 pm, 7 pm and 10 pm particles in a sheath-less flow at a throughput of 150 pL / min. The presented disclosure sheds light on the complex particle transport in elasto-inertial flows for applications in high-throughput and high-resolution particle separation. Schematic illustration of the high AR channel contains particle focusing section (a) followed by a migration section (b) for size-based particle separation is shown in Figure 2.

[0098] The systematic analysis is performed using 3 pm, 5 pm and 10 pm particles in two different high aspect ratio microchannels with AR = 1 .5 and AR = 3 at four different concentrations of PEO (between 500-4000 ppm). The results reveal that it is possible to tune the parameters to achieve the particle focusing at broad range of flow rates from 1 pL / min to 250 pL / min. Although particle size plays a dominant role, none of the parameters can dictate the particle focusing alone. For studying particle migration and separation application using the novel devices, we pre-focus the particles and then split the channel into two to force particles to take a position near the channel wall and observed their migration toward the middle of the channel (see Figure 2). The obtained data reveals the trajectories, as well as their dependency on particle size, fluid flow, viscoelastic concentration, and channel geometry (Figure 8). Finally, as a proof of principle of sheath-less focusing and separation, we demonstrate separation of 5 pm, 7 pm and 10 pm particles at flow rates of 50 and 100 pL / min (Figure 18). The presented work has great potential for the development of high-throughput particle separation for biomedical applications.

[0099] According to a second example there is provided sheathless focusing of nanoparticles in elasto-inertial microfluidics.

[0100] We report elasto-inertial focusing of nanoparticles, down to 50 nm, for the first time using straight high aspect ratio (AR=height / width) microchannels in a sheath-less flow. Moreover, the present disclosure provides a comprehensive study of parameters affecting nanoparticle focusing in elasto- inertial flow, dominated by the elasticity and it covers the Reynolds number from 0.03-1.22, Weissenberg number from 48-1110, and Elasticity number from 63-5955. These experimental findings have a great potential to be the initial steps for the applications that require high-resolution particle separation and manipulation in various fields.

[0101] The manipulation of nanoparticles is crucial in biomedical applications. Although inertial and elasto-inertial microfluidics have been receiving an increasing attention to focus, sort and separate particles in many fields, these methods have difficulties for manipulating the submicron particles due to the physical limitations occurring from the channel geometry and smaller particle size. Previously, the blockage ratio defined as the ratio of particle size over characteristic dimension of the channel (a / L) to determine the focusing of the particles in a microfluidic channel was suggested 0.06 for the elasto-inertial flow. In this disclosure, using a high AR microfluidic channel, we demonstrate particle focusing down to 50 nm in size.

[0102] In the present disclosure, we use two different microfluidic channels with the aspect ratio of 6 (height=60 pm, width=10 pm) and 12 (height=60 pm, width=5 pm), at a length of 3 mm while the rest of the channel length of 1 cm is wider (Figure 1 ). The present approach benefit from the high AR geometry of the microchannels, where the smaller dimension of the channel (width) determines the focusing. We initially show the elasto-inertial focusing of 50 nm particles at the blockage ratio of 0.005. Then, we provide results on the effect of channel width and PEO concentration (500-4000 ppm) using 50 nm particles. We also investigated the focusing of larger particles (100 nm - 1 pm) particles, and as expected the focusing improves as the particle size gets larger, and the increasing the viscoelasticity of the fluid allows focusing the particles at the lower flow rates. Finally, we show the complete focusing of all the particle sizes at the channel center for the optimized PEO concentration of 2000 ppm and flow rate of 0.5 pL / min.

[0103] Our results show that the elasto-inertial focusing of nanoparticles is possible in a sheathless flow and the limitations of the blockage ratio can be reduced using high AR microchannels. Furthermore, the ability to focus nanoparticles in a simple and small footprint microfluidic channel has a potential to increase the throughput by the parallelization of the microchannels. Therefore, the presented results can lead to many applications in the field of biomedicine that high-throughput and high- resolution particle separation are needed, such as separation of exosomes in diagnostic applications.

[0104] According to a third example, detailed experimental results for microparticle focusing and separation are provided. Elasto-inertial particle focusing occurs due to the complex relationship between FE and FL, and is affected by various parameters such as particle size, channel geometry, and polymer concentration in the fluid as stated in the introduction. Here, we experimentally show how each of these parameters impact the particle focusing over a wide range of flow rates. Experimentally, the data were analyzed at the end of the focusing section of the microfluidic channels (see Figure 1a). Detailed information regarding the microfluidic channels can be found in materials and methods section. Below, each of the parameters affecting the particle focusing are described.

[0105] To study the effect of particle size on focusing, 3, 5 and 10 pm particles were used in a microfluidic channel (h=60 pm, w=40 pm) with a fixed PEO concentration of 4000 ppm over four different flow rates (25, 50, 100 and 250 pL / min). The normalized fluorescence intensities across the channel width are shown in Figure 2. In addition to the intensity graph, the focusing quality of particles is calculated and shown in the corresponding figures. Regardless of the flow rate, the largest particle (10 pm) shows the highest focusing quality compared to 3 and 5 pm particles while the smallest particle (3 pm) shows the lowest focusing behavior at any recorded flow rates. Increasing the flow rate 10 times from 25 pL / min (Re=1 .03, Wi=149.52) to 250 pL / min (Re=10.30, Wi=1495.15) did not have any effect on the focusing of the 10 pm particles as they maintained single-line focusing at the middle of the channel. Although 3 pm particles showed a slight improvement with respect to focusing quality at 250 pL / min, particles could not achieve the single-line focusing at any flow rates, reaching less than 25% focusing quality at best. On the other hand, the focusing quality of 5 pm particles was significantly enhanced at a flow rate of 100 pL / min, reaching almost single-line focusing. However, a further increase of flow rate to 250 pL / min caused a drop in focusing quality while the 10 pm particles were fully focused at this high flow rate. These results indicate that particle size plays a major role on single-line focusing in viscoelastic fluids. Further investigation on particle focusing was performed by altering the channel width and PEO concentration while keeping the height of the channel constant (see supplemental material Figure 18). For any experimental condition, we observe that focusing improves as particle size becomes larger. The dominant role of the particle size can be attributed to the cubic scaling of the elastic force (FE ~ a3).47

[0106] Moreover, when Re<1 and the PEO concentration is in the dilute regime (c<858 ppm), particles tend to be in the comers of the channel, the regions of lower stress48and this behavior is more pronounced for smaller particles (|3<0.1 ). Under the same flow conditions, as the particle size increases, the probability to observe particles in the comers decreases (see supplemental material Figure 19). Moreover, increasing the flow rate (thus increasing the Reynolds number) confines low stress regions in viscoelastic fluid36and a corresponding increase of the elastic force drives particles away from the channel corner. This migration is faster for larger particles (|3>0.2), leading to focusing at the channel center earlier than for smaller particles.

[0107] To understand the effect of channel width on particle focusing in high aspect ratio microchannels, we used two different widths (20 and 40 pm) while keeping the channel height at 60 pm (AR=3 and 1.5) as illustrated in Figure 5a, where we also display the focusing quality of the 5 pm particles in both microfluidic channels at flow rates of 1 , 5, 50 and 100 pL / min (PEO=1000 ppm). Experimental data shows that the focusing quality of 5 pm particles improves in each case as the channel width reduces (w=20 pm) and a significant decrease of focusing quality is observed when the channel width increases (w=40 pm). This behavior can be explained by the inverse proportionality between elastic forces and channel width (FE~1 / W3).49’50

[0108] Although a decrease in channel width increases the focusing quality, the enhancement ratio varies with the change of flow rate. The highest improvement was observed when the flow rate is 5 pL / min, indicating that the effect of channel width is more significant at lower flow rates.

[0109] Increasing the flow rate from 1 pL / min to 100 pL / min lowered the focusing quality for each data set (Figure 5a). The reduction of focusing quality at 50 and 100 pL / min can be explained by the increased effect of inertia, pushing particles away from the channel center.4851Moreover, the decrease of focusing quality was more significant for smaller channels (w=20 pm). This might be the result of a stronger N2-induced secondary flow in smaller channels.52From an application viewpoint, one aim is to focus particles at high flow rates to increase the throughput. We therefore tested the effect of channel depth while maintaining the channel width. Figure 5b shows the focusing quality of 5 pm particles in channels with aspect ratio 4.5 (h=90 pm, w=20 pm) and 3 (h=60 pm, w=20 pm) at flow rates of 10 pL / min and 50 pL / min. In the channel with lower aspect ratio, particles are found to be focused with 80% quality at 5 pL / min. However, increasing the flow rate to 10 pL / min and 50 pL / min causes a reduction of focusing quality to 46% and 26%, respectively. On the other hand, our results show that when the channel aspect ratio is increased to 4.5, particles reach a focusing quality of 92% for 10 pL / min and 55% for 50 pL / min. To further investigate this aspect, we compare the focusing quality of 10 pm particles in channels with aspect ratios of 3 (h=120 pm, w=40 pm) and 1.5 (h=60 pm, w=40 pm). The focusing quality is 40% and 17% at 50 pL / min (0.1 wt. % PEO) and 100 pL / min (0.05 wt.% PEO) in the smaller channel. When doubling the aspect ratio, we observe that particles are completely focused at flow rate 50 pL / min (0.1 wt.% PEO) and the focusing quality increases from 17% to 80% at 100 pL / min (0.05 wt.% PEO) (see supplemental material Figure 20). As expected, our findings suggest that in high aspect ratio channels, increasing the channel height enables particles to focus at higher flow rates when using viscoelastic fluids. In addition to the effect of channel width and height, we also investigated the effect of channel length on particle focusing. Our results show that longer the channel length better the focusing (see supplemental material Figure 21).

[0110] The variation of PEO concentration directly affects the elastic (FE~A)47and viscous forces (Re~1 / p)22acting on a particle flowing in the channel. Therefore, particle focusing is strongly influenced by the concentration of PEO. To analyze the effects of elasticity and viscosity due to varying the PEO concentration, four different solutions of PEO were prepared (500, 1000, 2000 and 4000 ppm). The rheological properties of these solutions are shown in supplemental material Figure 18.

[0111] Fluorescence imaging of the 10 pm particles at different PEO concentrations shows the effect of elasticity on particle focusing at 50 pL / min (see Figure 6a). Moreover, the focusing qualities of 10 pm particles in a microchannel (h=60 pm, w=40 pm) with flow rates varying from 5 pL / min to 150 pL / min for all PEO concentrations are shown in Figure 6b. At 5 pL / min in 500 ppm PEO solution, the particles were fully focused and increase in PEO concentration maintained the focusing quality. However, increasing the flow rate to 50 pL / min caused a significant decrease of focusing quality in the solution with 500 ppm PEO due to stronger inertial and elastic forces generated by higher flow rate.48Increasing the PEO concentration to 1000, 2000, and 4000 ppm resulted in continuous improvements until the particles are fully focused at the highest PEO concentration. Similar trend can be observed for the flow rate of 100 pL / min. These improvements of particle focusing can be attributed to the increase of the elasticity in the channels at higher PEO concentrations. Similar results are obtained for the 5 pm particles at relatively high flow rates (100-150 pL / min) (see supplemental material Figure 22 in the supplemental material). These results suggest that particle focusing at high flow rates (>50 pL / min) can be achieved by increasing the viscoelasticity of the fluid.

[0112] As shown above, particle focusing depends on various parameters (particle size, channel geometry, viscoelasticity) and focusing can be achieved by tuning these parameters at low and high flow rates. Obtaining fully focused particles is essential for our high throughput and high-resolution particle separation strategy that will be described in detail below.

[0113] Knowledge on the migration velocity is fundamental to be able to sort particles by size, see below, and to design devices with desired throughput and reasonable dimensions. To this end, we have used the migration section of the microfluidic channels (see Figure 1 b) and followed the particle trajectory throughout the microfluidic channel, as well as the final focusing positions close to the outlet. Particles are first focused, and then the channel split into two in order to track the particle migration from the side wall toward the center. Each data point was recorded in the expansion section of the microchannels.

[0114] To understand the transient dynamics behind the migration of particles toward the centerline, we must consider the competition between the elastic and inertial forces in the fluid. The particles are pushed away from the centerline by the shear gradient lift force (Fs) and toward the centerline by elastic forces. Our simulations, with values of Wi=13.55 and Re=6.65, reveal that elastic forces are more influential than inertial forces in our setup. This results in particles being mainly directed toward the center of the channel by the prevailing elastic forces. To clarify, the distribution of the first normal stress difference of the viscoelastic fluid, N = Txx 1-yy, across the channel cross-section is depicted in Figure 7. Note that the first normal-stress difference indicates tension in the streamline direction. The streamlines surround the particle and exerts a lateral hooping thrust on each side of the particle causing it to move to the side of the particle with the lowest first normal stress difference. The simulations show that N is the greatest near the four walls of the channel, while it is significantly lower close to the channel center and comers. As a result, gradients of the first normal stress difference tend to push the particles toward the center of the channel where the elastic stresses are minimum.

[0115] It is noteworthy to mention that although migration is consistently significant along the short channel size (Z-axis), migration along the longer edge (Y-axis in Figure 7) is not as pronounced because the region with the lowest f i values at the center of the channel has a rectangular shape. When elastic effects are substantial, particles are inclined to move toward this central rectangular region, as evidenced in Figure 7b. As a result, migration along the long side is slower, and several locations in the midplane cutting along the Y-direction can potentially act as an equilibrium position.

[0116] To further understand the of dynamics of particle migration, we investigate the influence of the particle size on the migration. Specifically, we numerically simulate particles with diameters of 10 pm and 7.5 pm under constant flow rate and fluid rheological properties. The migration behaviour of these particles is illustrated in Figure 7(c-f). The results in panel (c) indicate that both particles migrate toward the channel center at (Z / Zz=0.5), because elastic forces prevail inertial forces. Notably, the particle with a smaller diameter (7.5 pm) reaches the final steady state later than its larger counterpart (10 pm). The larger particle has already reached the final equilibrium position, while the smaller particle continues its gradual migration toward the channel center. The migration velocities of the particles are compared in Figure 7d: the larger particle exhibits a higher migration velocity than the smaller particle. This difference can be attributed to elastic effects arising from the imbalance in the distribution of N over the particle surface. This is expressed by E O a3V( / Vi) where the cubic dependence results from the product between surface area over which the stresses act and the gradients in normal stresses proportional to the particle size. Consequently, the larger particle experiences a more pronounced elastic force, speeding up its migration toward the centerline of the channel. In addition, for both smaller and larger particles, the migration velocity decreases as the particles approach the channel center. This is due to the decreasing gradient of the first normal stress difference as the particles get closer to the center of the channel (see Figure 7a), causing a reduction in elastic forces. In panel (e), the normalized stream- wise velocities of the particles by the bulk velocity (u / U) are presented. It indicates an increment in the particles stream-wise velocity as the fluid dynamics compels the particle to align with the prevailing flow. As the particles approach a stable state, their stream-wise velocity becoming constant, closely aligning with the velocity of the fluid at the equilibrium point (at the center of the microchannel). Finally, we present in panel (f) the particle angular velocity around the y-axis. It is evident that the angular velocities decrease and eventually approach zero. This behaviour can again be attributed to the diminishing gradient in both N and vanishing shear rate as particles move closer to the center of the channel.53Since this force governs the particle rotation, the angular velocity undergoes a gradual decrease, eventually approaching zero.

[0117] Following the numerical study, we investigate elasto-inertial particle migration in high aspect ratio straight microchannels in detail. To this end, after the straight portion of the microfluidic device where focusing occurs, we split the microchannel into two parallel straight channels, one being slightly longer (see Table 1 ). This causes higher resistance in the longer channel and drives the particles toward the lower resistance side, near the channel wall. In this way, we achieve a controlled positioning of the particles near the channel wall for a more accurate analysis of the migration. As introduced above (Figure 1 ), parallel channels were designed with expansion and contraction units to observe particle migration to the center. Figure 8a shows the fluorescence data from two representative experimental results using 3 pm and 5 pm particles (left side), and 5 pm and 10 pm particles (right side). The results show that the larger particles migrate toward the channel center earlier than smaller particles in both cases. Notably, as the particles approach the channel center the migration speed slows down, in agreement with the numerical study above. The variation of migration speed for different sized particles can be utilized for separation. Since the larger particle slows down and eventually stops migrating at the center, small particles reduce this distance by continuing their migration if the channel offers enough length. Figure 8(b-c) shows the effect of PEO concentration on particle migration for two different flow rates. As the PEO concentration increases, the larger (5 pm) particles migrate faster and reach the center earlier. This is indicative of the relatively dominant viscoelastic force (FE) over the lift force (FL). For instance, the dimensionless numbers for the case of 2000 ppm for a flow rate of 2.5 pL / min is as follows: Re=0.45 and Wi=38,11 while for the 4000 ppm the corresponding Re=0.13 and Wi=59.81 . This shows that while the influence of FL is moderate the influence of FE is the dominant forcing particles across the channel towards the center. As can be seen in Figure 8d, the trend is similar for the microchannel with AR=1.5. The 10 pm particles reach channel center earlier for the PEO concentration of 4000 ppm compared to 2000 ppm (corresponding Re=0.35 and 0.1 and Wi=9.53 and 14.95). At these relatively low flow rates, there is a strict size based differential particle migration (Figure 8(b-d)). As the flow rate increases, the size dependence on particle migration diminishes. At a flow rate of 50 pL / min (for flow through the channel AR=1 .5), both 10 pm and 5 pm particles are migrating at similar speed (Figure 8e). Most notably, for the PEO concentration of 4000 ppm, is difficult to differentiate the migration path between the 10 pm and 5 pm particles, making separation practically impossible. This effect is presumably due to dominant FE over FL (Re=2.06, Wi=299.03) at these high PEO concentrations. All in all, these results document the size-dependence of particle migration at optimized flow rates, and can be exploited for high- resolution separation.

[0118] For more insights on the complex relationship between the forces affecting the particle migration towards the channel center, we analyzed a large number of experimental data at the outlets (position 9, see Figure 8a) using different sized particles, PEO concentrations, channel aspect ratio and flow rates. Our observations are summarized in the supplementary material (see supplemental material Figure 23). Briefly, to analyze the final particle positions at the outlet, we denominated Wnas the normalized channel width, from 0 at the inner wall to 1 at the outer wall of the channel. Our analysis shows that particles are majorly positioned in two regions: the channel center and a region denoted from 0.28 to 0.35Wn. We observe that this trend is more significant at higher flow rates (>50 pL / min) suggesting the effect of secondary flow (see supplemental material Figure 23). Particles that are large enough and under the influence of dominant FE are expected at the equilibrium position at the center. However, the second focusing region (0.28 to 0.35Wn) is distinguished and somehow surprising. We believe the secondary flow present at high flow rates becomes significant to compete with the dominant FE pushing particles away from the channel center. In such case, the combined effect of FL and secondary forces would balance the effect of FE. Note that we can observe this phenomenon since all particles are forced to start from the inner wall and migrate towards the channel center due to channel design that allows for pre-focusing the particles before splitting.

[0119] While outside the focus of the current work, a more detailed study is necessary to decipher the effect of the secondary flows due to the viscoelastic property of the medium and how this interacts with the FE and FL in focusing particles.

[0120] For particle separation, high sample throughput is desirable without compromising the separating resolution. As described above, pre-aligning the particles without a sheath flow is attractive and allows for strict size-based particle migration towards the channel center after splitting. From the numerical and experimental results, we observe that particles start to slow down in migration when they are approaching the channel center. Hence, it is possible to build a strategy based on straight channels that allows the larger particles to migrate a reach the channel center, while not providing enough length / time to smaller particles to reach the channel center. Experimentally, for the channel AR=3, the largest difference is observed just before the larger particles start to slow down (see position 6 in Figure 8b-c). For high throughput separation application, we fabricated a deeper device microchannel (w=40 pm, h=120 pm, keeping the AR=3) and analyzed particles at position 6. As described above, the PEO concentration is another important parameter to be optimized for particle separation at high flow rates.

[0121] As can be seen in Figure 9, at PEO concentration of 1000 ppm, we demonstrate high-resolution separation of 5, 7, and 10 pm particles at high flow rates (50, 100, and 150 pL / min). As expected, the lower flow rate (50 pL / min) resulted in larger separation distance and we also observe that 7 pm particles take an intermediate position between the 5 and 10 pm, confirming the size-based differential migration. While at slightly different positions, we observe the particles entering the second section of the channel around 0.1 W (close to the inner wall). Independent of the initial position the larger 10 pm particles differentially migrate faster the smaller particles towards the channel center. Moreover, high throughput is achieved by increasing the channel depth to 120 pm. Note that the aspect ration (AR=3) is maintained constant by keeping the width to 40pm. By designing collection outlets, it should be straightforward to separate the particles at high resolution.

[0122] Straight microfluidic channels have been used in the past for particle separation based on size.36’5455However, these studies have used two inlets: one containing the fluid with particles and the other one carrying only the fluid as sheath flow.37’55 56In these configurations, the sheath flow serves to initially define the particle position in the channel and move the particles to the chosen side for further migration. Although these designs work well for particle separation, the main particle-laden flow is often at very low flow rates and consequently the sheath flow causes a dilution of the solution, significantly lowering the overall sample throughput. Spiral devices are attractive for focusing and separating the particles. The combination of the Dean force that arises from a curvature and elasto-inertial flow causes particles to focus at the outer wall of the microchannel57and it allows sizebased particle separation5859. However, these spiral geometries also suffer from the lowering the throughput due to the employment of sheath flow. In addition, such systems require additional control systems to operate with multiple inlets and more complicated designs to initially define the particle positions in order to enable size-based manipulation. Here, we demonstrate that by first pre-aligning the particles, the difference in the migration speed can be utilized for separating particles at high throughput and high resolution based on their sizes.

[0123] In this work, we report numerical and comprehensive experimental investigation of elasto-inertial particle focusing and migration in flows through straight high aspect ratio microchannels. The data shows how particle size, channel geometry, flow rate, and the concentration of polymer additives affect particle focusing for Reynolds numbers, Re, in the range of 0.05-85, Weissenberg number, Wi, between 1.55 and 3800 and large range of Elasticity number (=Wi / Re), El, in the range of 5.75-462. This range of Wi and El numbers are investigated experimentally for the first time and based on the experimental data, we conclude that elasticity and inertia can be used to focus particles by tuning various parameters. Among the parameters, particle size plays a dominant role for particle focusing. In addition to focusing, we report particle migration trajectories from the near wall toward the channel center and show how particle size, flow rate, and PEO concentration affect this migration. We show particles migrate faster when particles are near the channel wall and becomes slower as the particles approach the center of the channel. Leveraging on this, we show how the differences in migration speed can be utilized for separating particles at high throughput and high resolution. As a proof of principle, we demonstrate successful separation of 5 pm, 7 pm and 10 pm particles at a throughput of 150 pL / min using a single inlet channel without sheath flow to pre-alight the particle. Microfluidic devices were designed using the AutoCAD software (Autodesk), and the master mold was prepared with SLIEX (dry Sll-8 film) on a silicon wafer following a standard photolithography process.60To fabricate the PDMS (polydimethylsiloxane) chips, SYLGARD™ 184 elastomer (Dowsil, Sweden) was mixed with the curing agent at the ratio of 10:1 , and the final mixture was poured over the master mold, degassed in a desiccator and baked at 65 °C for 6 hours. After the curing process, the PDMS was peeled off, individual devices were cut, and inlet and outlet holes were punched using a puncher with a hole size of 0.75 mm. The resulting PDMS device and a microscope glass slide were exposed to oxygen plasma to activate the surfaces for bonding. After bonding the PDMS device on the glass substrate, the chip was post-baked at 120 °C for 15 minutes to improve sealing.

[0124] To study the effect of the channel width on particle focusing and migration, straight microfluidic channels with two different widths (20 pm and 40 pm) and constant height (60 pm) were designed. Both microfluidic chips contain a first section aiming at focusing all particles in the middle which is followed by a second section where the already-focused particles are quickly displaced toward the inner channel wall and observed as they migrate back to the center. In the second section, the trajectories can be observed, and their dependencies on the particle size, channel width, flow rate, and concentration of elasticity can be studied. The first section is a straight microchannel (Figure 1a) and in the second section, the channel splits into two branches, which receive 55% and 45% of the fluid (Figure 1 b). Pre-focused particles enter the second section very close to the wall of the channel receiving the 55% portion of the flow and start migrating toward the center of the new channel. To properly observe the position of the particles, this second focusing channel is segmented in 8 parts with an expanded peek with high resolution at 8 different points of the trajectory. The 40 pm wide channel was designed with an 8 mm long particle focusing section followed by a second section with 8 segments of 500 pm. The 20 pm chip was designed with a 4 mm long focusing section and 8 segments of 250 pm (see Table 1 ).

[0125] Table 1 . The dimensions of microfluidic channels

[0126] Non-Newtonian fluid was prepared by dissolving PEO (Polyethylene Oxide) powder, which is used as an elasticity enhancer, into deionized water. The PEO powder (Mw=2x106g / mol, Sigma Aldrich) was added into the deionized water at concentrations of 500 (0.05 wt.%), 1000 (0.1 wt.%), 2000 (0.2 wt.%) and 4000 (0.4 wt.%) ppm. After rheology measurements, zero-shear viscosities of 1.26, 1.59, 2.39, and 8.23 mPa.s were obtained, respectively.

[0127] Fluorescent polystyrene particles (Fluoro-Max, ThermoFisher Scientific) with diameters of 3 pm (red), 5 pm (green), 7 pm (red) and 10 pm (green) were suspended in the prepared non-Newtonian fluids (with 0.1 % Tween-20 to prevent agglomeration).

[0128] The rheometric analysis was performed on a dual-motor Anton Paar Modular-Compact-Rheometer (MCR) 702e Space. Given the low viscosity of the fluid samples, a concentric cylinder geometry (bob-and- cup) was chosen for the measurements, with 45 mm as the internal diameter of the exterior cylinder, and 43 mm as the diameter of the internal cylinder. Thus, a gap of 1 mm was achieved between the concentric surfaces. The interior cylinder is positioned with a fixed 3 mm gap from the bottom of the exterior cylinder, and for the sake of symmetry, the sample volume is kept at ~16 mL to duplicate the 3 mm gap on the top of the interior cylinder. The measurements were performed at ambient temperature (~20°C), similar to the temperature during the flow experiments. An evaporation preventing lid was placed on the geometries to ensure constant volume of the fluid samples during the experiments. The flow curves were obtained through a logarithmic ramp-down on the shear rate starting at 1031 / s, to remove any, if existing, memory effects in the sample, through a pre-shearing scheme. Depending on the viscosity range of the samples, the lower limits for the shear rate differ from 10 to 1021 / s for the highest to lowest viscosity fluids. The flow curves contain viscosity and shear stress as functions of the shear rate in the mentioned range (see the supplemental material Figure 24). There are seven (7) points measured per decade of the shear rate, which is kept constant at each point until steady state has been reached. The rheology properties of the four PEO concentrations are shown in the supplementary Table S1 (see the supplementary material on how relaxation times are calculated and see Table S2 and S3 for dimensionless numbers).

[0129] The microfluidic experiments were performed with a 5 mL steel syringe using a mid-pressure pump (neMESYS CETONI GmbH). Flow rates ranging from 1 to 250 pL / min were tested, and each data point was recorded 5 minutes after changing the flow rate to ensure the stabilization of flow due to the viscoelastic effect. The imaging was accomplished using an inverted microscope (Nikon Eclipse Tl) with a sCMOS camera (Andoe Zyla) and LED lighting system (Lumenor Spectra X LED). Optical TRITC and FITC filters were used to capture the red and green fluorescent particles, respectively. To control the microscope and record the images, an open-source software Micro Manager was used.

[0130] The recorded data was visualized and processed by Imaged software. The focusing qualities of the particles were calculated based on the ratio of the particle diameter to the full width at half maximum (FWHM) of the fluorescence intensity of the particles along the channel width.61

[0131] We perform three-dimensional direct numerical simulations to investigate the cross-streamline migration of particles suspended in viscoelastic fluids within a high aspect ratio straight microchannel. These simulations aim to offer additional insights to elucidate the experimental observations. We employ our in-house code62utilizing a direct forcing immersed boundary method (IBM)63to simulate the particles as moving Lagrangian grids. The carrier fluid is discretized within a stationary Eulerian frame, in which the Navier-Stokes and the viscoelastic constitutive equations are discretized using finite differences (see the supplementary material on code validation). The solver was previously used for particle migration in elastoviscoplastic channel flow.53The suspending fluid motion is governed by the continuity constraint and conservation of momentum as follows:

[0132] V- U = 0, ( 4 ) where, U is the fluid velocity, p is the pressure field, T is the total deviatoric stress tensor, and Re is Reynolds number. The extra term f on the right-hand side of Eq. (5) is the immersed boundary force field representing the particle-fluid interaction. Details of immersed boundary method are given in the supplementary material. The total deviatoric stress tensor, T, is composed of contributions from the solvent (Newtonian fluid) and polymer parts as T = TS+ TP. The solvent stress tensor is defined as TS= ps(VU + VUT), where ?s= S / is the ratio of the solvent viscosity to the total viscosity. In addition to the equations mentioned earlier, a constitutive equation should be employed to model the evolution of the non-Newtonian contribution (TP) of the viscoelastic material. We simulate the Oldroyd-B model64to take into account the viscoelasticity of the material.

[0133] The particle translational and rotational velocities are obtained by solving Newton-Euler equations for each particle. where upand copare the linear velocity of the center of mass and angular velocity of the particle. Additionally, a denotes the Cauchy stress tensor for the viscoelastic fluid and defined as a = -pl + TP + / 3s (VU +VUT), while r shows the distance from the center of the particle, and dV represents the particle domain. The density, volume, and moment of inertia of the particle are denoted by pp, Vp, and Ip, respectively. Finally, Fcand Tcrepresent the total force and torque generated by potential particle-wall collisions.

[0134] According to a fourth example, details of the nanoparticle focusing experiments are provided.

[0135] In this study, PEO (Polyethylene Oxide, Mw=2x106g / mol), elasticity enhancer, was used for the preparation of viscoelastic fluids. The PEO powder was dissolved in deionized water at four different concentrations (500 ppm, 1000 ppm, 2000 ppm and 4000 ppm) (See Table S1 for the rheological properties of the fluids). The fluorescent polystyrene particles (Fluoro-Max, ThermoFisher Scientific) with diameters of 50 nm, 100 nm, 200 nm, 500 nm and 1 pm were suspended in the prepared viscoelastic fluids prior to the flow experiments.

[0136] The microfluidic experiments were performed with a mid-pressure pump (neMESYS CETONI GmbH) using a 3 mL steel syringe. The data acquisition was accomplished using an inverted microscope (Nikon Eclipse Tl) with a sCMOS camera (Andor Zyla) and LED lightning system (Lumenor Spectra X LED). Micro Manager software was used to control the microscope and record the images. The recorded images were processed by Imaged software.

[0137] We initially start with the comparison of inertial and elasto-inertial focusing of 200 nm, 500 nm and 1 pm particles in the same microchannel. Then, we investigate each parameter effecting elasto- inertial focusing. To study elasto-inertial focusing of nanoparticles, we used two different microfluidic channels by varying the width dimension (5 pm and 10 pm) at constant height (60 pm). Four different elasticity concentrations (500 ppm, 1000 ppm, 2000 ppm, 4000 ppm), five different particle sizes (50 nm, 100 nm, 200 nm, 500 nm, and 1 pm) in six different flow rates (from 0.5 pL / min to 3 pL / min) were experimented in these channels. Below, we describe the effect of these parameters on elasto-inertial focusing. in inertial focusing, particles are suspended in Newtonian fluid (water) while in elasto-inertial focusing particles are suspended in nonNewtonian fluid (PEO) as previously introduced. Figure x shows the experimental images along with the fluorescence intensity graphs for the comparison of particle focusing in water and PEO (1000 ppm) by flowing 200 nm, 500 nm, and 1 pm particles at fixed flow rate (3 pL / min) and channel geometry (h=60 pm, w=5 m). In Newtonian fluid, the 1 pm particles show the focusing tendency near the two long sides of the microchannel as expected.1030However, the smaller particles remain unfocused, showing the size dependence on inertial focusing.31Therefore, we confirm that the focusing of nanoparticles using inertial focusing is not possible under these experimental conditions. On the other hand, all particles in PEO solution show focusing behavior at the channel center, while the 1 pm particles having the highest fluorescence intensity comparing the 200 nm and 500 nm particles, indicating the size-dependence on elasto-inertial focusing as well.32These results signify the difference between inertial and elasto-inertial microfluidics for number of focusing positions in straight high aspect ratio microchannels. Moreover, they suggest the possibility of nanoparticle focusing using elasto-inertial microfluidics that is not feasible in inertial microfluidics. Such particle focusing is important prior to develop separation strategies. Prefocusing the particles and then aligning these particles to the channel wall for size-based migration was shown previously.33Similar to this strategy, we have also showed how to separate 5 pm, 7 pm, and 10 pm particles from each other in a sheathless high aspect ratio microchannels by prefocusing and allowing size-based migration for the separation. Therefore, focusing these particles at the channel center is crucial.

[0138] After successfully focusing of 200 nm and 500 nm particles in high aspect ratio microchannels, we investigated the focusing of even smaller particles. The figure shows the focusing behavior of 50 nm particles at fixed 500 ppm PEO solution in microchannel with aspect ratio of 6 (h=60 pm, w=10 m) in the range of four different flow rates (0.5, 1 , 1.5 and 2 pL / min). The fluorescence intensity graph and focusing bandwidth (FWHM) results show that the particles are majorly focused at the channel center with some distortion around the center. It is noteworthy to mention that the blockage ratio (a / W) is 0.005, nearly 10 times smaller than what has been previously shown for particle focusing. Here, both inertia and viscoelasticity play a role on particle focusing while the viscoelasticity is the more dominant parameter (Re<1 , Wi>10, El-63). We believe that this strong contribution of viscoelasticity leads focusing of 50 nm particles at such low blockage ratio (0.005). These results suggest that using smaller microchannel width and increasing the PEO concentration can further improve the focusing quality, lowering the number of unfocused particles around the channel center.

[0139] We investigated the effect of channel width by using microchannels with two different widths: 5 pm and 10 pm, while keeping the channel height constant at 60 pm, making the aspect ratios of 12 and 6, and the blockage ratios of 0.01 and 0.005, respectively. In figure 11 , we show the fluorescence intensity results of 50 nm particles at 1000 ppm PEO solution as well as the focusing bandwidths for the flow rates from 0.5 pL / min to 3 pL / min. The fluorescence intensity results show that particles are majorly focused in the channel center regardless of the channel width and flow rate. On the other hand, the focusing quality varies depending on the parameters as shown in the graphs. Particles are focused better (smaller FWHM / W) at the microchannel center with the smaller channel width due to the increasing elasticity, which drives particles to the lower stress region at the channel center. Although the difference in focusing is almost nothing at 2 pL / min, focusing bandwidth is always smaller for all the flow rates tested in the narrower channel and it significantly increases at the highest flow rate of 3 pL / min for the larger channel width. To the best of our knowledge, the single-line particle focusing at the blockage ratios of 0.005 and 0.01 was not achieved previously. We believe that the increased elasticity component and the utilization of high-aspect ratio microchannels are the driving factors for nanoparticle focusing at such low blockage ratios. We investigated the effect of particle size by flowing 50 nm, 100 nm, 200 nm, 500 nm, and 1 pm particles af fixed PEO concentration (2000 ppm) in a microchannel with AR of 12 (h=60 m, w=5pm). The PEO concentration of 2000 ppm was chosen to avoid the repetitiveness of data as we previously showed the PEO concentrations of 500 ppm and 1000 ppm for the focusing of 50 nm particle and the effect of channel width. Figure 9 shows the normalized fluorescence intensity of the particles over the channel width at the flow rate of 1 pL / min. In this experimental condition, both fluid inertia and elasticity are finite while the elasticity being the dominant factor (Re=0.21, Wi=235.56, El=1102.22). The intensity graph shows that all particles are majorly focused at the channel center, while the largest particles (1 pm) show the smallest focusing bandwidth and the smaller particles (<500 nm) have slightly larger focusing bandwidth. These results indicate that the focusing quality increases as the particle size gets larger, which correlates with the forces acting on particles (FE~a3, Fi_~a4)34’35as they strongly depend on the particle size. Nevertheless, we are still able to observe focusing of nanoparticles at the channel center. Moreover, observing the focusing of particles that have 20 times difference in size (50 nm and 1 pm) in the same microfluidic channel is significant. We believe that this shows the complex relation of ferees and parameters in elasto-inertial focusing, and how a single parameter, particle size in this case, cannot determine the focusing behavior alone. The concentration of PEO determines the rheological properties of the viscoelastic fluid, which affects the corresponding elasticity component (FE~ )36and viscous component (Re~1 / )37generated in the flow. Table x shows the rheological properties of the PEO solutions used in this study. The relaxation times can be found in the supplemental material (see Table S1 ). As shown in the table, increasing the PEO concentration increases the relaxation time as well as the fluid viscosity. Figure 18 shows the effect of four different PEO concentrations on focusing of 100 nm particles in microchannel with AR of 12 (h=60 pm, w=5pm) at constant flow rate of 0.5 pL / min. It should be noted that although the flow rate is constant, Re number lowers due to the increasing viscosity (Re~1 / p). The experimental images and normalized fluorescence data illustrate that the particles are majorly focused at the channel center even at the lowest PEO concentration of 500 ppm (Re=0.2, Wi=47.78, El=235.72). On the other hand, increasing the PEO concentration to 4000 ppm (Re=0.03, Wi=185) caused particles to be focused in a narrower bandwidth in the channel, eliminating the number of unfocused particles around the channel center. These results suggest that increasing the dominance of elastic component in elasto-inertial focusing can improve the focusing quality for nanoparticles.

[0140] The figure shows the combination of experimental data with corresponding intensity graphs to observe the effect of increasing flow rate for all the particle sizes at the fixed PEO concentration of 2000 ppm. We observe that in lower flow rates (0.5 and 1 pL / min), all particle sizes are majorly focused at the channel center, while the 1 pm particles are fully focused providing the smallest bandwidth at the channel center. Full width at half maximum analysis also supports this finding that even the smallest particle size, 50 nm, is majorly focused at the channel center at these two flow rates. Moreover, the FWHM analysis shows that the focusing quality improves for all the particles from 0.5 to 1 pL / min. On the other hand, further increase of flow rate to 1.5 pL / min caused disturbance on focusing of 50 nm particles, giving rise to two additional positions near the channel center while the majority of the particles remained at the center. Although such disturbance was also slightly observed for other larger particles, the impact was not as significant as the 50 nm particles. When the flow rate was increased to 2 and 2.5 pL / min, three focusing position became clearer for 50 nm and 100 nm particles, one position at the channel center and two positions at the sides of the center. Meanwhile, the 200 nm particles became unfocused around the channel center at these flow rates, however, not showing three distinct focusing positions. When we reached the flow rate of 3 pL / min, three focusing positions also appeared for the 200 nm particles. Although focusing quality gradually lowered for both 500 nm and 1 pm particles as the flow rate increased from 1 to 3 pL / min, the majority of these particles kept their focus at the channel center and did not show any additional focusing positions unlike 50 nm, 100 nm, and 200 nm particles. The disturbance of focusing is expected in elasto-inertial focusing as the inertia increases. On the other hand, we did not only observe losing the focus but also formation of two new focusing positions for the smaller particles (50 nm, 100 nm, and 200 nm). We believe that these positions occur due to the development of secondary flow vortices in high aspect ratio channels as the flow rate increases. The presence of secondary flow in straight channels was previously shown38and the secondary flow causes particles to move away from the channel center.39Here, we propose that the effect of the vortices are size dependent and these secondary flow vortices can trap the particles, giving rise to new focusing positions around the channel center. Therefore, we believe that the formation of two new focusing positions were initially detected for the smallest 50 nm particles. Further increase of the flow rate caused stronger vortices, capturing the larger 100 nm particles and this trend was followed by the 200 nm particles at the highest flow rate of 3 pL / min. However, this effect was only limited to causing disturbance of focusing for the larger 500 nm and 1 pm particles, not indicating the new focusing positions around the channel center. The similar results were found with the other PEO concentrations from low to high flow rates. Figure 14 shows the focusing bandwidths of all particle sizes as a heat map at four different PEO concentration and six different flow rates. These results suggest that elasto-inertial focusing is ideal for focusing 50 nm particles at low flow rates when the elastic component is dominant over inertia (4000 ppm). Furthermore, such high elasticity also suggests more disturbance of focusing of particles as the flow rate increases, unlike the usage of lower PEO concentrations (500 ppm and 1000 ppm), which caused all the particle sizes to have almost constant focusing behavior from low to high flow rates.

[0141] Elasto-inertial microfluidics is a powerful method that offers label-free, high-throughput and high-resolution particle manipulation. Although elasto- inertial microfluidics has significant advantages and increasingly been used in many applications, the smallest particle size to focus in a straight microchannel was 200 nm. This size was lowered to 100 nm using relatively complex spiral microchannels. In this paper, we present first time the elasto- inertial focusing of 50 nm particles in a straight high aspect ratio microchannels. Moreover, we provide an extensive experimental data on elasticity dominant flow (0.03<Re<1 .22, 11 ,94<Wi<1110, 63<EI<5960) to enhance the understanding of the focusing of nanoparticles. We believe that these results are the initial steps before the size-based separation of the nanoparticles (<500 nm) using elasto-inertial microfluidics. Furthermore, the ability to focus nanoparticles in a simple and small microfluidic channel has a potential to increase the throughput by the parallelization of the microchannels. Therefore, the presented results can lead to many applications in the field of biomedicine that high-throughput and high- resolution particle separation are needed.

[0142] System Components:

[0143] - Microchannel Substrate: Fabricated from PDMS, glass, or other materials.

[0144] - Microchannel Design: High-aspect-ratio straight microchannels (width: 1-10 pm, height: 10-200 pm) with a focusing segment and separation section. - Fluid Handling: Viscoelastic fluids containing polyethylene oxide (PEO) or polyacrylamide at concentrations ranging from 10 ppm to 10,000 ppm.

[0145] - Pumping Mechanism: Syringe or peristaltic or pressure based pumps driving laminar flow at controlled rates.

[0146] Method of Operation:

[0147] Sample Introduction: Nanoparticles suspended in a viscoelastic fluid are introduced into the microchannel.

[0148] Focusing Mechanism: Elasto-inertial forces act on nanoparticles, focusing them into localized streamlines at the channel center.

[0149] Separation: Focused particles are directed into multiple outlet branches for size-based separation.

[0150] Theoretical explanation for Nanoparticle Focusing: Recent theoretical advancements demonstrate that the interplay between viscoelastic forces and Brownian motion can be quantified using a dimensionless parameter (H), which compares viscoelastic normal stresses to Brownian diffusion forces.

[0151] This model predicts the efficiency of nanoparticle trapping and supports the robust performance of our system, particularly at the nanoscale.

[0152] By novel channel geometry design:

[0153] The system's trapping efficiency is further enhanced as flow rates increase, with performance scaling with the square of the flow rate. This relationship allows for predictable, high-throughput operation while maintaining precision focusing.

[0154] Applications:

[0155] Biomedical: Isolation of lipoproteins (HDL, LDL), extracellular vesicles, exosomes, and other bioparticles for diagnostics.

[0156] Environmental: Detection and enrichment of nanoplastics in water samples.

[0157] Industrial: Nanoparticle sorting for material science applications.

[0158] The present disclosure discloses a sheathless elasto-inertial microfluidic system for high-resolution focusing and separation of nanoparticles as small as 10 nm. The system employs high-aspect-ratio microchannels and viscoelastic fluids to achieve efficient particle alignment without external fields. Quantifying viscoelastic and Brownian force interactions enhances the predictability and scalability of the system. The dual-section microchannel design enables high throughput and low-pressure operation, making the present disclosure suitable for biomedical diagnostics, nanomedicine, and environmental applications.

[0159] Nanoscale biological particles, such as lipoproteins (10-80 nm) or extracellular vesicles (30-200 nm), play pivotal roles in health and disease, including conditions like cardiovascular disorders and cancer. Their effective analysis is crucial for applications in diagnostics, quality control, and nanomedicine development. While elasto-inertial focusing offers a powerful method to manipulate particles without external fields, achieving consistent focusing of nanoparticles (<500 nm) has remained a challenge. In this study, we experimentally demonstrate elasto-inertial focusing of nanoparticles as small as 25 nm using straight high-aspect-ratio microchannels in a sheathless flow. Systematic investigations reveal the influence of channel width, particle size, viscoelastic concentration, and flow rate on focusing behavior. Numerical simulations provide insights into particle migration dynamics, complementing our experimental observations. Finally, we successfully focus biological particles, including liposomes (90-140 nm), extracellular vesicles (100 nm), and lipoproteins (10-25 nm), at optimized conditions. These findings mark a significant advancement toward size-based high-resolution particle separation, with implications for biomedicine and environmental sciences.

[0160] The ability to manipulate nanoparticles is crucial for many fields ranging from disease diagnostics to drug delivery.1Nanoscale bioparticles in the body play an indispensable role in health and their dysregulation causes many diseases. For example, lipoproteins, such as high-density lipoprotein (HDL) and low-density lipoprotein (LDL), transfer lipids through the body. Their imbalance, as well as their deviation from canonical physical properties such as size, is a marker of dyslipidemia and metabolic diseases.2Moreover, certain types of lipoproteins are associated with neurodegenerative diseases such as Alzheimer’s.34Extracellular Vesicles (EVs) enable intercellular communication in the body, and certain types of EVs are associated with diseases like cancer.5Current methods to sort biological nanoparticles, such as size exclusion chromatography (SEC),6asymmetrical flow fieldfractionation (AF4)7or centrifugal techniques8are cumbersome, expensive, and rarely result in pure fractions. Therefore, developing advanced methods to sort and study particles based on their physical properties, such as size, is crucial.

[0161] In addition to biomedical applications involving biological nanoparticles, environmental nanoparticles are also relevant for human health. For example, microplastics in water pose a significant threat to human health. The toxicity and environmental impact of these contaminants is highly affected by particle size and properties.9Therefore, size-based enrichment of nanoparticles is critical for downstream analysis in environmental studies towards determining the toxicities of these particles in solution.10

[0162] Microfluidics has emerged as a promising technology over the last few decades, revolutionizing fields ranging from biomedicine to chemistry and environmental science.11-13The ability to manipulate fluids at the microscale provides unparalleled control over particle sorting, focusing, and separation, making microfluidics a powerful tool for research and industrial applications.14Microfluidic manipulation methods are broadly categorized into active and passive methods, depending on whether external forces are used to manipulate particles. Active methods rely on external forces, such as electric,15magnetic,16or acoustic17’18waves to direct particle movement. These methods offer high precision micrometer sized particles but often require complex setups and significant operational costs. In contrast, passive methods utilize inherent fluid properties and microchannel geometry to achieve particle manipulation without external actuation, making the methods simpler and more cost-effective. Among passive methods, inertial microfluidics19and elasto-inertial microfluidics20have garnered significant attention due to their ability to perform label-free focusing and separation at high-throughput. Inertial microfluidics leverages the interplay of shear-induced lift forces and wall-induced lift forces to focus particles at equilibrium positions within Newtonian fluids.21 22A single, stable focusing position23 24and high resolution separation25can be achieved by the addition of curvature, but the systems demand very high pressures (tens to hundreds of bar) to focus sub-micron particles, leaving nanoparticles out of reach. Elasto-inertial microfluidics extends the principles of inertial microfluidics by introducing viscoelastic fluids, which generate an additional elastic force arising from the fluid’s normal stress differences.26The combination of elastic, shear-induced, and wall-induced lift forces enables the focusing of particles at a single, stable equilibrium position,27even for submicron particles. This enhanced control makes elasto-inertial microfluidics particularly suitable for nanoparticle applications. One important advantage of elasto-inertial focusing is its enhanced control over submicron particles, eliminating the effect of Brownian motion, which becomes more significant as particle size decreases.28

[0163] Despite the promise of elasto-inertial microfluidics, its application to nanoparticle manipulation remains underexplored. Previous studies have achieved focusing of particles down to 100 nm in curved, spiral microchannels29and 200 nm in straight microchannels.30However, focusing particles smaller than 100 nm in straight microchannels has remained a challenge due to the high pressures required for effective manipulation. In this study, we experimentally investigate elasto-inertial focusing of nanoparticles as small as 25 nm using high-aspect-ratio microchannels in sheathless flow conditions. Numerical simulations complement these experiments by providing detailed insights into the forces and dynamics governing particle migration towards the equilibrium position. We systematically evaluate the effects of particle size, channel geometry, viscoelastic fluid properties, and flow rates on focusing behavior. Our experiments include the use of polystyrene beads (25, 50, 100, 200, 500 nm and 1 pm), two different channel widths (5 and 10 pm) and four viscoelastic fluid concentrations (500, 1000, 2000 and 4000 ppm of PEO). Additionally, we demonstrate the successful focusing of biological nanoparticles, including liposomes (90 - 140 nm), extracellular vesicles (100 nm), high and low- density lipoproteins (10-25 nm), at the optimal experimental conditions. These findings lay the foundation for advanced nanoparticle manipulation strategies and their applications in biomedicine and environmental sciences.

[0164] Elasto-inertial microfluidics relies on a detailed understanding of the flow regime and the forces acting on particles within a microchannel. To better understand how these forces affect particle behavior under different flow conditions, the use of dimensionless numbers such as the Reynolds number (Re), Weissenberg number (Wi) and Elasticity number (El) are useful. Re describes the ratio of inertial to viscous forces in a fluid and determines the flow regime and is formulated as21Re = ?UmL / iJ, where / ? is fluid density, Um is the average fluid velocity, L is the characteristic channel length, and / J is the fluid viscosity. The Weissenberg number quantifies the ratio of elastic to viscous effects in a viscoelastic fluid, providing insight into the role of fluid elasticity on particle behavior. Wi is expressed as31I / V7 = 2 Q / hw2, where is the relaxation time of the viscoelastic fluid, Q is the volumetric flow rate, / ? is the height of the channel and w is the channel width. The importance of the Weissenberg number arises as it involves the characteristic relaxation time of the polymers, which is an intrinsic property of non-Newtonian fluids and varies with the polymer concentration of the fluid. This parameter is crucial for understanding elastic contribution to particle migration. Finally, the Elasticity number combines Re and Wi to describe the relative importance of elastic and inertial effects. It is defined as (E / = W / / Re)31and is instrumental in interpreting experimental data, as it reflects the balance between inertial and elastic forces.

[0165] The blockage ratio is another dimensionless number that plays a role in particle focusing. It is defined as the ratio of particle size over characteristic dimension of the channel ( / 3 = a / L).32In this study, we define the blockage ratio as / 3 = a / w, since the microchannel width represents the characteristic length of the high aspect ratio microchannels (ZtR= / ? / w) considered in this study. E lasto-inertial focusing occurs when the lift force and the elastic force balance each other in a microchannel. The lift force (FL) is considered as the combination of shear-induced lift force and wall-induced lift force and formulated as33FL = CL ?Um2a4 / Dh2, where CL is the lift coefficient, a is the particle size, and Dh is the hydraulic diameter of the channel. The presence of non-Newtonian fluid in a microchannel causes unequal normal stress differences (Ni and N2), which results in the formation of an elastic force.34The elastic force is expressed as35FE = a3FNi. The final equilibrium position of the particles depends on the complex relation between the lift force and the elastic force, and the geometry of the cross-section of the microchannel. In previous studies, it has been shown that particles can be found at the channel corners or at the center in single or multiple positions depending on the flow conditions and channel geometry.20

[0166] In this section, we present experimental and numerical results on nanoparticle focusing and migration in elasto-inertial microfluidics. First, we compare inertial and elasto-inertial focusing for 200 nm, 500 nm, and 1 pm particles. Then, we systematically investigate the effects of particle size, channel width, viscoelastic fluid concentration, and flow rate on focusing behavior. Additionally, we explore particle migration dynamics using numerical simulations to understand the interplay between elastic and inertial forces during size-based migration toward equilibrium positions. Finally, we demonstrate the potential of this method for biological nanoparticle focusing under optimized conditions, paving the way for applications in diagnostics, particle enrichment, and high-resolution size-based separation.

[0167] The ability to focus nanoparticles is a critical challenge in microfluidics, primarily because the forces governing particle migration scale with particle size. As we will be described below, this is the case particularly when comparing inertial and elasto-inertial approaches. As shown schematically in Figure 1(a), inertial microfluidics typically focuses particles along the channel’s center-face, resulting in two equilibrium positions in high-aspect- ratio straight channels. However, when viscoelastic fluids, such as PEO solutions, are used in elasto-inertial microfluidics, the addition of elastic forces drives particles to focus at a single central position, fundamentally altering their behavior. Experimental results for 200 nm, 500 nm, and 1 pm particles under identical flow rates (3 pL / min) and channel geometry (h = 60 pm, w = 5 pm) are shown in Figure 1 (b). In Newtonian fluids, 1 pm particles exhibit partial focusing near the two long sides of the microchannel, as expected in inertial focusing within high-aspect-ratio channels.21 36However, this focusing is incomplete, and smaller particles (200 nm and 500 nm) show no focusing behavior due to insufficient inertial forces37, emphasizing the size dependency of inertial focusing. Achieving nanoparticle focusing with inertial microfluidics would require impractically high flow rates, making this approach unsuitable for such applications.

[0168] In contrast, elasto-inertial microfluidics using a 1000 ppm PEO solution demonstrates successful focusing for all three particle sizes at the channel center, with 1 pm particles displaying the highest fluorescence intensity. These results highlight the size-dependent nature of elasto-inertial focusing38, where elastic forces significantly enhance the manipulation of smaller particles. Importantly, this study demonstrates that elasto-inertial microfluidics overcomes the limitations of inertial focusing, enabling nanoparticle alignment under practical experimental conditions.

[0169] The ability to focus sub-100 nm nanoparticles represents a significant milestone in elasto-inertial microfluidics, addressing long-standing challenges in manipulating nanoscale particles effectively. After successfully focusing 200 nm and 500 nm particles, we extended our investigation to particles ten times smaller. Figure 10 shows the focusing behavior of 25 nm particles under a fixed PEO concentration of 500 ppm in a microchannel with an aspect ratio of 6 (h=60 pm, w=10 m), at four different flow rates (0.5, 1 , 1.5 and 2 pL / min).

[0170] These experimental conditions (500 ppm of PEO and channel w=10 pm) were chosen to identify the lower limit of polymer concentration required to maintain focusing behavior at larger channel widths. Fluorescence intensity graphs reveal that 25 nm particles predominantly focus at the channel center, albeit with slight distortions. The highest focusing quality was observed at the lowest flow rate (0.5 pL / min), with quality gradually decreasing as flow rates increased due to reduced residence time hindering particles migration fully to the center. With a blockage ratio (a / W) of 0.0025, these results are approximately 20 times smaller than previously reported.

[0171] To achieve such high focusing efficiency without significant pressure drops, we implemented an innovative microchannel design previously introduced by our team. This design features a short segment with a small channel width, creating a high aspect ratio that enhances focusing. Following this segment, the channel widens, reducing overall resistance and preventing significant pressure increases within the system. This configuration ensures that particles maintain their focused positions at the channel center even after transitioning into the wider section.

[0172] By implementing this design, we effectively balance the benefits of high aspect ratio focusing with manageable pressure drops, enhancing the practicality of elasto-inertial microfluidic systems, we achieve precise nanoparticle focusing without the drawbacks associated with uniformly narrow channels, such as excessive pressure drops. Building on these results, we next investigate the influence of channel geometry and fluid properties on the focusing behavior, aiming to further optimize particle manipulation in elasto- inertial microfluidics.

[0173] The focusing of nanoparticles in elasto-inertial microfluidics is strongly influenced by both channel geometry and fluid properties, such as the concentration of PEO. We systematically investigated these factors to optimize focusing behavior, using microchannels with different widths and viscoelastic fluids of varying PEO concentrations.

[0174] We used microchannels with widths of 5 pm and 10 pm, while keeping the channel height constant at 60 pm, resulting in aspect ratios of 12 and 6, respectively. As shown in Figure 11 , fluorescence intensity profiles of 50 nm particles at PEO concentration of 1000 ppm and flow rates ranging from 0.5 pL / min to 3 pL / min indicate that particles are primarily focused at the channel center, independent of width and flow rate. However, a higher intensity signal at the channel center was observed in the narrower channel (w = 5 pm). This behavior likely results from stronger elastic forces in the smaller channel dimensions, where enhanced stress differences40drive particles towards the minimum stress region at the channel center. Despite the consistent central focusing, the likelihood of unfocused particles increases with wider channels due to reduced elastic force.

[0175] The focusing bandwidth (FWHM / W) is smaller across all flow rates for the narrower channel, with a significant increase in bandwidth observed at the highest flow rate of 3 pL / min in the wider channel (w = 10 pm). The focusing bandwidth (FWHM / W) is smaller across all flow rates in the narrower channel (w=5pm), with a significant increase in bandwidth observed at the highest flow rate of 3 pL / min in the wider channel (w=10 pm) (see Figure 18). These trends are supported by numerical simulations (Figure 19), which reveal that channels with higher aspect ratios generate greater first normal stress differences (Ni), intensifying elastic forces and improving focusing efficiency. Moreover, as expected, longer relaxation times (or higher Weissenberg numbers) correlate with increased elastic stresses and higher maximum N) (see Figure 19(a)). To the best of our knowledge, single-line particle focusing at the blockage ratios as low as 0.005 and 0.01 has not been achieved previously. We believe that the increased elasticity component and the utilization of high-aspect ratio microchannels are the driving factors for nanoparticle focusing at such low blockage ratios.

[0176] The concentration of PEO significantly influences the viscoelastic fluid properties, which in turn govern the elasticity and viscosity components critical for elasto-inertial focusing. Table S1 details the rheological properties of the PEO solutions used in this study. Increasing PEO concentration enhances the relaxation time (A) and fluid viscosity (p), thereby strengthening the elastic component (FE~ )41while reducing the Reynolds number (Re~1 / p)42.

[0177] Figure 12 illustrates the impact of four different PEO concentrations (500 ppm, 1000 ppm, 2000 ppm, and 4000 ppm) on the focusing behavior of 25 nm and 100 nm particles in a microchannel with an aspect ratio (AR) of 12 (h=60 m, w=5 pm) at a constant flow rate of 0.5 pL / min. Notably, the particles primarily focus at channel center even at the lowest PEO concentration of 500 ppm (Re=0.2, Wi=47.78, El=235.72), but some unfocused particles are observed. Increasing the concentration to 2000 ppm narrows the focusing bandwidth, eliminating unfocused particles around the center for the 100 nm particles. At 4000 ppm, focusing further improves for 100 nm particles, but no significant enhancement is observed for the 25 nm particles, which maintain their position at the center with slight distortions. These results suggest that increasing PEO concentration improves focusing quality for larger nanoparticles, but its effectiveness diminishes at smaller particle sizes due to competing effects between elasticity and Brownian motion.

[0178] The interplay between channel geometry and PEO concentration is crucial for achieving optimal nanoparticle focusing. Higher aspect ratio channels amplify elastic stresses, leading to sharper focusing, while increasing PEO concentrations enhances viscoelastic effects that further stabilize particle focusing. , further improving focusing efficiency. However, at higher concentrations, additional elasticity does not necessarily improve focusing for the smallest nanoparticles, indicating a need for balance between design parameters and fluid properties. These results highlight the importance of tailoring both geometric and fluidic parameters to the specific particle size and application requirements.

[0179] With these insights into the effects of geometry and fluid properties, we now turn to the roles of particle size and flow rate in further refining the focusing behavior.

[0180] The performance of elasto-inertial microfluidics for nanoparticle focusing is strongly influenced by particle size and flow rate, which together determine the balance between elastic and inertial forces. To systematically investigate these effects, we studied six particle sizes (25 nm, 50 nm, 100 nm, 200 nm, 500 nm, and 1 pm) 25 nm, 50 nm, 100 nm, 200 nm, 500 nm, and 1 pm) at a fixed PEO concentration of 2000 ppm in a microchannel with an aspect ratio (AR) of 12 (h = 60 pm, w = 5 pm) across a range of flow rates from 0.5 to 3 pL / min. Figures 13 and 14 summarize the experimental results, highlighting the interplay between these parameters.

[0181] At a fixed flow rate of 1 pL / min (Figure 13), all tested particles exhibit focusing at the channel center, with the sharpest fluorescence intensity profile observed for 1 pm particles. As particle size decreases, the fluorescence intensity at the center weakens, reflecting an increased proportion of unfocused particles. This trend suggests that larger particles experience stronger elastic forces (FE~a3, Fi_~a4),43 4leading to a more confined and stable focusing profile, whereas smaller particles are more prone to Brownian motion and secondary flow effects. Notably, particles as small as 25 nm still demonstrate focusing behavior, albeit with broader intensity distribution compared to larger particles. These results confirm the feasibility of using elasto-inertial microfluidics for sub-100 nm particle focusing, overcoming previous limitations in label-free nanoparticle manipulation.

[0182] Beyond this fixed flow rate analysis, we explored the effect of increasing flow rate on nanoparticle focusing at the fixed PEO concentration of 2000 ppm (Figure 14). At lower flow rates (0.5 and 1 pL / min), all particle sizes predominantly focus at the channel center, with larger particles (500 nm and 1 pm) achieving the sharpest focusing profiles. Full-width at half maximum (FWHM) analysis confirms that even the smallest particles (25 nm) exhibit focusing at the channel center, albeit with a broader intensity distribution. As flow rate increases to 1.5 pL / min, a transition occurs: smaller particles (50-200 nm) begin to develop additional focusing positions, while larger particles remain centered. At 2 pL / min and higher, three stable focusing positions emerge for the 50 nm and 100 nm particles — one at the channel center and two symmetrically positioned near the sides. The 200 nm particles also deviate from their single central position, instead showing a weaker three-position focusing pattern at 3 pL / min. In contrast, 500 nm and 1 pm particles maintain a single focused position at the channel center across all tested flow rates, though with decreasing fluorescence intensity at higher flow rates, suggesting a weakening of elastic forces as inertia grows dominant. The loss of a distinct focusing at the channel center is expected in elasto- inertial focusing as the flow rate increases and inertia becomes stronger.45These results align with force scaling predictions: elastic and lift forces scale differently with particle size (FE~ a3, FL~ a4), leading to stronger focusing of larger particles. However, the emergence of multiple focusing positions for smaller nanoparticles at higher flow rates suggests the influence of secondary flow effects in high-aspect-ratio microchannels. Previous studies have reported that secondary vortices can develop in straight channels at increased flow rates, displacing particles from the centerline due to transverse flow recirculations,4647. Further research is required to fully characterize these effects in elasto-inertial focusing.

[0183] These findings suggest that for optimal nanoparticle focusing, lower flow rates (<1 pL / min) are preferable, where elastic forces dominate over inertia. At these conditions, increasing PEO concentration enhances focusing quality by reinforcing viscoelastic effects. However, at higher flow rates, increasing inertia not only disrupts focusing but also introduces new stable focusing positions for smaller nanoparticles, requiring careful optimization for size-based separations.

[0184] In the following section, we further explore particle migration mechanisms for application in high-resolution nanoparticle separation, integrating numerical and experimental analyses.

[0185] The ability to manipulate nanoparticles for size-based separation relies on a detailed understanding of their migration behavior in viscoelastic fluids. Our previous work demonstrated that prefocusing particles at the channel center is a crucial first step before achieving effective size-based separation. In this study, we extend this approach to nanoparticles and investigate both numerically and experimentally how elastic forces guide particle migration.

[0186] To elucidate the physical mechanisms underlying particle migration, we analyze the competition between elastic and inertial forces in a viscoelastic fluid. The shear gradient lift force pushes particles away from the centerline,48while elastic forces counteract this by pulling the immersed particle toward the centerline for fluids which are not shear-thinning.47 49-51As shown in Figure 15(a), numerical simulations of the first normal stress difference (Ni = Txx - TYY) reveal that stress is highest near the channel walls and significantly lower at the center, effectively creating a lateral thrust that drives particles to stable equilibrium positions50. As a result, the gradient of N drives particles toward the channel center, where they encounter minimal elastic stress. This effect is particularly important in high-aspect-ratio channels, where it promotes single- line focusing.

[0187] To quantify size-dependent migration, we performed numerical simulations for 1.6 pm, 1 pm, and 750 nm particles. As can be seen in Figure 15(b), all particles migrate toward the channel center (z / lz= 0.5), but larger particles reach a steady-state position significantly faster than smaller ones. This is attributed to the scaling of elastic force, which increases with particle size (FE ~ a3). Consequently, 750 nm particles require more time to fully migrate, whereas 1 pm and 1.6 pm particles reach equilibrium more rapidly. The data clearly show that the migration velocity of the largest particles is the highest. Moreover, migration velocity decreases as particles approach the centerline due to the progressively lower elastic stress gradients because of the lower local values of Ni. The difference in migration velocity is attributed to elastic force arising from the imbalance in the distribution of N over the particle volume, FE O a3V( / Vi), where “a" represents the radius of a spherical particle.3849Consequently, the larger particle experiences a more pronounced elastic force, which accelerates its migration toward the centerline more than the smaller particles.

[0188] It is important to highlight that while particle migration along the Z-axis is consistently substantial, cross-stream motions along the K-axis are less pronounced. This can be again explained by the distribution of the first normal stress difference (Ni) within the rectangular channel. In other words, while migration along the primary axis (z-direction) is well-defined, cross-stream migration along the lateral axis (y-direction) remains limited, as the lowest Ni values form a vertically extended region, allowing for consistent particle alignment along this plane. To validate these numerical predictions, we conducted experimental studies tracking the migration of 500 nm and 1 pm particles in a two-stage microfluidic device (Figure 16). In the first section, particles were prefocused at the channel center, after which the channel split into two branches, enabling observation of migration back toward the centerline. The results confirm that 1 pm particles migrate significantly faster than 500 nm particles, in agreement with numerical predictions. Figure 16B shows the intensity profile for the 1 pm particles and 500 nm particles where the 1 pm particles migrate and reach the center line faster while the 500 nm particles are lagging behind and exhibit broader spatial distribution. , increasing overlap with 1 pm particles, which could pose challenges for high-purity separation.

[0189] However, further optimizations are needed to achieve complete sizebased separation since 500 nm particles are spread wider while migrating towards the channel center, overlapping with 1 pm particles. Under similar conditions, we successfully separated 2 pm and 3 pm particles, indicating that separation resolution is size-dependent (see Figure 20), with smaller nanoparticles requiring additional optimizations.

[0190] These findings demonstrate that elasto-inertial migration can effectively enrich nanoparticles, but further refinements are needed to achieve complete separation at the sub-micron scale. At this size range, Brownian motion and reduced elastic force gradients introduce challenges that must be addressed by optimizing channel geometry, flow conditions, and viscoelastic properties. Despite these complexities, the observed migration behavior paves the way for high-resolution nanoparticle sorting using elasto-inertial microfluidics.

[0191] Future efforts will focus on multi-stage separation strategies and further tuning of viscoelastic stress distributions to enhance separation fidelity.

[0192] To demonstrate the potential of elasto-inertial microfluidics in high- aspect-ratio microchannels for biomedical applications, we investigated the focusing behavior of biologically relevant nanoparticles. We conducted experiments using high-density lipoproteins (HDL, 10 nm), low-density lipoproteins (LDL, 25 nm), liposomes (90 nm), and extracellular vesicles (EVs, 100 nm) in a viscoelastic fluid at 1000 ppm PEO (detailed size distributions of biological particles are provided in Figure 21 ).

[0193] Our results, presented in Figure 17, reveal that all biological particles exhibit central focusing within the microchannel, consistent with the behavior observed for polystyrene nanoparticles. The smallest particles (HDL, 10 nm) exhibited the highest background signal, likely due to their small size and increased diffusion. However, LDL (25 nm), liposomes (90 nm), and EVs (100 nm) were fully focused at the channel center, demonstrating the ability of elasto-inertial forces to counteract Brownian motion and drive nanoscale bioparticles to a single equilibrium position.

[0194] These findings establish the feasibility of elasto-inertial focusing for the manipulation of biological nanoparticles, which is crucial for applications requiring particle enrichment, high-purity isolation, and potential size-based separation. Unlike conventional methods such as size-exclusion chromatography, ultracentrifugation, and asymmetrical flow field-flow fractionation (AF4), which often require multiple processing steps and specialized equipment, elasto-inertial microfluidics provides a label-free, single-step approach with minimal sample preparation. Additionally, compared to microfluidics based active methods such as acoustofluidics and dielectrophoresis, which rely on external fields and complex device architectures, the method presented here enables high-throughput nanoparticle manipulation with a simple, single-inlet design.

[0195] Previous studies have explored viscoelastic microfluidics for extracellular vesicle and lipoprotein enrichment, but these methods have been limited in their ability to precisely focus particles below 50 nm in sheathless conditions. The present work extends the lower focusing limit to 10 nm, demonstrating that high aspect ratio channels combined with optimized viscoelastic conditions provide a scalable platform for sub-100 nm particle manipulation. Beyond focusing, our findings lay the groundwork for future developments in size-based separation of nanoparticles (<500 nm) using elasto-inertial forces. This study establishes elasto-inertial focusing of nanoparticles as small as 25 nm in a sheathless flow, high-aspect-ratio channels. While elasto- inertial focusing has previously demonstrated advantages for microscale particle manipulation, its application to nanoscale particles has been significantly limited. Prior studies reported a lower focusing limit of 200 nm in straight microchannels. Here, we extend this boundary by demonstrating single-line focusing of nanoparticles down to 10 nm, marking a substantial advancement in elasto-inertial microfluidics.

[0196] Through integrated numerical and experimental analyses, we provide new insights into nanoparticle migration dynamics in elasticity-dominated flow regimes (0.03 < Re < 1.22, 11 < Wi < 1110, 63 < El < 6000). Our systematic study confirms the feasibility of elasto-inertial focusing for biologically relevant nanoparticles, including HDL (10 nm), LDL (25 nm), liposomes (90-140 nm), and EVs (100 nm), under optimized flow conditions. The ability to focus biologically relevant nanoparticles, including those used in drug delivery (e.g., liposomes for mRNA vaccines), opens new avenues for high-resolution fractionation of biomolecular carriers, with implications for both diagnostics and therapeutic applications. We envision that this approach will pave the way for next-generation microfluidic systems capable of high-throughput particle separation, bioparticle enrichment, and precision medicine applications. Future work will explore further refinements in device geometry, polymer formulations for elasticity enhancing, and separation protocols to enhance resolution and throughput.

[0197] Although elasto-inertial microfluidics has significant advantages and has increasingly been used in many applications, in previous work, the smallest particle size focused in a straight microchannel was 200 nm. In this paper, we present focusing of nanoparticles down to size of 10 nm in a straight high-aspect-ratio microchannels. Numerical and experimental analyses together provide a deeper understanding of particle migration dynamics, reinforcing the robustness of this approach. We provide extensive experimental data on elasticity dominated flow (0.03<Re<1 .22, 11 <Wi<1110, 63<EI<6000) using fluorescently labelled particles and show the focusing of HDL (10 nm), LDL (25 nm), lipoproteins (90 - 140 nm) and EVs (100 nm) in optimum conditions. We believe that these results are the initial steps in view of size-based separation of nanoparticles (<500 nm) using elasto-inertial microfluidics. Furthermore, the ability to focus nanoparticles in a simple and small microfluidic channel has the potential to increase the throughput by the parallelization of the microchannels. Therefore, the presented results can lead to numerous applications in the field of biomedicine where high-throughput and high-resolution particle separation are needed.

[0198] Microfluidic devices were designed with the AutoCAD software (Autodesk). The master mold to fabricate the PDMS (polydimethylsiloxane) chips was prepared with SLIEX (dry Sll-8 film) on a silicon wafer through photolithography process.56The PDMS base (SYLGARD 184) was mixed with the curing agent at the mixing ratio of 10:1 . The mixture was poured onto the master mold. Degassed in a desiccator and baked at 65 °C for 6 hours for curing. The cured PDMS was peeled off, and inlet and outlet holes were punched. The prepared PDMS chip and microscope glass slide were bonded using oxygen plasma activation. The final device was post-baked at 120 °C for 15 minutes for better sealing.

[0199] Two different high aspect ratio microfluidic channels were designed to study the nanoparticle focusing. Both microfluidic channels contain 1.5 mm long straight channel with width 20 pm followed by 3 mm long straight channel, which is then followed by another 1 .5 mm long straight channel with width 20 pm. The only difference between the wo microfluidic channels is the width of the 3 mm long straight channel. First design has 5 pm width (AR=12) while the second design has 10 pm width (AR=6). Two different widths are therefore used to investigate the effect of the channel geometry. The channel height was kept constant at 60 pm for all the experiments. Both channels have an expansion area (width=150 pm) before the outlet to observe the particles in high-resolution. (See Figure 1 for the channel design). The data used and analyzed in this study were recorded in these expansion areas. In this study, PEG (Polyethylene Oxide, Mw=2x106g / mol), elasticity enhancer, was used for the preparation of viscoelastic fluids. The PEO powder was dissolved in deionized water at four different concentrations (500 ppm, 1000 ppm, 2000 ppm and 4000 ppm) (See Table S1 for the rheological properties of the fluids and see Table S2 for the dimensionless numbers). The fluorescent polystyrene (PS) particles (Fluoro-Max, ThermoFisher Scientific) with diameters of 25 nm, 50 nm, 100 nm, 200 nm, 500 nm and 1 pm were suspended in the prepared viscoelastic fluids prior to the flow experiments (3 pL of particles at the concentration of 1 % solids were suspended at 3 mL of PEO).

[0200] We perform three-dimensional direct numerical simulations to investigate the cross-streamline migration of particles suspended in viscoelastic (VE) fluids within a relatively high aspect ratio straight microchannel. These simulations aim to further confirm and explain the experimental observations. We employ our in-house code utilizing a direct forcing immersed boundary method (IBM) to simulate the particles as moving Lagrangian grids, while the carrier fluid is discretized within a stationary Eulerian frame, in which the Navier-Stokes and the viscoelastic constitutive equations are discretized using finite differences.57The suspending fluid motion is governed by the incompressibility constraint and conservation of momentum as follows:

[0201] V ■ it = 0, (1 )

[0202] Here, u is the fluid velocity, p is the pressure field, T is the total deviatoric stress tensor, and Re is Reynolds number. The extra term f on the right-hand side of Equation (2) is the immersed boundary force field representing the particle-fluid interaction; details of immersed boundary method can be found in the work of Breugem.58The total deviatoric stress tensor, T, is composed of contributions from the solvent (Newtonian fluid) and polymer parts as T = TS+ TP. The solvent stress tensor is defined as TS= ps(Vu + Vu7), where ps= pslp is the ratio of the solvent viscosity to the total viscosity. In addition to the equations mentioned earlier, a constitutive equation should be employed to model the evolution of the non-Newtonian contribution (TP) of the VE material. We implement the Oldroyd-B model59to consider the viscoelasticity of the material.

[0203] Lipoproteins were isolated from the blood plasma of apparently healthy donors, obtained from Blood transfusion station of Karolinska Hospital. The density of 3 ml of blood plasma was adjusted to 1.021 g / mL using KBr powder. The KBr buffers of different densities (1.006 g / ml, 1 ,019g / ml, 1.063 g / mL, 1.24 g / ml) and blood plasma were layered in a gradient, transitioning from denser to less dense solutions in 14 mL tubes (14 x 95 mm, Open-Top Thinwall Ultra-Clear Tubes, Backman Coulter, USA). The tubes were ultracentrifuged for 48 hours at 37000 rpm at 15°C (Optima-XE Ultracentrifuge, SW 40 Ti Swinging-Bucket Rotor, Backman Coulter, USA). Post-centrifugation, LP fractions containing separately Very Low-Density Lipoproteins (VLDL), Low Density Lipoproteins (LDL) and High-Density Lipoproteins (HDL) were carefully removed using a medical needle and syringe avoiding the blending of different classes of LPs. Furthermore, VLDL, LDL and HDL were concentrated using Ultra Centrifugal Filter, 30 kDa MWCO (Am icon). Protein concentration was measured using Bradford assay (Biorad) at NanoDrop Microvolume Spectrophotometer (ThermoFisher). The sizes of lipoproteins were confirmed using Dynamic Light Scattering at Zetasizer (Malvern). HDL and LDL were labeled with TopFluor-Cholesterol (Avanti Polar Lipids). Finally, 50 pL of HDL and LDL particles at the concentration of 0.5 mg / mL were diluted to 1 mL with PEO prior the flow experiments.

[0204] For production of extracellular vesicles (EVs), immortalized fibroblasts (BJ-5ta cell line, ATCC CRL-4001 ) were cultured in a 4:1 mixture of Dulbecco’s medium supplemented with 4 mM L-glutamine, glucose (4.5 g / L) and sodium bicarbonate (1.5 g / liter) and Medium 199 supplemented with Hygromycin B (0.01 mg / mL) (ThermoFisher Scientific) and 10% fetal bovine serum (Invitrogen). Cells were cultured at 37°C and 5% CO2 in a humidified atmosphere and regularly tested for the presence of mycoplasma. For EV harvesting, media was changed to OptiMem (Invitrogen) 48 hours before harvest of conditioned media (CM) as described before.60Collected CM was directly subjected to a low-speed centrifugation step at 500 x g for 5 min followed by a 2000 x g spin for 10 min to remove larger particles and cell debris. Precleared CM was subsequently filtered through 0.22 pm bottle top vacuum filters (Coming, cellulose acetate, low protein binding) to remove any larger particles. EVs were then prepared by tangential flow filtration (TFF) as described before.61In brief, precleared CM was concentrated via TFF by using the KR2i TFF system (Spectrum Labs) equipped with modified polyethersulfone hollow fiber filters with 300 kDa membrane pore size (MidiKros, 370 cm2surface area, Spectrum Labs) at a flow rate of 100 mL / min (transmembrane pressure at 3.0 psi and shear rate at 3700 sec-1) as described previously. Amicon Ultra-0.5 10 kDa MWCO spin-filters (Millipore) were used to concentrate the sample to a final volume of 100 pL. Final EV samples were stored at -80°C in PBS-HAT [PBS supplemented with HEPES, human serum albumin and D-(+)-Trehalose dihydrate] until usage.62

[0205] Synthetic Liposomes were prepared using the lipid 1 ,2-Dioleoyl-sn- glycero-3-phosphocholine (DOPC). DOPC was dissolved in 2 ml of chloroform at 0.25 mg / ml in the glass vial. Chloroform was then evaporated under the nitrogen flow. The lipid residue was hydrated using the buffer (150 mM of NaCI, 10 mM of HEPES) and vortexed harshly until the solution became turbid whereas the lipid residue disappeared from the wall of the glass vial. Then, the liquid was transferred to the 15 ml falcon tube and sonicated at power 3, duty cycle 40%, for 10 min using a Branson Sonifier 250. The second aliquot, instead of sonication was extruded 21 times using the mini extruder (Avanti) with filter size of 100 nm. The size was verified using DLS (Malvern) (see Figures 20).

[0206] The microfluidic experiments were performed with a mid-pressure pump (neMESYS CETONI GmbH) using a 3 mL steel syringe. The data acquisition was accomplished using an inverted microscope (Nikon Eclipse Tl) with a sCMOS camera (Andor Zyla) and LED lightning system (Lumenor Spectra X LED). Micro Manager software was used to control the microscope and record the images. The recorded images were processed by Imaged software. Itemized list of embodiments

[0207] 1 . A system for sheathless focusing of nanoparticles, comprising:

[0208] - A substrate with at least one straight microchannel;

[0209] - A viscoelastic fluid containing nanoparticles;

[0210] - A pumping mechanism to drive laminar flow;

[0211] - Wherein the fluid, channel geometry, and flow conditions generate elasto- inertial forces that focus nanoparticles as small as 10 nm, overcoming Brownian motion through optimized viscoelastic stress profiles.

[0212] 2. The system according to embodiment 1 , wherein the microchannel has a dual-section design with a focusing segment and a widening segment to maintain particle alignment while reducing pressure drops.

[0213] 3. The system according to embodiment 1 , wherein the nanoparticles include biological particles such as lipoproteins, extracellular vesicles, and exosomes.

[0214] 4. The system according to embodimentl , wherein the viscoelastic fluid contains polyethylene oxide (PEO) at concentrations between 10 ppm and 10,000 ppm.

[0215] 5. A method for sheathless focusing and separation of nanoparticles, comprising:

[0216] - Introducing a nanoparticle suspension into a microchannel;

[0217] - Driving laminar flow through the channel to generate elasto-inertial forces;

[0218] - Focusing nanoparticles into localized streamlines;

[0219] - Separating nanoparticles into multiple outlet branches based on size.

[0220] 6. A system for focusing nanoparticles in a fluid, comprising: - a substrate; - at least one straight microchannel provided on the substrate, the microchannel having an inlet and an outlet;

[0221] - a fluid moving along the channel in a laminar flow, the fluid having suspended nanoparticles; and

[0222] - a pumping element driving the laminar flow of the fluid, wherein the fluid, channel, and pumping element are configured to cause elasto-inertial forces to act on the nanoparticles, focusing them into one or more localized stream lines.

[0223] 7. The system according to embodiment 6, wherein the microchannel has a width between about 5 micrometers and about 500 micrometers and a height between about 10 micrometers and about 200 micrometers

[0224] 8. The system according to embodiment 6, wherein the nanoparticles range in size from about 20 nm to about 1000 nm.

[0225] 9. The system according to embodiment 6, wherein the viscoelastic fluid comprises an elasticity enhancer selected from the group consisting of polyethylene oxide (PEO), polyacrylamide, xanthan gum, and hyaluronic acid.

[0226] 10. The system according to embodiment 6, wherein the viscoelastic fluid has a concentration ranging from about 50 ppm to about 10000 ppm.

[0227] 11 . A method for focusing nanoparticles in a moving fluid, comprising:

[0228] - providing nanoparticles suspended in a fluid into a channel; and

[0229] - flowing the fluid through the channel under conditions such that elasto- inertial forces acting on the nanoparticles result in their localization into one or more stream lines.

[0230] 12. The method according to embodiment 11 , wherein the channel has a width between about 2 micrometers and about 500 micrometers and a height between about 10 micrometers and about 200 micrometers. 13. The method according to embodiment 11 , wherein the nanoparticles range in size from about 20 nm to about 1000 nm. 14. The method according to embodiment 11 , wherein the viscoelastic fluid comprises an elasticity enhancer selected from the group consisting of polyethylene oxide (PEO), polyacrylamide, xanthan gum, and hyaluronic acid.

[0231] 15. The method according to embodiment 11 , wherein the viscoelastic fluid has a concentration ranging from about 100 ppm to about 5000 ppm.

[0232] In the above the inventive concept has mainly been described with reference to a limited number of examples. However, as is readily appreciated by a person skilled in the art, other examples than the ones disclosed above are equally possible within the scope of the inventive concept, as defined by the appended claims.

Claims

CLAIMS1 . A system for sheathless focusing of nanoparticles, comprising: a substrate with at least one straight microchannel; a viscoelastic fluid containing nanoparticles; a pumping mechanism to drive laminar flow; wherein the fluid, channel geometry, and flow conditions generate elasto-inertial forces that focus nanoparticles as small as 10 nm, overcoming Brownian motion through optimized viscoelastic stress profiles.

2. An arrangement (100) for sheahtless focusing of nanoparticles contained in a viscoelastic fluid, comprising: a substantially straight microchannel (110), a pumping mechanism configured to drive the viscoelastic fluid as a laminar flow through the microchannel (110), wherein the microchannel’s (110) geometry is configured to together with the visco-elastic fluid’s composition generate elasto-inertial forces on the nanoparticles to separate the nanoparticles on different levels in the laminar flow, such that the nanoparticles are focused based on the size of the nanoparticles.

3. The arrangement (100) according to claim 2, wherein the microchannel (110) is designed as a dual-section microchannel, with a focusing section (120) upstream and a separation section (130) downstream, the focusing section (120) having a smaller cross-section than the separation section (130), where the focusing section’s (120) cross-section has a width, w of 1-30 pm and a height, h of 10-200 pm, preferably with the width about 5 pm and a height of about 60 pm, wherein the microchannel (110) is split into two or more sub-channels downstream the focusing section (120) towards the separation (130).

4. The arrangement (100) according to claim 3, wherein an aspect ratio, AR, where AR=h / w is between 20 and 2 for the focusing section (120), and between 10 and 2 for the separation section (130), preferably AR for the focusing section (120) is about 12, and AR for the separation section (130) is about 6.

5. The arrangement (100) according to any of the claims 1 to 4, wherein the nanoparticles in the viscoelastic fluid are in a range between 10 nm and 1000 nm, preferably between 20 nm and 500 nm, and more preferably between 50 nm and 200 nm.

6. The arrangement (100) according to any of the claims 1 to 5, wherein the viscoelastic fluid comprise at lease one elasticity enhancer from a group comprising: polyethylene oxide, PEO, polyacrylamide, xanthan gum, and hyaluronic acid.

7. The arrangement (100) according to any of the claims 1 to 6, wherein the viscoelastic fluid has a concentration in a range from about 50 ppm to about 80000 ppm.

8. The arrangement (100) according to any of the claims 1 to 7, wherein the pumping mechanism is configured to provide the laminar flow in a range from about 0.5 pl / min to about 200 pl / min.

9. The arrangement (100) according to any of the claims 1 to 8, wherein the microchannel (110) is arranged on a substrate designed as a plastic chip, an elastomer-based chip, a silicon-based chip, a Polydimethylsiloxane, PDMS, based chip, a thermoplastic chip, a glass-based substrate, or a glass- silicon-based substrate.

10. The arrangement (100) according to any of the claims 1 to 9, wherein the focusing section (120) extends between 2 and 4 mm, preferably about 3mm, and wherein the total length of the microchannel (110), including the focusing section (120) and the separation section (130) is between 5 and 10 mm, preferably about 6 mm.

11. A method for sheathless focusing of nanoparticles contained in a viscoelastic fluid, comprising: arranging (500) an arrangement according to any of the claims 1 to 10, and pumping (502) the viscoelastic fluid comprising the nanoparticles as a laminar flow through the microchannel of the arrangement, to generate elasto-inertial forces on the nanoparticles to separate the nanoparticles on different levels in the laminar flow, such that the nanoparticles are focused based on the size of the nanoparticles.

12. The method for according to claim 11 , wherein: the nanoparticles in the viscoelastic fluid comprises a sample comprising lipid nanoparticles, LNPs, the sample having been introduced in the microchannel, the LNPs are aligned and separated by the elasto-inertial forces along a streamline in the microchannel, wherein the method further comprises: simultaneously when aligning and separating the LNPs, exchanging (504) a solvent or a buffer phase of the viscoelastic fluid by co-flowing the viscoelastic fluid with a second fluid through the microchannel.

13. The method for according to claim 12, further comprising: focusing (506) the nanoparticles and exchanging (508) a solvent or a buffer phase using at least one of tangential flow filtration, TFF, dialysis, or diafiltration.

14. The method according to method claim 12 or 13, further comprising: encapsulating, within the LNPs, therapeutic nucleic acids from at least one of mRNA, siRNA, or plasmid DNA.

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