Microfluidic oscillatory asymmetrical traps

Abstract

Microfluidic chips and microfluidic systems containing the same for implementing microfluidic oscillatory asymmetrical traps are described herein. In one example, an oscillatory microfluidic system for trapping particles contained in a fluid flowing within a channel is provided. The oscillatory microfluidic system including: the channel to conduct the fluid, where the channel includes a longitudinal axis and one or more geometric features that provide at least one asymmetry along the longitudinal axis; a source of pressure or flow to move the fluid through the channel; a fluid oscillator to provide an oscillating pressure on the fluid within the channel; and a controller arranged and configured to transmit control signals to the fluid oscillator to generate a repeating oscillation flow profile of the fluid within the channel, thereby trapping the particles in one or more zones centered on the one or more geometric features within the channel.

Description

MICROFLUIDIC OSCILLATORY ASYMMETRICAL TRAPSSTATEMENT REGARDING FEDERALLY FUNDED RESEARCH

[0001] This invention was made with government support under one or more of grant numbers 5R21CA260989-02 and 5R01CA260304-03, both of which were awarded by the National Institutes of Health-National Cancer Institute. The government has certain rights in the invention.CROSS REFERENCE TO RELATED APPLICATIONS

[0002] This application claims the benefit of priority to US Provisional Patent No. 63 / 578,267, filed on August 23, 2023, which is incorporated herein by reference in its entirety.TECHNICAL FIELD

[0003] The present disclosure relates generally to microfluidic chips and microfluidic systems containing the same for implementing microfluidic oscillatory asymmetrical traps.BACKGROUND

[0004] Inertial focusing is a phenomenon in microfluidics where particles or cells flowing in a microchannel become focused into specific, stable positions within the channel cross-section due to the effects of inertia. This is in contrast to the behavior of particles in fluids at very low Reynolds numbers, where inertial effects are negligible, and particles generally follow the streamlines of the fluid.

[0005] Inertial focusing with oscillatory flow is a variation of the inertial focusing phenomenon, where an oscillatory or pulsatile flow, rather than a steady flow, is used to manipulate the position and focusing of particles within a microchannel.SUMMARY

[0006] Inertial focusing, a powerful technique for particle manipulation, faces limitations in efficiently focusing small particles due to extended channel length requirements, resulting in elevated resistance and pressure across devices. To surmount these challenges, we used oscillatory flow in specialized microfluidic devices to subject particles to quasi-infinite channels, which enables focusing of particles smaller than about one micron. The present disclosureprovides microfluidic chips, systems, and methods for implementing a microfluidic phenomenon, termed the “Microfluidic Oscillatory Asymmetrical Trap” (or “MOAT”) herein, which can provide contact-free particle trapping in oscillatory flow, despite the presence of significant net flow rates, in microfluidic devices in which the channels have an asymmetry along their length.

[0007] Experiments were conducted on 3D-printed, pseudo-2D microfluidic chips. Trapping efficiency and trap retention strength were measured and a parameter space in which the MOAT phenomenon occurs is provided. Notably, the MOAT manifests across diverse devices and particle types, spanning from plastic beads to white blood cells, red blood cells, and cultured cell lines. Furthermore, the MOAT exhibits a distinctive tunable functionality, allowing trapping of particles with a desired size while letting other particles flow through.

[0008] These and other features relating to microfluidic chips and microfluidic systems described herein are summarized below.

[0009] According to a first aspect, this disclosure provides an oscillatory microfluidic system for trapping particles contained in a fluid flowing within a channel. The oscillatory microfluidic system includes: the channel to conduct the fluid, where the channel includes a longitudinal axis and one or more geometric features that provide at least one asymmetry along the longitudinal axis; a source of pressure or flow to move the fluid through the channel; a fluid oscillator to provide an oscillating pressure on the fluid within the channel; and a controller arranged and configured to transmit control signals to the fluid oscillator to generate a repeating oscillation flow profile of the fluid within the channel, where the repeating oscillation flow profile includes at least one step in a direction of net flow parallel to the longitudinal axis and at least one step in a direction opposite to the direction of net flow, such that fluid step lengths have a magnitude similar in size to a size of one of the one or more geometric features, thereby trapping the particles in one or more zones centered on the one or more geometric features within the channel.

[0010] In some implementations of the oscillatory microfluidic system, the control signals to generate the repeating oscillation flow profile are determined by performing a simulation of an oscillatory flow of the fluid within the channel, and the simulation establishes that the fluid step lengths are of a magnitude that is about the same as the size of the geometric features if, in the simulation, the following constraints are satisfied: one or more fluid particle paths exist withinthe channel during the oscillatory flow of the fluid; and for each fluid particle path: a time- averaged magnitude of a relative acceleration along the fluid particle path, multiplied by a stroke duration of a cycle along the fluid particle path, is 10% or more of a time-averaged magnitude of a velocity along the fluid particle path, where the relative acceleration along the fluid particle is defined as a total acceleration of the fluid minus a transient rate of change of the velocity along the fluid particle path.

[0011] In some implementations of the oscillatory microfluidic system, the longitudinal axis is straight, and the one or more geometric features include at least an expansion or a contraction of the channel along the longitudinal axis.

[0012] In some implementations of the oscillatory microfluidic system, the longitudinal axis is curved, the one or more geometric features include a curve of the channel along the longitudinal axis, and the channel has a constant cross-section along the longitudinal axis.

[0013] In some implementations of the oscillatory microfluidic system, the longitudinal axis is straight, and the one or more geometric features include an array of polygonal microstructures, e.g., L-shaped, rectangular, or square microstructures, arranged within the channel along the longitudinal axis.

[0014] In some implementations of the oscillatory microfluidic system, the source includes a syringe pump or a hydrostatic pressure system.

[0015] In some implementations of the oscillatory microfluidic system, the fluid oscillator further includes a pulse generator.

[0016] In some implementations of the oscillatory microfluidic system, the magnitude of the fluid step lengths is between 1 and 5 times, e.g., between 2 and 3 times, the size of one of the one or more geometric features.

[0017] In some implementations of the oscillatory microfluidic system, the dimensions of the channel are configured and the flow rate of the fluid within the channel is controlled such that a particle Reynolds number of the particles within the channel is from 0.01 to 10, e.g., from 0.1 to

[0018] In some implementations of the oscillatory microfluidic system, the dimensions of the channel are configured and the flow rate of the fluid within the channel is controlled such that Womersley number within the channel is from 0.1 to 10, e.g., from 1 to 3.

[0019] In some implementations of the oscillatory microfluidic system, a frequency of the oscillating pressure is from 0.01 Hertz to 800 Hertz, e.g., 0.1 Hertz to 500 Hertz, or 1.0 Hertz to 150 Hertz.

[0020] According to a second aspect, this disclosure provides a microfluidic chip. The microfluid chip includes: a planar surface; and a superstate disposed on the planar surface, the superstate and planar surface defining a microfluidic structure including: a first port and a second port; and a fluidic lumen extending from the first port to the second port along a longitudinal axis parallel to the planar surface, the fluidic lumen including one or more geometric features that provide at least one asymmetry along the longitudinal axis, where the one or more geometric features within the fluidic lumen includes: a first channel extending from the first port along the longitudinal axis, the first channel having a first height from the planar surface; a second channel extending to the second port along the longitudinal axis, the second channel having a second height from the planar surface that is greater than the first height; and a bridging expansion between the first and second channels, the bridging expansion having a third height from the planar surface that increases from the first height to the second height along the longitudinal axis.

[0021] In some implementations of the microfluidic chip, the third height increases linearly from the first height to the second height at an acute angle from the planar surface.

[0022] In some implementations of the microfluidic chip, the third height increases from the first height to the second height in a number of discrete steps having increasingly greater heights from the planar surface.

[0023] In some implementations of the microfluidic chip, the first and second channels each extend linearly along the longitudinal axis.

[0024] In some implementations of the microfluidic chip, the fluidic lumen has a width in a direction parallel to the planar surface and orthogonal to the longitudinal axis, and the width is greater than both the first height and the second height.

[0025] According to a third aspect, this disclosure provides a microfluidic chip. This microfluidic chip includes: a planar surface; and a superstate disposed on the planar surface, the superstate and planar surface defining a microfluidic structure including: a first port and a second port; and a channel extending from the first port to the second port along a longitudinal axis parallel to the planar surface, where the channel includes a number of geometric features inthe form of an array of polygonal microstructures arranged along the longitudinal axis to provide a number of asymmetries within the channel along the longitudinal axis.

[0026] In some implementations of the microfluidic chip, each polygonal microstructure in the array is an L-shaped, rectangular, or square microstructure, arranged within the channel along the longitudinal axis.

[0027] In some implementations, the microfluidic chip further includes a substrate having the planar surface, e.g., the substrate is transparent, e.g., the substrate is a glass slide.

[0028] In some implementations of the microfluidic chip, the superstrate is 3D-printed.

[0029] According to a fourth aspect, this disclosure provides an oscillatory microfluidic system including: the microfluidic chip of the second or third aspect in any of its abovementioned implementations; a first tube connected to the first port of the microfluidic chip; a second tube connected to the second port of the microfluidic chip; a source of pressure or flow to move a fluid containing particles through the one or more channels of the microfluidic chip; a fluid oscillatory system to provide an oscillating pressure on the fluid within the one or more channels; and a controller arranged and configured to transmit control signals to the fluid oscillatory system to generate a repeating oscillation flow profile of the fluid within the one or more channels, where the repeating oscillation flow profile includes at least one step in a direction of net flow parallel to the longitudinal axis and at least one step in a direction opposite to the direction of net flow, such that fluid step lengths have a magnitude similar in size to a size of one of the one or more geometric features, thereby trapping the particles in one or more zones centered on the one or more geometric features within the channel.

[0030] In some implementations of the oscillatory microfluidic system, the fluid oscillatory system is mechanically coupled to any one or more of the first tube, the second tube, or the microfluidic chip.

[0031] In some implementations of the oscillatory microfluidic system, the fluid oscillatory system includes one or more speakers.

[0032] According to a fifth aspect, this disclosure provides a method for implementing a microfluidic oscillatory asymmetrical trap (MOAT). The method includes: providing the microfluidic chip of the second or third aspect in any of its abovementioned implementations; moving a fluid containing particles between the first and second ports of the microfluidic chip;and imparting oscillations to the fluid flowing within the one or more channels within the microfluidic chip.

[0033] In some implementations of the method, moving the fluid between the first and second ports of the microfluidic chip includes applying a pressure via a syringe pump or a hydrostatic pressure system.

[0034] In some implementations of the method, moving the fluid between the first and second ports of the microfluidic chip includes: attaching a first tube to the first port of the microfluidic chip; attaching a second tube to the second port of the microfluidic chip; moving the fluid into the first or second tube; and applying a source of pressure or flow to the first or second tube to move the fluid between the first and second tubes.

[0035] In some implementations of the method, imparting the oscillations to the fluid includes coupling an oscillatory system to any one or more of a length of the first tube, a length of the second tube, or the microfluidic chip, and activating the oscillatory system to impart the oscillations to the fluid in the first tube, the second tube, or the microfluidic chip.

[0036] Particular embodiments of the subject matter described herein can be implemented to realize one or more of the following advantages.

[0037] Inertial focusing leverages lift forces to manipulate particles in microchannels, and it finds utility for cell sorting, among other applications. Its subsequent extension into oscillatory flow has created effectively infinite channel lengths that enabled focusing of sub-micron particles, reduction in shear stresses on cells, and reduced inlet pressure requirements. For discussions of inertial focusing, see U.S. Patent Nos. 9,808,803; 9,895,694; and 9,610,582; and U.S. Published Patent Application No. US2016 / 0123858, all of which are incorporated herein by reference in their entireties. However, current techniques for oscillator flow set the net flow rate to zero to keep particles centered, e.g., in a field-of-view, overlooking the potential effects of asymmetry along the flow direction.

[0038] Implementations of the microfluidic chips and microfluidic systems disclosed herein can be used for various microfluidic applications including, but not limited to, timed filtration and release, micro-scale suspension culturing, size fractionation, particle metering, and density-based separation.

[0039] The MOAT can provide contact-free trapping in devices where the channels have asymmetry along their length, either in their cross-sectional dimensions, e g., an expansion orcontraction, or simply a channel curvature. This phenomenon occurs in asymmetric oscillatory microflows, at significant particle Reynolds number, significant Womersley number, and operates on particles, including cells. The parameter space in which the phenomenon occurs was identified the trapping efficiency and robustness at various flow rates, oscillatory velocities, and oscillatory frequencies was measured. The MOAT’s efficacy was demonstrated in capturing an array of particles such as polystyrene particles, HeLa cells, red blood cells in diluted blood, and white blood cells in whole blood. Through optimization of device dimensions to cater to various end goals, many possibilities arise, including the potential to achieve efficient trapping, manipulation of individual target particles, or size-based fractionation. In contrast to optical trapping, MOAT can operate in a highly parallelized format without a microscope. In contrast to di electrophoretic trapping, the MOAT does not require electrodes or low conductivity buffers to protect cells.

[0040] In contrast to traditional filtration, the MOAT works on particles much smaller than the channel and without contact. In contrast to inertial focusing with vortices, the MOAT can be tuned in real time and operates in a broader parameter space for wide flexibility. Beyond particle manipulation, the MOAT can be used for cell culture in suspension, advanced material fabrication, and water filtration, where its tunability, low achievable shear stresses, and larger aperture size confer significant advantages over alternative, existing technologies. In effect, the MOAT phenomenon can be used to provide a contactless and “filter-free” filtration process.

[0041] All publications, patents, and patent applications mentioned in this specification are herein incorporated by reference to the same extent as if each individual publication, patent, or patent application was specifically and individually indicated to be incorporated by reference. To the extent publications and patents or patent applications incorporated by reference contradict the disclosure contained in the specification, the specification is intended to supersede and / or take precedence over any such contradictory material.

[0042] The details of one or more embodiments of the subject matter of this specification are set forth in the accompanying drawings and the description below. Other features, aspects, and advantages of the subject matter will become apparent from the description, the drawings, and the claims.BRIEF DESCRIPTION OF THE DRAWINGS

[0043] FIGs. 1 A to 1C are schematic diagrams depicting an example of a microfluidic chip.

[0044] FIGs. 2A-1 to 2A-3 are a series of three plots showing the results of a simulation of particle trajectory in oscillatory flow for the microfluidic chip of FIGs. 1A to 1C under average pressures of 5 Pascals (Pa), 10 Pa, and 20 Pa.

[0045] FIGs. 2B-1 to 2B-3 are a series of plots showing results of a simulation of particle trajectory in oscillatory flow for the microfluidic chip of FIGs. 1 A to 1C with a ramping average pressure condition. FIG. 2B-1 shows the flow at the inlet of the microfluidic chip, FIG. 2B-2 shows the flow in the bridging expansion region of the microfluidic chip, and FIG. 2B-3 shows the results at the outlet of the microfluidic chip.

[0046] FIG. 2C shows the average location of one hundred particles over time as they pass through the microfluidic chip during the simulation of particle trajectory in oscillatory flow of FIGs. 2B-1 to 2B-3.

[0047] FIG. 3A is an isometric view of an OpenSCAD model of a 3D-printed microfluidic chip including four pseudo-2D microfluidic devices.

[0048] FIG. 3B is a photograph depicting an isometric view of the 3D-printed microfluidic chip of FIG. 3A.

[0049] FIG. 4A is a schematic diagram depicting an example of a microfluidic system for implementing a microfluidic oscillatory asymmetrical trap (MOAT).

[0050] FIGs. 4B-1 to 4B-4 are a series of images depicting a timelapse of the MOAT phenomena.

[0051] FIGs. 5A-1 to 5A-5 are a series of experimental plots of trapping efficiency of 10 micron, 20 micron, and 40 micron beads at 25 Hertz (Hz), 50 Hz, 75 Hz, 100 Hz, and 125 Hz oscillation frequencies.

[0052] FIGs. 5B-1 to 5B-5 are a series of experimental plots of robustness of 10 micron, 20 micron, and 40 micron beads at 25 Hz, 50 Hz, 75 Hz, 100 Hz, and 125 Hz oscillation frequencies.

[0053] FIGs. 6A-1 to 6A-3 are a series of plots of trapping efficiency dimensional analysis versus particle Reynolds number for 10 micron, 20 micron, and 40 micron beads.

[0054] FIGs. 6B-1 to 6B-3 are a series of plots of trapping efficiency dimensional analysis versus Womersley number squared for 10 micron, 20 micron, and 40 micron beads.

[0055] FIGs. 6C-1 to 6C-3 are a series of plots of robustness dimensional analysis versus particle Reynolds number for 10 micron, 20 micron, and 40 micron beads.

[0056] FIGs. 7A and 7B are a series of timelapse images depicting of HeLa cells trapped in a device as described herein.

[0057] FIG. 7C is a series of timelapse images depicting trapping of 20 micron beads in fluid seeded with 2 micron particles, in a curved microfluidic channel as described herein.

[0058] FIG. 8-1 is a schematic diagram showing an example of a microfluidic structure of a microfluidic chip defined by an array of L-shaped microstructures.

[0059] FIGs. 8-2A to 8-2D are a series of images of experiments on the microfluidic chip of FIG. 8-1.

[0060] FIGs. 8-3 A and 8-3B are a pair of images of experiments on the microfluidic chip of FIG. 8-1 with increasing particle load size.

[0061] FIG. 8-4 is an image of an experiment on the microfluidic chip of FIG. 8-1 for performing stable and effective trapping of CTC cancer cell line (MGH-BRX-142).

[0062] FIG. 9-1 is a schematic diagram showing an example of a microfluidic structure of a microfluidic chip defined by an array of square-shaped microstructures.

[0063] FIGs. 9-2 to 9-5 are a series of images of experiments run on the microfluidic chip shown in FIG. 9-1.

[0064] FIG. 10A is a schematic diagram depicting another example of a microfluidic system for implementing a MOAT.

[0065] FIG. 10B is a schematic diagram depicting an example of an oscillatory system including two speakers.

[0066] FIG. 11 is a schematic diagram depicting an example of a microfluidic system including a fluid oscillator for implementing a MOAT.

[0067] Like reference numbers and designations in the various drawings indicate like elements.DETAILED DESCRIPTION

[0068] In microfluidics, inertial focusing is a phenomenon that manipulates and concentrates particles within microchannels through the application of inertial lift forces, finding utility across diverse technologies, particularly in the biomedical domain. The confined flows involving particles with finite Reynolds numbers give rise to distinctive patterns of lateral focusing andlongitudinal alignment. Inertial focusing was initially observed when particles migrated to an annulus in a pipe under laminar flow conditions, resulting in the tubular pinch effect.

[0069] Inertial focusing in straight channels arises from the interplay of two primary forces: shear gradient lift and wall interaction lift. These forces act perpendicular to the flow direction, causing particles to settle into stable positions within the cross-sectional plane of the channel. Curvature introduces secondary flow and associated drag, pushing particles to new equilibria. These positions are determined by factors such as the particle Reynolds number, channel shape (including curvature), and particle size. Notably, inertial focusing requires significant fluid inertia and strengthens with particle size as described by the particle Reynolds number, itself a product of the channel Reynolds number and square of particle diameter to channel hydraulic diameter.

[0070] A limitation of inertial focusing is the focusing of small particles, particularly at diameters of about one micron and below. These require longer channels leading to higher resistance and higher pressure across the channel, posing feasibility challenges. However, inertial manipulation of such particles is of significant interest. Alternatively, for nucleated cells, inertial focusing often involves supra-physiologic shear stresses, e g., of greater than 5 Pascals (Pa), to reach sufficient focus quality in realistic channel lengths of a few centimeters.

[0071] Oscillatory inertial microfluidics can relieve these challenges by periodically reversing the flow direction, leading to particles being subjected to a quasi-infinite channel. Because inertial lift forces remain uninfluenced by the flow direction, particles converge to the same position regardless of the flow’s orientation if the channel geometry is symmetric to the flow direction (as in straight channels). Extended length of oscillatory flows enables inertial focusing in very low particle Reynolds numbers, e.g., enabling focusing of 500 nanometer (nm) particles and submicron bacteria. In addition, oscillatory flow can enable inertial focusing at lower shear stresses by increasing channel size relative to the particle (or cell).

[0072] As an improvement to oscillatory inertial focusing, oscillatory microflow was investigated with added asymmetry along the channel length. In contrast to constant crosssection channels, where particles must always pass through with even a tiny forward bias flow, strong trapping of particles (including cells) was observed at points of streamwise asymmetry in a diverse array of device geometries, even in the presence of significant forward bias flow rates. In addition to other applications in on-chip particle manipulations, this phenomenon, termed the“microfluidic oscillatory asymmetrical trap” (or “MOAT”) provides contact-free filtration in channels many times larger than required for a mechanical filter (which can anyway pass cells which slowly squeeze through). The MOAT phenomenon’s parameter space is identified from experiments on a simplified pseudo-2D rigid channel, where a height transition along the flow direction is the only asymmetry. This disclosure also provides a theoretical model that combines effects of lift and drag on the particle, phase lag of the fluid to driving pressure, and phase lag of the particle to forward bias flow. A broad array of experimental scenarios where trapping occurs is also catalogued herein, illustrating the widespread presence of MOAT behavior in oscillatory microfluidics, wherever geometrical asymmetry exists along the length of the microfluidic channels.

[0073] These and other features are described in further detail below.

[0074] Examples of Microfluidic Chips and Microfluidic Systems for Implementing MOAT

[0075] FIGs. 1 A to 1C are schematic diagrams depicting an example of a microfluidic chip 100. FIG. 1A is a cross-sectional sideview of the microfluidic chip 100 along a bisecting plane, FIG. IB is a cross-sectional view of the microfluidic chip 100 along Section A-A’, and FIG. 1C is a cross-sectional view of the microfluidic chip 100 along Section B-B’.

[0076] The microfluidic chip 100 is an example of a microfluidic device that is configured to implement a MOAT. Particularly, when a particle-containing fluid exhibits oscillatory flow within a fluidic lumen 130 of the microfluidic chip 100, the particles can be trapped by the combination of oscillatory motion and the asymmetrical geometry of the fluidic lumen 130. Note, the fluidic lumen 130 may also be referred to as a fluidic channel. The generic term “lumen” is used herein to avoid confusion with portions of the fluidic lumen 130 that are also referred to as channels. For example, the fluidic lumen 130 may be referred to as an asymmetrical (micro-)fluidic channel that includes two linear (micro-)fluidic channels 132-1 and 132-2 interposed by a bridging expansion 134.

[0077] In more detail, the microfluidic chip 100 is defined relative a Cartesian coordinate system having three mutually orthogonal directions, including an x-, y-, and z-direction. For example, the z-direction can correspond to a longitudinal (or horizontal) direction, the y-direction can correspond to a transverse (or vertical) direction, and the x-direction can correspond to another transverse (or lateral) direction.

[0078] The microfluidic chip 100 includes a substrate 110 and a superstate 120 disposed thereon. The substrate 110 is generally planar. The substrate 110 can be composed of a material that is transparent (e.g., substantially transparent) to optical wavelengths, e.g., ultraviolet, visible, and / or infrared wavelengths. For example, the substrate 110 can be composed of glass or a polymer. Examples of polymers include, but are not limited to, poly(methyl methacrylate) (PMMA), poly dimethyl siloxane (PDMS), polycarbonate, polyimide, poly vinylidene fluoride (PVDF), poly(ethylene terephthalate) (PET), polypropylene, ethylene tetrafluoroethylene (ETFE), other fluoropolymers, or the like, or any combination thereof. In some implementations, the substrate 110 is a glass slide.

[0079] The substrate 110 has a planar surface 112 that is orthogonal to the y-direction and parallel to the x- and z-directions. The superstrate 120 is disposed on the planar surface 112 of the substrate 110. Together, the superstrate 120 and the planar surface 112 of the substrate 110 define the microfluidic structure 150 of the microfluidic chip 100. Particularly, the features of the superstrate 120 and the planar surface 112 of the substrate 110 define the microfluidic structure 150 of the microfluidic chip 100. Here, the microfluidic structure 150 includes an inlet port 140- 1, an outlet port 140-2, and the fluidic lumen 130 which is connected between the inlet 140-1 and outlet 140-2 ports. As shown, the fluidic lumen 130 extends from the inlet port 140-1 to the outlet port 140-2 in the z-direction. Note, in some implementations, the inlet port 140-1 can be an outlet port and the outlet port 140-2 can be an inlet port, e.g., such that net fluid flow through the microfluidic chip 100 is in a reverse direction.

[0080] The superstrate 120 can be composed of a material that transparent (e.g., substantially transparent) to optical wavelengths. The superstrate 120 can be composed of the same or a different material than the substrate 110. For example, the superstrate 120 can be composed of glass or a polymer, such as any of those listed above for the substrate 110. In some implementations, the superstrate 120 is fabricated via 3D-printing or other additive manufacturing process. For example, the superstrate 120 can be 3D-printed directly on the substrate 110. Alternatively, the superstrate 120 can be 3D-printed and thereafter bonded to substrate 110 with an adhesive. In these implementations, the superstrate 120 can be composed of a resin (e.g., a photopolymer or thermosetting resin) that has been cured (or otherwise hardened) during the 3D-printing process. For example, the superstrate 120 can be composed ofa 3D-printer resin, e g., Generative Resin GR-1, which is curable with ultraviolet light, e g., generated from a laser of a 3D-printer.

[0081] The fluidic lumen 130 includes a first channel 132-1, a second channel 132-2, and a bridging expansion 134 interposed between the first 132-1 and second 132-2 channels. The first 132-1 and second 132-2 channels are parallel and collinear with each other along the z-direction.

[0082] The fluidic lumen 130 extends longitudinally in the z-direction and has a fixed width (w) in the x-direction. The fluidic lumen 130 has a height in the y-direction direction that varies along its length in the z-direction, corresponding to a varying rectangular cross-section of the fluidic lumen 130 in the z-direction. As shown in FIGs. 1 A to 1C, the fluidic lumen 130 is asymmetrical in the z-direction. In other words, the fluidic lumen 130 lacks reflection symmetry with respect to the x-y plane. This may also be stated as lacking inversion symmetry in the z- direction. Conversely, the fluidic lumen 130 has reflection symmetry about the bisection in the z- y plane.

[0083] The first channel 132-1 extends linearly in the z-direction from the inlet port 140-1. The first channel 132-1 has a first length (Z- in the z-direction and has the fixed width in the x- direction. The first channel 132-1 has a first height (Zi- extending in the y-direction from the planar surface 112 of the substrate 110. The first channel 132-1 is a wide channel. In other words, the width of the first channel 132-1 is greater than the first height — > 1. For example, in hi some implementations, the width of the first channel 132-1 can be about 2, 3, 4, 5, 6, 7, 8, 9, 10, 15, 20, 25, or more times greater than the first height.

[0084] The second channel 132-2 extends linearly in the z-direction to the outlet port 140-2. The second channel 132-2 has a second length (Z2) in the z-direction and has the fixed width in the x- direction. The second channel 132-2 has a second height extending in the y- direction from the h planar surface 112 of the substrate 110. The second height is greater than the first height - > 1.For example, the second height can be about 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5 or more times greater than the first height. The second channel 132-2 is also a wide channel. In other words, the width of the second channel 132-2 is greater than the second height 7 > 1. For example, the width of “2 the second channel 132-2 can be about 2, 3, 4, 5, 6, 7, 8, 9, 10, 15, 20, 25, or more times greater than the second height.

[0085] The bridging expansion 134 extends longitudinally in the z-direction to a third length (Z3) and has the fixed width in the x-direction. The total length (Z) of the fluidic lumen 130 is thus the sum of the first, second, and third lengths, I = Zx+ Z2+ Z3. In general, the bridging expansion 134 is the portion of the fluidic lumen 130 responsible for its varying cross-section and corresponds to the “trap” region of the fluidic lumen 130. Particularly, the bridging expansion 134 has a third height (3) that is pitched (or sloped) at an acute angle (0) from the planar surface 112 of the substrate 110. The third height varies, along the length of the bridging expansion 134, between: (i) the first height at an interface with the first channel 132-1, and (ii) the second height at an interface with the second channel 132-2. Hence, the third length can be defined as Z3= cot0 (Zi2— h^. As shown in FIG. 1A, in this implementation, the third height increases from the first height to the second height in multiple discrete steps 136 having increasingly greater heights from the planar surface 112 of the substrate 110. In other implementations, the third height can increase linearly from the first height to the second height at the acute angle, such that3(5) = h±+ tan 6 8, where 8 = [0, Z3] is a coordinate defined along the length of the bridging expansion 134 in the z-direction. More generally, the third height Zt3(<5) can be defined as a function of <5, that satisfies Zi3(0) = h and Zt3(Z3) = h2at the respective interfaces with the first 131-1 and second 132-2 channels. For example, the third height may be a quadratic or other nonlinear function of 8, e.g., corresponding to a curved geometry of the fluidic lumen 130.

[0086] The inlet 140-1 and outlet 140-2 ports are on opposite sides of the fluidic lumen 130, along the z-direction, for providing inflow and outflow of fluid into and out of the fluidic lumen 130. The inlet port 140-1 extends from an exterior surface 122 of the superstrate 120 to the first channel 132-1. The inlet port 140-1 can be used to allow inflow of particle-containing fluid into the fluidic lumen 130. Examples of fluids include, but are not limited to, water, aqueous solutions, organic solvents, biological fluids, cell suspensions, emulsions, ionic liquids, hydrogels, ferrofluids, colloidal suspensions, electrolyte solutions, or the like, or any combination thereof. Examples of particles include, but are not limited to, plastic beads, white blood cells, red blood cells, HeLa cells, other types of cells, or the like, or any combination thereof. The outlet port 140-2 extends from the exterior surface 122 of the superstrate 120 to the second channel 132-2. The outlet port 140-2 can be used to allow outflow of fluid out of the fluidic lumen 130. In general, the fluidic lumen 130 is configured to selectively direct fluid fromthe inlet port 140-1 to the outlet port 140-2 while trapping particles contained in the fluid between the inlet 140-1 and outlet 140-2 ports. Particularly, the fluidic lumen 130 traps the particles when the fluid experiences oscillatory motion in the y-direction, as well as a net flow rate (Q) in the y-direction from the inlet port 140-1 to the outlet port 140-2, e.g., due to a pressure gradient between the inlet 140-1 and outlet 140-2 ports or an applied force on the fluid.

[0087] As shown in FIGs. 1 A to 1C, in this implementation, the exterior surface 122 of the superstate 120 is parallel to the planar surface 112 of the substrate 110, such that the inlet 140-1 and outlet 140-2 ports extend linearly in the y-direction and interface with the first 132-1 and second 132-2 channels at the base of the fluidic lumen 130. However, in other implementations, the exterior surface 122 of the superstate 120 can be a lateral surface that is orthogonal to the planar surface 112 of the substrate 110. In these cases, the inlet 140-1 and outlet 140-2 ports may extend linearly in the z-direction from the exterior surface 122 of the superstate 120 to the first 132-1 and second 132-2 channels. Alternatively, the inlet 140-1 and outlet 140-2 ports may follow an L-shaped (or other curved-shaped) path in the z-y plane from the exterior surface 122 of the superstate 120 to the first 132-1 and second 132-2 channels. In some implementations, the inlet port 140-1 is a first inlet port and the microfluidic chip 100 further includes a second inlet port extending from the exterior surface 122 of the superstate 120 to the first channel 132-1. The second inlet port can be used to allow inflow of fluid, e.g., buffer fluid, significantly devoid of particles into the fluidic lumen 130.

[0088] Implementations of the microfluidic chip 100 for performing MOAT can be used for various microfluidic applications including, but not limited to, timed filtration and release, micro-scale suspension culturing, size fractionation, particle metering, and density-based separation. This specification also provides general methodological principles for implementing MOAT in microfluidic systems, as well as possible physical explanations of the phenomenon, which are described in detail below.

[0089] Particularly, when a purely oscillatory flow is added to a steady fluid flow in one direction of similar or lesser magnitude, suspended particles become trapped at points where the channel geometry changes, e.g., in the bridging expansion 134, despite not touching the walls. A microfluidic chip, e.g., the microfluidic chip 100, for particle trapping is described by a combination of specific geometric, material, and flow parameters, as described above with reference to FIGs. 1 A to 1C.

[0090] In some cases, there can be one primary and one secondary physical mechanism responsible for the simplest forms of particle trapping. First, and primary, as the flow is made to accelerate, decelerate, or change direction, suspended particles take a finite amount of time to respond to the new velocity of the fluid at their location. This lag manifests as particle acceleration (or deceleration), and it can be approximated by equating the Stokes drag on a sphere, 67r / zr(Vy - Vp) to particle mass, pp(4n / 3)r3, times acceleration, a, where p is fluid dynamic viscosity, r is particle radius, ppis particle mass density, Vpis the particle velocity, and Vf is the fluid velocity in the absence of the particle, each at a particular location and time. Rearranging, the particle acceleration is, a = [9^ / (2ppr2)](Vy - Vp), noting that a and V are vectors.

[0091] The fact there is a net flow rate means that the fluid is not retained within the same location of geometrical change as are the particles. In contrast, particles can remain in the “trap”, e.g., the bridging expansion 134, if they lag the fluid more in the upstream direction than in the downstream direction, integrated through a full oscillation, and the upstream migration relative to the fluid must overcomes the net downstream migration. MOAT can occur strongly in simple channel expansions, but also in channel contractions, owing to the complexity in the actual path taken by particles, which can include multiple directional changes. Since this effect can disappear in the unchanging sections of channel, e.g., the first 132-1 and / or second 132-2 channels, particles either persist in the trap or pass by if the net migration upstream cannot overcome the net fluid motion downstream.

[0092] Superimposed upon this effect of particle inertia on lag to the fluid flow is that of particle migration due to inertial focusing. Inertial focusing has the effect to move particles toward preferred streamlines which can differ before and after the trap region due to the change in channel geometry. Particle migration due to inertial focusing can eliminate a large majority of accessible streamlines for a particle in the trap, any of which may be effective at net migration upstream in the flow. Even when particles become stably trapped, inertial focusing can cause cross-stream migration towards the preferred focusing streamlines all along the changing channel geometry at the trap. This can push the particles further downstream or upstream as a result according to the detailed path taken by a given particle.

[0093] To summarize, particles are trapped in a region with a net forward flow rate and no physical barrier to prevent the particles from moving forward, referred to as the MOAT phenomenon, e.g., behaving like a contactless filter.

[0094] FIGs. 2A-1, 2A-2, and 2A-3 are a series of three plots showing the results of a simulation of particle trajectory in oscillatory flow for the microfluidic chip 100 of FIGs. 1A to 1C under average pressures of 5 Pascals (Pa), 10 Pa, and 20 Pa, respectively. FIGs. 2A-1 to 2A-3 show an overlay of the trajectories of one hundred particles over 0.8 seconds. In addition to a constant pressure of Pavg, the inlet pressure includes a sine wave component with 75 Hz frequency and 800 Pa magnitude.

[0095] FIGs. 2B-1 to 2B-3 are a series of plots showing results of a simulation of particle trajectory in oscillatory flow for the microfluidic chip 100 of FIGs. 1A to 1C with a ramping average pressure condition. FIG. 2B-1 shows the flow at the inlet 140-1 of the microfluidic chip 100, FIG. 2B-2 shows the flow in the bridging expansion 134 of the microfluidic chip 100, and FIG. 2B-3 shows the results at the outlet 140-2 of the microfluidic chip 100. FIGs. 2B-1 to 2B-3 show trajectories of two individual particles in the ramping Pavg condition. Pavg is 5 Pa in the first second to trap the particles in the expansion region, then increased over time until particles leave the trapping area, simulating particle retention experiments.

[0096] FIG. 2C shows the average location of one hundred particles over time as they pass through the microfluidic chip during the simulation of particle trajectory in oscillatory flow of FIGs. 2B-1 to 2B-3.

[0097] COMSOL 6.2 by COMSOL Inc. was used to simulate the particle trajectory in oscillatory flow conditions and generate the plots in FIGs. 2A-1 to 2A-3, 2B-1 to 2B-3, and 2C.Specifically, laminar flow and particle tracing for fluid flow modules were used in a 2D domain. Given the low particle concentration, one-way coupling was applied between the fluid and particle motion. For laminar flow, the inlet pressure was set to the sum of a sine wave (i.e., the oscillatory flow with the magnitude of 800 Pa and frequency of 75 Hz), and a constant pressure value (i.e., the forward net flow). To investigate the impact of forward net flow on trapping efficiency, different conditions of constant pressure were tested, including 5, 10, and 20 Pa. To investigate particle retention, a pressure ramp from 5 Pa to 60 Pa was also tested. In all cases, the outlet pressure was set to 0 Pa. Water was used as the fluid, with viscosity of 1.3 mPa-s to account for inclusion of Optiprep™ (a density gradient medium) used in the experimentsdescribed below. Tn the particle tracing module, particle size was set to 20 pm, and density was set to 1000 kg / m3 to match the fluid. The Stoke’s drag force and wall induced lift force were applied to the particles with built-in functions. The physics-controlled mesh was used.

[0098] Considering the high aspect ratio of the fluidic lumen 130, the simulation was performed in 2D cross-section, allowing symmetry about the z-y plane to simplify the problem. Here, the geometry of the fluidic lumen 130 was composed of three regions including (i) the first channel 132-1 with 100 pm height and 1800 pm length to inertially focus the particles, (ii) the bridging expansion 134 with a length of 480 pm, and (iii) the second channel 132-2 with 200 pm height and 1400 pm length. As shown in FIGs. 2A-1 to 2A-3, the particles were successfully trapped for Pavg of 5 and 10 Pa, but were not trapped for 20 Pa, indicating decreasing trapping efficiency at increasing net flow rate (as shown in FIGs. 5A-1 to 5A-5). In addition, when particles were trapped, the time-dependent trajectories converged and suggested two equilibrium paths close to the top and bottom of the fluidic lumen 130.

[0099] The condition with ramping net flow rate was also simulated, similar to the experiments reported in FIGs. 5B-1 to 5B-5. Pavg was set to 5 Pa to first trap the particles and then increased gradually to test whether the particles remain trapped at increasing net flow rate. Within the different regions of the fluidic lumen 130, FIGs. 2B-1 to 2B-3 show the trajectory of two individual particles, color-coded with the Pavg values to visualize the ramp. In the expansion region, the particles remained trapped when Pavg was below about 30 Pa (i.e., the blue areas in FIGs. 2B-1 to 2B-3), then drifted towards the wall and left the trapping area at increasing Pavg. The averaged location of one hundred particles in FIG. 2C also signals successful trapping with Pavg up to about 30 Pa. Although the particles were not trapped with a constant Pavg in the range of 20-30 Pa (see FIGs. 2A- 1 to 2A-3), the simulation indicated that the ramping Pavg strategy can extend particle trapping to higher net flow rate, similar to observations recorded in FIGs. 5B-1 to 5B-5.

[0100] FIG. 3 A is an isometric view of an OpenSCAD model of a microfluidic chip 101 including four pseudo-2D microfluidic chips (or devices) 100-1, 100-2, 100-3, and 100-4 each configured according to FIGs. 1 A to 1C. FIG. 3B is a photograph depicting an isometric view of the microfluidic chip 101 fabricated via 3D-printing. Here, the microfluid chips 100-1 to 100-4 have a common superstrate 120 that, in combination, with a planar surface 112 of a commonsubstrate 110 (e g., a glass slide) defines a respective fluidic lumen 130-1 to 130-4 for each microfluidic chip 100-1 to 100-4.

[0101] In the experiments described below (see Examples 1A to ID), selected microfluidic chips 100 were 3D-printed using a Asiga® Max X27 printer and Generative Resin GR-1. This printer’s fine lateral (xy) resolution (27 pm) and thin (10 pm) slice thickness enabled accurate microchannel printing. The pseudo-2D microfluidic chip 100 contained two wide channels 132-1 and 132-2 with a bridging expansion 134 in the z-axis. The first, upstream channel 132-1 had a length of 2 cm, a width of 4 mm, and a height of 100 pm. The second, downstream channel 132- 2 had a length of 2 cm, a width of 4 mm, and a height of 200 pm. The bridging expansion 134 had a length of 400 pm that transitioned between the heights of the first 132-1 and second 132-2 channels in 10 slice steps, corresponding to the 10 pm slice thickness of the printer. The geometry of the pseudo-2D microfluidic chips 100 is shown in FIGs. 3A and 3B. Due to the 40: 1 and 20: 1 width-to-heigh aspect ratios of the first 132-1 channel and second 132-2 channels, respectively, the overall device effectively mimicked the geometry of infinite parallel plates, allowing a simplification of the physics into a 2D problem.

[0102] To complete the microfluidic chip 100 and geometry of the fluidic lumen 130, the 3D- printed superstate 120 was bonded to a 3 : 1 glass slide 110. As the glass slide 110 was not suitable by itself, a thin coating of uncured resin was applied to the glass slide 110 prior to bonding with the superstate 120. Because the resin was viscous, this process involved dissolving Generative Resin GR-1 in isopropyl alcohol (IP A) at a resin-to-IPA ratio of 1 :6, then applying the coating to an empty petri dish lid. After about 40% of the IPA had evaporated, the glass slide 110 was pressed into the resin and quickly removed, leaving a thin coating of resin on the glass slide 110. Subsequently, the glass slide 110 was placed in a dark environment to prevent resin curing while the remaining IPA evaporated from the coating. Finally, the superstate 120 was positioned on top of the glass slide 110, clamped, and subjected to ultraviolet post curing from all sides.

[0103] FIG. 4A is a schematic diagram depicting an example of a microfluidic system 10 for implementing MOAT. The microfluidic system 10 includes a microfluidic chip 100, an inlet tube 230-1 connected to the inlet port 140-1 of the microfluidic chip 100, an outlet tube 230-2 connected to the outlet port 140-2 of the microfluidic chip 100, and an oscillatory system 200 mechanically coupled to the inlet tube 230-1. A microscope objective 240 is placed beneath themicrofluidic chip 100 for imaging of particle-containing fluid flowing therein. The microscope objective 240 has an optical axis 242 parallel to the y-axis and intersecting the substrate 110 of the microfluidic chip 100. Here, the substrate 110 can be transparent.

[0104] The inlet tube 230-1 is connected to a supply reservoir 234-1 that holds particlecontaining fluid that is injected into the inlet port 140-1 of the microfluidic chip 100. The outlet tube 230-2 is connected to a waste reservoir 234-2 to collect fluid ejected from the outlet port 140-2 of the microfluidic 100. The difference in height (H) between the supply 234-1 and waste 234-2 reservoirs establishes a pressure difference Ap = pgH on the fluid between the input and output of the microfluidic system 10, where p is the density of the fluid and g is the gravitational constant. The pressure difference generates a net flow rate (Q = p / R) through the microfluidic system 10, where R = 8pL / (nr3) is the total fluidic resistance of the tubing 230, p is dynamic viscosity of the fluid, L is the total length of the tubing 230, and r is the radius of the tubing 230. Note, while hydrostatics is employed for this implementation of the microfluidic system 10, in other implementations, the supply reservoir 234-1 can be replaced with a syringe pump (or other source of pressure or flow) to generate the net flow in a controllable manner.

[0105] The oscillatory system 200 is configured to impart oscillations on the inlet tube 230-1 to generate oscillatory flow within the microfluidic chip 100. In general, an oscillatory system is a system that exhibits repetitive patterns of activity. Examples of oscillatory systems include, but are not limited to, audio systems, mechanical resonators, cantilever beams, rotating machinery, among others. In this example, the oscillatory system 200 includes a speaker 210, a 3D-printed structure (or column) 220, and two posts 222-1 and 222-2. The speaker 210 has a speaker spider 212. The 3D-printed structure 220 is attached to the speaker coil which in turn is connected to the speaker spider 212. A portion of the inlet tube 230-1 is attached to the 3D-printed structure 220. The speaker coil oscillates which then drags the speaker spider 212 and 3D-printed structure 220 along with it. This imparts oscillations to the 3D-printed structure 220 and thereby the inlettube 230-1. These oscillations manifest as an oscillation pressure posc— paL on the fluid which generates oscillatory flow in the fluid. Here, a is the oscillatory acceleration of the inlet tube 230-1 that is imparted to the fluid flowing within the microfluidic system 10. To stabilize the microfluidic system 10 under such oscillations, the inlet tube 230-1 is further secured to the posts 222-1 and 222-2 via respective tubing fasteners 224-1 and 224-2. A controller 211 provides automated control of the speaker 210 to generate oscillations with a particular, specifiedfrequency. The controller 211 has a headphone jack 214 that is connected to the speaker 210 via an amplifier 216.

[0106] Additional Examples of Microfluidic Chips and Microfluidic Systems for Implementing MOAT

[0107] In addition to single channel features of expansion (or bifurcation), contraction (or joining), and curvature, these can be combined to generate improved devices, and these can be arrayed in parallel and in series. When considering how to arrange the repeating features into an array, one can consider that additional devices in parallel will increase the trapping capacity of a microfluidic chip 100 proportionally, while also reducing the effective fluid resistance. These are both helpful to performance, but lead to larger devices. On the other hand, putting more MOAT devices in series will again lead to higher trap capacity, but they also improve the yield of trapping, guarding against any small fluctuations that may jostle one particle to the next traps in series. Besides again increasing the size of the microfluidic chip 100, the resistance will instead increase, leading to lower achievable oscillatory pressure gradient amplitudes and also a lower cutoff frequency for passing the oscillations through the microfluidic chip 100 (owing to fluidic compliances). The cutoff frequency can be increased with making the microfluidic chip 100 and any connected tubing 230 more rigid, but the peak oscillation amplitudes will still fall even below the cutoff frequency. So, MOAT devices in an array format should, in general, have maximum parallelization with just enough trap features in series to ensure secure trapping. This leads to a design with branching inlet microchannels or a simple expansion to feed fluid in parallel to a wide area of trapping features in a standard 2D device.

[0108] Moving to 3D examples, arrays can be stacked to further increase capacity and reduce overall fluidic resistance. However, it ceases to become possible to see all the trapped cells, yet this can be the best format for a fully optimized device, e.g., for contactless filtering, because parallelization into multiple layers carries fewer challenges in spreading the flow laterally, and it in principle enables 10-100 fold increases in capacity without greatly increasing the overall size. For example, packed particle beds in this sense are a very attractive configuration for trapping, being comprised of many parallel paths with asymmetries between spheres. This can be an important practical implementation due to the ease of manufacture and parallelization. Particle size can be precisely chosen as can the area and depth of the packed bed MOAT device.

[0109] FIG. 8-1 is a schematic diagram showing an example of a microfluidic structure 150 of a microfluidic chip 100 defined by an array of L-shaped microstructures 158. Particularly, FIG. 8- 1 shows a cross-section of the microfluidic chip 100 in the x-z plane. Similar to the microfluidic chip 100 of FIGs. 1A to 1C, the microfluidic structure 150 is defined by the superstrate 120 and the planar surface 112 of the substrate 110, that is, is the structure of the microfluidic chip 100 that conducts a fluid.

[0110] As shown in FIG. 8-1, the microfluidic structure 150 includes an inlet port 140-1, an outlet port 140-2, and a channel extending from the inlet port 140-1 to the outlet port 140-2 in the z-direction. As shown, the channel includes a dense network of coplanar microchannels connected between the inlet port 140-1 and the outlet port 140-2. Particularly, the network of coplanar microchannels expands longitudinally in the z-direction from the inlet port 140-1 and contracts longitudinally in the z-direction at the outlet port 140-2. The microfluidic structure 150 is asymmetrical in the z-direction. In other words, the microfluidic structure 150 lacks reflection symmetry with respect to the x-y plane. This may also be stated as lacking inversion symmetry in the z-direction.[OHl] Here, the network of coplanar microchannels includes a subnetwork 152-1 of inlet microchannels 153-1, a subnetwork 152-2 of outlet microchannels 153-2, and a subnetwork 156 of intermediate microchannels 157 connected between the subnetwork 152-1 of inlet microchannels 153-1 and the subnetwork 152-2 of outlet microchannels 153-2. As shown, the subnetwork 156 of intermediate microchannels 157 has a higher density of channels than the subnetwork 152-1 of inlet microchannels 153-1 and the subnetwork 152-2 of outlet microchannels 153-2.

[0112] The subnetwork 152-1 of inlet microchannels 153-1 expands longitudinally in the z- direction from the inlet port 140-1. The subnetwork 152-1 of inlet microchannels 153-1 is defined by multiple first (e.g., inlet) structures 154-1 of the superstrate 120 that extend linearly to the planar surface 112 in the y-direction. Particularly, the subnetwork 152-1 of inlet microchannels 153-1 has an expanding (or diverging) tree topology that, from left to right in FIG. 8-1, starts from the inlet port 140-1 and ends with connections to the subnetwork 156 of intermediate microchannels 157.

[0113] In a similar, but opposite sense, the subnetwork 152-2 of outlet microchannels 153-2 contracts longitudinally in the z-direction to the outlet port 140-2. The subnetwork 152-2 ofoutlet microchannels 153-2 is defined by multiple second (e.g., outlet) structures 154-2 of the superstate 120 that extend linearly to the planar surface 112 in the y-direction. Particularly, the subnetwork 152-2 of outlet microchannels 153-2 has a contracting (or converging) tree topology that that, from left to right in FIG. 8-1, starts from connections to the subnetwork 156 of intermediate microchannels 157 and ends at the outlet port 140-2. Here, subnetwork 152-2 of outlet microchannels 153-2 has a higher density of channels than the subnetwork 152-1 of inlet microchannels 153-1. However, in other implementations, they may have the same density, e.g., being mirror images of each other, or the subnetwork 152-1 of inlet microchannels 153-1 may have higher density.

[0114] The subnetwork 156 of intermediate microchannels 157 is defined by the array of L- shaped microstructures 158. The L-shaped microstructures 158 correspond to structures of the superstate 120 that extend linearly to the planar surface 112 in the y-direction. Particularly, each of the microstructures 158 has an L-shaped cross-section parallel to the planar surface 112 of the substrate 110. The L-shaped microstructures 158 define a dense network of interconnected, asymmetric microchannels 157 in the microfluidic structure 150. The array of microstructure 158 are regular (or periodic) in the z-direction, meaning that the array repeats itself after a certain interval in the z-direction. Particularly, a unit cell of the array (boxed region in the inset of FIG. 8-1), repeats itself at each interval in the z-direction. Here, the unit cell also repeats itself in the x-direction for a certain number of intervals. As shown, the unit cell includes two pairs of opposing L-shaped microstructures 158-1 and 158-2. A trapping region 159 between the two opposing L-shaped microstructures 158 is designed specially to trap cells owing to its high degree of asymmetry (expansi on / contracti on). For example, due to the asymmetric geometry of the L-shaped microstructures 158, the unit cell lacks inversion symmetry along the z-direction.

[0115] FIG. 9-1 is a schematic diagram showing an example of a microfluidic structure 150 of a microfluidic chip 100 defined by an array of square-shaped microstructures 158. The microfluidic structure 150 of FIG. 9-1 is configured similarly the microfluidic structure 150 of FIG. 8-1 except the array of L-shaped microstructures 158 has been substituted with the array of square-shaped microstructures 158. Particularly, each of the microstructures 158 has a squareshaped cross-section parallel to the planar surface 112 of the substrate 110. In this example, the square-shaped microstructures 158 define a dense network of interconnected, symmetric microchannels 157 in the microfluidic structure 150. As shown, the unit cell includes one square-shaped microstructure 158 and is symmetrical in the z-direction. Here, the asymmetry between the subnetwork 152-1 of inlet microchannels 153-1 and the subnetwork 152-2 of outlet microchannels 153-2 provides the asymmetry of the microfluidic structure 150 in the z-direction.

[0116] FIG. 10A is a schematic diagram depicting yet another example of a microfluidic system 10 for implementing a MOAT. The microfluidic system 10 is configured similarly to the microfluidic system 10 of FIG. 4A except the oscillatory system 200 is mechanically coupled to the outlet tube 230-2 and the posts 222-1 and 222-2 are omitted. Instead, a portion of the outlet tube 230-2 is attached to the 3D-princted structure 220 via tubing fasteners 225-1 and 225-2. Here as well, hydrostatics can apply constant pressure to control net flow rate according to Ohm’s law even in the presence of speaker-induced oscillations and a slowly draining medium bottle at the inlet. This is controlled by overall fluidic resistance and liquid height.

[0117] In general, a steady flow rate can be controlled by volumetric displacement at the inlet port 140-1 (e.g., infusion) or even at the outlet port 140-2 (e.g., withdraw mode on a syringe pump). It can also be controlled by adjusting the pressure between the inlet 140-1 and outlet 140- 2 ports, e.g., using a pressure source. However, these approaches come with added complexity of the microfluidic system 10 and significant trapped (dead) volumes of liquid that limit the minimum sample volume to be processed to several hundred microliters or more. Syringe pumps also introduce ripples to flow rate which can dislodge trapped cells and particles when too sharp.

[0118] As an alternative, steady flow can be controlled more simply and smoothly by gravity acting on a height of liquid (e.g., hydrostatics). Here, the steady flow rate can be determined according to the fluidic equivalent of Ohm’s law, where the pressure drop along the entire fluid path must be equal to the steady flow rate multiplied by the total fluidic resistance, itself equal to R = Q1L / (TIT3') . Using a short length of inlet tubing 230-1 at the inlet port 240-1 of the microfluidic chip 100, held a short distance above the distal end of the outlet tubing 230-2 drip, particles or cells can be loaded from a few microliters simply by dipping the tubing into the suspension or connecting a pipette tip loaded with sample, as in FIG. 10A as well as in FIG. 4A. This can be quickly alternated from one liquid to another by transferring the inlet tubing 230-1 from one supply reservoir 234-1 to another in quick succession.

[0119] To control the flow rate in this configuration, a tubing resistance 227 is preferentially placed downstream of the oscillatory system 200, and upstream of the outlet tubing 230-2 drip point (see FIG. 10A). This resistance may be the primary resistance in the microfluidic system10. The height difference driving flow rate is then the height between the atmospheric air pressure contact at the inlet of the supply reservoir 234-1 to the liquid on one side, to the drip out point at the very end of the outlet of the outlet tubing 230-2. Placing the tubing resistance 227 downstream of the oscillatory system 200 ensures that oscillatory pressures propagate unimpeded in the upstream direction, toward the microfluidic chip 100. These oscillations can be partly damped at the outlet tubing 230-2 drip point, but this has no effect on the functionality of the microfluidic chip 100 as intended since oscillations do proceed within the primary sections of the chip 100. This is the preferred mode of operation when the microfluidic chip 100 is used for initial cell or particle loading to the trapping structures therein, washing and in general applying one liquid after another through the low dead volume inlet path. In general, the liquid exiting the outlet drip is considered waste. When the cells are to be extracted, the outlet drip can be raised above the inlet tubing 230-1 such that net flow pushes cells backwards, and the oscillations are turned off to enable cells or particles to be removed from the inlet tubing 230-1. This backflow can also be done when switching from one liquid to another to avoid introduction of air bubbles to the tubing 230-1 and 230-2.

[0120] When applied to cell culture, there is a need to load a large volume of cell culture medium to the inlet of the supply reservoir 234-1 and let the microfluidic system 10 continuously feed it at a slow rate to the trapped cells in the chip 100. However, as the cell culture medium depletes, the meniscus where air meets medium falls, leading to a reduced head height of liquid (and pressure) driving the flow to a lower speed over the course of culture. To mitigate this, one can use a Mariotte’s bottle, an invention from the 1600’s. This again uses hydrostatics principles, but in such a manner that the flow rate does not change over time. It is set up in a sealed bottle of culture medium which has one tubing connected to the inlet port 140-1 of the microfluidic chip 100 (either at the bottom of a syringe or as a dip tube that exits through the bottle’s cap). What is then needed is an additional connection from a submerged point in the bottle’s liquid out to a controlled gas pressure (e.g. room air). Thus, the pressure at the air interface at the bottom of the air tubing inside the bottle will always be the atmospheric pressure. The pressure from that point to the outlet tubing 230-2 drip point will not change as the medium surface falls during culture. Rather, the gas pressure within the top of the medium bottle will continuously increase to account for the changing height of liquid above the air contact tubing point. To refill the bottle, it is only necessary to clamp the inlet tubing 230-1 to the chip 100, open the bottle and refill withbuffer, close the bottle and unclamp the inlet tubing 230-1 . Tn this manner, cells can be held in culture for a long time under gentle (e.g. <5 Pa wall shear stress) flow conditions at or below 10 microliters net flow per minute medium consumption.

[0121] In cell culture in particular, bubbles can be a challenge owing to the long-term experiment. So, medium should be degassed to remove dissolved air. In addition, medium should be warmed to the desired temperature for incubation, to prevent medium from dissolving more air at room temperature, then releasing it later at body temperature (cold liquids hold more air).

[0122] FIG. 1 OB is a schematic diagram depicting an example of an oscillatory system 200 including a frame 202, two speakers 210-1 and 210-2, and two 3D-printed structures 220-1 and 220-2. Here, a portion of the inlet tube 230-1 is connected to the first 3D-printed structure 220-1 via tubing fasteners 225-1 and 225-2, and a portion of the outlet tube 230-2 is connected to the second 3D-printed structure 220-2 via tubing fasteners 225-3 and 225-4. The first 220-1 and second 220-2 3D-printed structures and are attached to the first 210-1 and second 210-2 speakers, respectively. Although not show, the microfluidic chip 100 is arranged between the two 3D-printed structures 220-1 and 220-2.

[0123] By connecting the two speakers 210-1 and 210-2 in opposite directions, vibrations of the microfluidic chip 100 are canceled, and oscillatory pressures are doubled. Note that the tubing 230 arrows indicate net flow direction when operating from the inlet port 140-1 of the chip 100 to the outlet of the outlet tubing 230-2. Tubing oscillations are 180 degrees out of phase between red and blue double arrows attached to speaker coil towers. The frame 202 provides structural stability for the oscillatory system 200 to sit on its side, e.g., on a substrate. Speakers 210-1 and 210-2 can receive identical driving waveforms.

[0124] Here the oscillatory flow rate is generated by applying an oscillatory voltage to power a common 8 Ohm speaker coil, driving the speakers 210-1 and 210-2 to oscillate at a controllable frequency in the audible range and a peak displacement amplitude of up to ~10 mm according to its maximum travel distance. By attaching a length of tubing 230 to the speaker coil’s axis of motion, via an attached 3D-printed structure 220, the acceleration of the speaker 210 creates an identical acceleration of the attached fluid column. This creates an oscillatory pressure magnitude equal to the product of fluid density, coil acceleration, and tubing length being oscillated along the coil displacement axis. The speaker cone can be removed to avoid excessivenonproductive noise during coil oscillations, and a 3D-printed structure 220 can been glued, e.g., using a two-part epoxy adhesive, to the moving coil (an isolated solenoid coil can also be used).

[0125] One challenge with using speakers 210 to generate oscillatory flow control is that the oscillations generate significant vibrations due to the inertia of the coil, 3D-printed structure 220 and attached tubing 230. This can be nearly eliminated by using two similar speakers 210-1 and 210-2 with their oscillations exactly canceling in direction. When oriented parallel to the supporting surface, the combined body thus has zero net acceleration and completely avoids vibrations as it sits on a surface. Additionally, by passing the attached tubing 230 in one direction on the first 3D-printed structure 220-1, then back in the opposite direction on the second 3D- printed structure 220-2, the applied oscillatory pressure magnitude is doubled. Tubing 230 can also perform several such loops, gaining additional increments of oscillatory pressure magnitude only at the cost of additional tubing length, but since that is on the outlet side, it has little functional detriment. Note that the speakers 210-1 and 210-2 can be connected to the same signal, with their direction of acceleration reversed simply by having them face one another as in FIG. 10B, e.g., with a slight lateral offset to make way for the 3D-printed structures 220-1 and 220-2.

[0126] FIG. 11 is a schematic diagram depicting another example of a microfluidic system 10 for implementing a MOAT. The microfluidic system 10 includes a fluid oscillator for alternating a direction of flow of a particle-containing fluid flowing through a microfluidic structure 150; and a controller 211 that transmits control signals to the fluid oscillator to control the flow of the fluid through the microfluidic structure 150. Details of the fluid oscillator is described in U.S. Patent No. 11,474,023 B2 which is incorporated herein by reference in its entirety. Note, the microfluidic structure 150 can be any of the asymmetrical microfluidic structures 150 described herein, such as those depicted in in FIGs. 1A to 1C, FIG. 8-1, or FIG. 9-1.

[0127] More generally, the microfluidic structure 150 can be any microfluidic structure that is configured to conduct a fluid from an inlet port 140-1 to an outlet port 140-2 along a longitudinal axis, while being asymmetric along the longitudinal axis. For example, the microfluidic structure 150 can be a channel including an expansion, contraction, or both along the longitudinal axis. Alternatively, the microfluidic structure 150 can be a curved channel having a curved longitudinal axis and a constant-cross section along the longitudinal axis.

[0128] In general, the controller 211 is configured to transmit control signals to the fluid oscillator to control the flow of the fluid in the microfluidic structure 150 to be in a first direction at a set flow rate, to change the first direction of flow to a second direction of flow opposite to the first direction of flow and at a set flow rate, and to oscillate the direction of flow between the first direction of flow and the second direction of flow at a set frequency and for a set period of time, thereby trapping the particles within one or more zones within the fluid flowing within the microfluidic structure 150. The net flow in the microfluidic structure 150 is adjusted by the duty cycle of the control signals, where 50% corresponds to zero net flow, and any bias towards 0% or 100% duty cycle correspond to a net flow in either direction. As shown in FIG. 11, in this example, the duty cycle is set to 75% to provide a net flow in one direction.

[0129] In some examples, the microfluidic system 10 can include a pressure source, such as a pump, which can be a constant or varying pressure source, and a signal (pulse) generator, a valve driving circuit, and two high-speed valves, such as three-way valves. As shown in FIG. 11, a constant pressure source, e.g., 0-25 psi, can be connected to 3 -way valves at opposite ends of the microfluidic structure 150, e.g., made of polydimethylsiloxane (PDMS) or other plastics, metal, ceramic, or glass. The fluid and travels through conduits to and from the microfluidic structure 150 through plastic tubing, e.g., a flexible polymer tubing, e.g., Tygon®. The pulse generator, e.g., 1 to 20 Hz, controls the valves via valve control 1 and valve control 2 according to the source signal (valve 1) or inverted signal (valve 2) to provide the oscillatory flow within the microfluidic channel. Output and / or waste of the microfluidic system 10 (sink) is not pressurized in the depicted configuration, but can be if desired. Imaging is performed in the imaging area shown in FIG. 11.

[0130] Integration into Other Devices

[0131] The MOAT devices can be operated with very low fluidic resistance, where the largest resistance by far is the tubing near the outlet, designed simply to slow the flow according to the head height of liquid to generate hydrostatic pressure. Besides the practical advantages of safety, simplicity and response time, low resistance means it can be attached to many other fluidic devices without affecting their internal flows, at least beyond a small entrance section of the other chip. For example, the CTC iChip can have its ~ 100 microliter / minute product flow directly connected to a MOAT cell trap. This enables the concentration of rare circulating tumorcells (CTCs) from the ~3 mL of product to only about 20 microliters, which is over a 100-fold concentration. Versions of the CTC iChip are described in Fachin F, et al. “Monolithic Chip for High-throughput Blood Cell Depletion to Sort Rare Circulating Tumor Cells,” Set Rep. (2017) Sep 7;7(1): 10936 and Edd JF, et al. “Isolation of circulating tumor cells,” iScience (2022) Jul 1;25(8): 104696.

[0132] Even simpler, the product of the CTC iChip (or another microfluidic chip) may be dripped directly into a pipette tip (or other reservoir) at the inlet of a MOAT chip as described herein. This also makes multiple steps of washing and liquid changes as simple as pipetting each liquid onto the inlet of the MOAT chip in sequence at the appropriate times. Alternatively, inlet tubing can be used as described earlier to pick liquid from one reservoir at a time, relying on the outlet drip height, tubing resistor on the outlet, and speaker to generate the MOAT behavior. More generally, the MOAT device can be connected to a steady flow cell concentrator, or indeed any other device that provides via drip a number of cells to be trapped below the capacity of the particular MOAT device.EXAMPLES

[0133] The following examples illustrate, but do not limit, the disclosures herein.

[0134] Example 1A -Testing of a Microfluidic System

[0135] To conduct experiments and explore the parameter space associated with the MOAT phenomenon, the microfluidic chip 100 of FIGs. 1A to 1C and the microfluidic system 10 of FIG. 4A were utilized, but with a syringe pump replacing the supply reservoir 234. The tubes 230-1 and 230-2 were affixed to the posts 222-1 and 222-2 to restrict the vibrations to the segment of tubing on the 3D-printed structure 220 of the microfl ui die system 10, and tubing length was minimized to avoid damping of the generated pressure waves between the oscillating 3D-printed structure 220 atop the speaker 210 and the microfluidic chip 100’s inlet port 140-1. This allowed the inlet tube 230-1 to connect to the syringe pump on one side of the oscillatory system 200, and to the inlet port 140-1 of the microfluidic chip 100 on the other side, in a static and un-oscillating fashion while still transmitting the oscillatory pressure waves. Except for the 3D-printed structure 220, speaker spider 212, and the portion of the inlet tube 230-1 attached to the 3D-printed structure 220, the entire setup remained static. The speaker 210 was driven by theheadphone jack 214, via the amplifier 216, enabling automated control of the speaker 210’s behavior using scripts from MATLAB by The MathWorks, Inc. to regulate the frequency of the oscillations and the time-averaged oscillatory velocity magnitude (F- of the particles.Automated control of the syringe pump was achieved using similar MATLAB scripting methods.

[0136] A 3D-printed microfluidic chip 101, as shown in FIGs. 3A and 3B, was designed to accommodate four microfluidic devices 100-1, 100-2, 100-3, and 100-4 per chip 101. Depending on the specific experiment, these devices 100-1 to 100-4 were designed with either one or two inlet ports 140-1. When two inlets 140-1 were involved, both inlet tubes 230-1 followed the same path and were affixed at the same locations on the posts 222-1 and 222-2 and the 3D- printed structure 220, thus applying the same inlet pressures to each path. During the experiments, the samples included polystyrene beads with diameters of 10 pm, 20 pm or 40 pm, in a solution containing about 104 beads per mL in phosphate buffer saline (PBS) supplemented with 0.2% F68 and 0.2% Tween 20 to assist priming and reduce fouling and bead aggregation. To achieve buoyancy matching between the beads and the fluid, Optiprep™ was added in a ratio of 1 : 10 Optiprep™ to sample.

[0137] Fluidic Control. Briefly, a hybrid of steady flow and oscillatory flow was achieved in two separate parts: (i) forward bias flow rate was set by the syringe pump, and (ii) oscillatory flow rate waveform was set by pressure, via a reciprocating column of fluid inline to the microfluidic chip 100. Total achieved pressure was equal to the steady pressure drop derived from the steady flow rate through the microfluidic device 100 resistance plus the product of instantaneous acceleration, fluid density, and length of the inlet tube 230-1 attached to the oscillating 3D-printed structure 220. Owing to the sinusoidal driving voltage, direct proportionality of voltage to coil force, and fixed mass of the microfluidic system 10, a pressure waveform approximating a sinewave was thus superimposed to the steady driving pressure.

[0138] Priming. Prior to introducing the sample into the microfluidic chip 100, 3 mL of isopropyl alcohol (IP A) was flushed through the fluidic lumen 130 to eliminate any remains of uncured resin. Subsequently, a 3 mL flush of 0.2% F68 solution was performed to ensure the complete removal of IPA from the fluidic lumen 130. The sample could then be introduced into the microfluidic chip(s) 100.

[0139] Steady flow control. Precise control over the time-averaged flow rate (of sample and of buffer as appropriate) was achieved using computer-controlled Harvard Apparatus PHD Ultrasyringe pumps. Despite using plastic syringes, the wide channels 132-1 and 132-2 exhibited low resistance, and the rigid 3D-printed microfluidic chips 100 minimized fluidic compliance, such that their RC product resulted in near instantaneous response of the fluidic lumen 130’ s flow rate to the syringe pump settings (as observed by particle image velocimetry (PIV)).

[0140] Oscillatory flow control. A sinewave fluid oscillation was superimposed onto the steady flow rate through the reciprocating motion of one or more inlet tubes (ID: 0.02”, OD: 0.06” Tygon® ND- 100-65, Saint-Gobain). To control the oscillation of the tubing, a 450 mm length of inlet tubing 230-1 of which 100 mm were taped to the 3D-printed structure 220, itself affixed to the speaker 210 (8 , 15 W; AS07808AS-R from PUI Audio). To reduce the reciprocating mass, and thereby increase the achievable acceleration, the 3D-printed structure 220 was thin-walled, and the surface cone was removed from the speaker 210, leaving just the voice coil and the speaker spider 212 to which it remained anchored. To actuate the speaker coil for oscillations, the speaker terminals were connected to a computer-controlled audio output after lOx amplification (TP A3125D2 EVM, Digi-Key). By delivering a sine wave to the speaker 210, the entire assembly including the speaker spider 212, 3D-printed structure 220, and attached inlet tube 230-1, vibrated precisely at the frequency of the sinewave. Moreover, the amplitude and frequency of the oscillation could be precisely adjusted controlling the output audio signal from the computer (MATLAB). This oscillation was transmitted to the attached column of fluid through its mechanical coupling with the inlet tube 230-1, inducing an oscillatory pressure that then led to fluid oscillation within the fluidic lumen 130. In addition, the outlet port 140-2 of the microfluidic chip 100 was pressurized to 5 psi in order to minimize the impact of bubbles which could otherwise enlarge during the low-pressure phase of the sinewave, and thereby dampen the oscillations by their added compliance.

[0141] FIG. 4B includes images depicting a timelapse of MOAT phenomena realized in an example experiment of the microfluidic system 10. Here, oscillations trapped particles from 0-20 minutes, being released at 21 minutes (speaker off). Arrow indicates forward bias flow direction. Each circle in the second image of FIG. 4B (at 0.5 minutes) surrounds a bead.

[0142] To illustrate the MOAT phenomenon, the 3D-printed pseudo-2D microfluidic chips 100- 1 to 100-4 of FIGs. 3A-3B were utilized as a trap geometry in the microfluid system 10 with a width-to-height aspect ratio of w / h > 20. The experiment shown in FIG. 4B was conducted with parameters set as follows: (i) infusion rate of 200 nL / s, (ii) oscillations at 75 Hz, (iii) VI =4.43 mm / s, and (iv) 20 pm beads. The MATLAB script was programmed to activate the oscillations and infuse buffer in the microfluidic chip 100 for an initial 10 seconds. Subsequently, buffer with beads was infused for a duration of 20 minutes to ensure the bead solution reached the microfluidic chip 100, followed by a return to buffer infusion alone to stop infusing particles. After 10 seconds of oscillations with the trapped particles, the oscillations were turned off, causing the beads to exit the trap. FIG. 4B illustrates different time points of the MOAT phenomenon, separated by a few seconds or minutes. The first image depicts the infusion of buffer only, hence the absence of beads. In the second image, five beads are visible. Four are already trapped and one is in the process of being trapped. The third image demonstrates the trap filled with multiple beads, and only buffer being infused. It is of note that no beads are leaving the trap in images 2 and 3, corresponding to near 100% yield of particles. Finally, the fourth image of FIG. 4B illustrates the outcome when the oscillations are interrupted - the forward bias flow rate of 200 nL / s carries the particles away from the trap.

[0143] The high-speed video camera (Phantom V4.2; Vision Research) used to obtain the timelapse video had 4 GB of on-board RAM which was split to 15 videos to cover multiple MOAT test conditions in sequence, leaving just a few seconds of recording per condition if multiple phase points of the oscillation were to be captured. To extend the duration of each video, and observe extended dynamics in the MOAT devices, intentional aliasing was employed to repeatedly take photos at defined phase points, separated in time by the full period of the pressure sinewave oscillation. Specifically, the frame rate was adjusted to be somewhat lower than the sinewave frequency, such that each successive picture was from the next phase point, plus a full period of oscillation in the future. For example, to obtain four phase point images when particles oscillated at 75 Hz, the frame rate was set to 60 fps, increasing video duration over four-fold in this case.

[0144] Example IB - Measurement of Oscillatory Velocity

[0145] Due to its role in the observed MOAT effect, it is valuable to know the oscillatory velocity of the fluid within the microfluidic chip 100 for each combination of frequency and oscillatory velocity of the oscillatory system 200. The actual oscillatory fluid velocity depends on the speaker 210’s voltage, height of the oscillating tubing, 3D-printed structure 220’ s mass, and the fluidic lumen 130’s channel resistance. To observe this velocity directly by high-speedvideo microscopy, the input solution was seeded with a low concentration of 10 pm diameter polystyrene particles (103 per mL). However, since aliasing was employed to extend the video length, and particles can be in different vertical planes (and faster or slower as a result), the inventors adjusted the method of particle image velocimetry (PIV). The PIV displacement measurements were fit to an equation of form: y — mt + b + A sin(2?r ft + ). Here, A is amplitude, cf> is phase offset, f is the sampling frequency, and t is time at which the image was taken. The mt + b linear function accounted for lateral drift of the untrapped particle due to the syringe-pump steady flow, while the sinewave accounted for the oscillatory flow velocity. From this equation, the bias ratio of forward to backward movement, denoted as B = (forward displacement) / (backward displacement), was estimated from the peaks and troughs of the fit function. When the bias flow rate is zero, this ratio is 1. As the known syringe flow rate increases, B will increase above 1 in a predictable manner reflecting the unknown oscillatory flow rate magnitude alone. Notably, this ratio is invariant when measured across single or multiple periods of oscillation, and it also does not change with particle location in the transverse direction (x-direction), so long as the particle does not excessively lag the flow (verified by comparing PIV measures for beads of multiple sizes, 10, 20, and 40 pm). It can be shown that this ratio B is also equal to (1 -I- 7sf) / (Vi —sf), where Vsfis the velocity magnitude of the untrapped (free) particle. This allows one to compute B from the observed particle motion. Particularly, the equation B = (Vr+ Vsf) / (Vt— Fsf) was used to determine l^, the oscillatory velocity corresponding to a specific combination of frequency and amplitude. It is important to note that V1is the average forward bias velocity of the oscillatory flow, during each half-cycle.

[0146] FIGs. 5A-1 to 5A-5 include experimental plots of trapping efficiency of 10 micron, 20 micron, and 40 micron beads at 25 Hz 50 Hz, 75 Hz, 100 Hz, and 125 Hz oscillation frequencies, various oscillatory velocities, and a range of forward bias flow rate values. FIG. 5A-1 includes subplots of trapping efficiency at 25 Hz for oscillatory velocities of 18 mm / s, 5.9 mm / s, 3.7 mm / s, and 1.5 mm / s. FIG. 5A-2 includes subplots of trapping efficiency at 50 Hz for oscillatory velocities of 16 mm / s, 14 mm / s, 14 mm / s, and 10 mm / s. FIG. 5A-3 includes subplots of trapping efficiency at 75 Hz for oscillatory velocities of 34 mm / s, 26 mm / s, 14 mm / s, and 10 mm / s. FIG. 5A-4 includes subplots of trapping efficiency at 100 Hz for oscillatory velocities of 7.3 mm / s, 7.3 mm / s, 7.3 mm / s, and 5.3 mm / s. FIG. 5A-5 includes subplots of trapping efficiency at 125 Hz for oscillatory velocities of 8.6 mm / s, 7.8 mm / s, 4 mm / s, and 3.1 mm / s.

[0147] As used herein, the “trapping efficiency” of the MOAT phenomenon is defined as the ratio of successfully trapped particles to the total number of particles entering the microfluidic chip 100. To evaluate the trapping efficiency, a series of experiments were conducted using three different bead sizes, five frequencies, and four oscillatory velocity (Vj) values per combination of bead diameter and frequency. The four differentvalues were obtained by adjusting designed channel resistance and displacement amplitude. Speaker volumes used to obtain different oscillatory velocities were 25%, 50%, 75%, and 100%. Each combination of frequency and oscillatory velocity was tested individually. The pseudo-2D microfluidic chip 100 used in this set of experiments had a single inlet port 140-1, as it was sufficient to infuse buffer containing beads. The experimental procedure involved a forward bias flow rate ramp-up for a specific set of conditions. This entailed increasing the syringe pump flow rate incrementally from 166.67 nL / s to 4166.7 nL / s with 166.67 nL / s steps between each value of flow rate (Q). Each flow rate was maintained for a duration of one minute. If, during this period, the microfluidic chip 100 became full, the oscillations were paused for two seconds to allow the particles to exit the microfluidic chip 100, after which the oscillations were reactivated. For each flow rate, the number of beads trapped in the MOAT were counted, as well as the total number of beads entering the microfluidic chip 100, enabling calculation of the trapping efficiency. The results are summarized in FIGs. 5A-1 to 5A-5, where each subplot illustrates the trapping efficiency plotted against normalized flow rate (Q’), which represents the ratio of the forward bias flow rate (m3 / s) to the width (4 mm) of the fluidic lumen 130 in the microfluidic chip 100 that was tested. The total number of trapped beads during the flow rate ramp up are indicated next to the bead size in each subplot.

[0148] With respect to FIGs. 5A-1 to 5A-5, the lower trapping efficiency at lower oscillatory velocities can be attributed to the shorter stroke distance of the particles relative to the channel expansion length. At lower oscillatory velocity, the stroke distance of the particles becomes significantly shorter than the trap length, failing to cover the entire span of the trap. However, higher oscillatory velocities, the stroke distance can be comparable to the trap length. With the 3D-printed microfluidic chip 100 in FIGs. 3A-3B, optimal trapping efficiency occurred at 75 Hz, where the stroke displacement of the fluid matched the length of the bridging expansion 134 between the first 132-1 and second 132-2 channels. As frequency is increased, stroke displacement decreases. Conversely, as frequency is decreased, stroke displacement increases. Ifthe stroke distance becomes too large, the portion of the particle’s oscillation spent over the bridging expansion 134 (trapping region) becomes insufficient for trapping.

[0149] Bead size can play a prominent role in trapping efficiency. As depicted in FIGs. 5A-1 to 5A-5, 10 pm beads consistently exhibited the lowest trapping efficiency, reaching a maximum value of 0.5. This observation could be explained in part by the focusing of particles in two distinct z-planes. When subjected to oscillation upstream of the microfluidic chip 100, particles tended to focus in two positions within the z-plane: one near the ceiling of the fluidic lumen 130 and another close to the planar surface 112. Particles focused near the ceiling were in closer proximity to the steps 136 of the bridging expansion 134 (trapping region), where the flow changes direction most strongly. However, larger beads incur stronger wall lift forces that act to keep the particles at a greater distance from the walls of the fluidic lumen 130. For intermediate frequencies, a noticeable opposite trend emerged where 20 pm beads were trapped more efficiently compared to 40 pm beads. Due to their larger size, 40 pm beads focused further from the walls of the fluidic lumen 130 where they experienced stronger drag forces deeper into the core of the flow. This can overcome the higher lift forces to efficiently trap the beads.

[0150] As expected, increasing the net flow rate led to decreased trapping efficiency. This can be explained by the fact that higher flow rates result in faster displacement of the beads away from the bridging expansion 134. In other words, the increased flow rate exerts a stronger drag force that pulls the beads away from the trap, making it less likely for them to remain within the bridging expansion 134.

[0151] FIGs. 5B-1 to 5B-5 include experimental plots of robustness of trapping of 10 micron, 20 micron, and 40 micron beads at 25 Hz, 50 Hz, 75 Hz, 100 Hz, and 125 Hz oscillation frequencies, various oscillatory velocities, and a range of forward bias flow rate values. FIG. 5B- 1 includes subplots of robustness at 25 Hz for 10 micron, 20 micron, and 40 micron beads. FIG. 5B-2 includes subplots of robustness at 50 Hz for 10 micron, 20 micron, and 40 micron beads. FIG. 5B-3 includes subplots of robustness at 75 Hz for 10 micron, 20 micron, and 40 micron beads. FIG. 5B-4 includes subplots of robustness at 100 Hz for 10 micron, 20 micron, and 40 micron beads. FIG. 5B-5 includes subplots of robustness at 125 Hz for 10 micron, 20 micron, and 40 micron beads.

[0152] As used herein, the “robustness” of the MOAT phenomenon is characterized by the ability of particles to withstand an increasing flow rate once they are already trapped in themicrofluidic chip 100 at a low forward bias flow rate. To assess the robustness of particle retention (“trapping”) in the MOAT system, a series of experiments was conducted using three different bead sizes, five frequencies, and three different oscillatory velocities per combination of bead size and frequency. Frequencies used were 25 Hz, 50 Hz, 75 Hz, 100 Hz, and 125 Hz. The three different oscillatory velocities were obtained by adjusting the speaker 210’s volume. Speaker volumes used in this experiment were 33%, 67%, and 100%. For each combination of oscillatory velocity, oscillation frequency, and bead size, an experiment was performed.

[0153] The experimental procedure involved initially trapping multiple beads at 75 Hz, high oscillatory velocity l^, and a low flow rate within the MOAT, conditions resulting in optimal trapping. Once enough beads were trapped, the infusion of beads was halted. Subsequently, the oscillatory velocity and frequency were adjusted to the desired values for the experiment, and the infusion of buffer at a low flow rate (50 nL / s) was initiated. A flow rate ramp up was then initiated and each flow rate value was maintained for 2.5 seconds before transitioning to a higher flow rate. The flow rate increased by 10% between each step, with the final flow rate set to 4000.9 nL / s. This experimental setup enabled the observation of bead behavior, including their release from the trap, at various combinations of frequency, oscillatory velocity (Ft), and bead diameter. High-speed video was employed to record the beads leaving the trap. The number of beads leaving the trap at each flow rate allowed us to calculate the fraction of beads leaving at each flow rate. In this experiment, a device with two inlet ports was used to allow the infusion of either pure buffer or buffer containing beads. Once all the beads had exited the trap, the experiment was repeated with the next combination of frequency, bead size, and oscillatory velocity. The results of these experiments are summarized in FIGs. 5B-1 to 5B-5. The initial number of trapped particles is indicated next to the oscillatory velocity in each subplot. Three oscillatory velocities are depicted in each subplot. The fraction of particles still trapped at each flow rate value was calculated as the ratio of the particles that remained trapped to the initial number of trapped particles.

[0154] As shown in FIGs. 5B-1 to 5B-5, oscillatory velocity (l^) emerges as a significant factor influencing the robustness of the microfluidic chip 100. The overall trend suggests that higher oscillatory velocities result in better resistance of particles against increasing flow rates, provided the stroke distance is not too much larger than required to transit the full asymmetry. Oscillation frequencies of 50 Hz and 75 Hz demonstrated the highest robustness in retaining trappedparticles, with beads exhibiting greater resistance to high flow rates at these frequencies. Among the different bead sizes, 20 pm beads exhibited the highest level of robustness compared to the other sizes when subjected to varying flow rates, like their higher trapping efficiency in FIGs. 5A-1 to 5A-5.

[0155] Example 1C - Dimensional Analysis

[0156] To understand the behavior of the MOAT and identify relevant parameters that govern the phenomenon, a dimensional analysis of the microfluidic chip 100 in FIGs. 1A to 1C was conducted. This analysis aimed to identify the relevant parameters governing the phenomenon and offer a means to optimize and design future devices. The variables involved in the problem encompass geometry of the microfluidic chip 100, properties of a fluid injected into the microfluidic chip 100, and external effects. Here, the variables include the time-averaged oscillatory fluid velocity (V^) in the first channel 132-1, the ratio (Q' = Q / w) of the net flow rate (Q) to the width (w) of the fluidic lumen 130, the oscillation frequency (m), the height (h- of the first channel 132-1, the diameter (a) of the particles (e.g., beads), the angle (0) of the bridging expansion 134 between the first 132-1 and second 132-2 channels, the fluid density (p), and the fluid viscosity (p). Given the number of variables (eight) and number of dimensions (three) of this problem, five pi-terms were involved. Chosen repeating variables were / i L], p [ML-3], and Vi1[ LLT-1] J. The resulting pi-terms were: 7ii = 7T2= — . °1 1aihizhiThese parameters were used to guide experimental design as well as to plot the obtained data. T1represents the stroke distance relative to the height of the first channel 132-1, TT2is the particle Reynolds number, and ?r3represents the ratio of a higher flow rate relative to the particle oscillatory velocity (higher values ultimately break trapping as particles are swept away). The dimensional analysis focused on one 0 value, one hrvalue, and three different bead diameters (a). However, the information pertaining to these parameters is implicitly considered in the remaining pi -terms.

[0157] FIGs. 6A-1 to 6A-3 are a series of plots of trapping efficiency dimensional analysis versus particle Reynolds number for 10 micron, 20 micron, and 40 micron beads. FIG. 6A-1 is a plot of trapping efficiency versus particle Reynolds number of 10 micron beads, FIG. 6A-2 is aplot of trapping efficiency versus particle Reynolds number of 20 micron beads, and FIG. 6A-3 is a plot of trapping efficiency versus particle Reynolds number of 40 micron beads.

[0158] In each of the plots, the flowrate at which the given trapping efficiency is reached is plotted on the z-axis. Larger circles correspond to 60% trapping efficiency, intermediate circles correspond to 40% trapping efficiency, and smaller circles correspond to 20% trapping efficiency. The y-axis represents 7TX: the stroke distance relative to channel height. The x-axis represents n2: the particle Reynolds number.

[0159] As can be seen in FIGs. 6A-1 to 6A-3, both 10 pm and 20 pm beads achieve optimal trapping efficiency atvalues between 2.5 and 3. This range corresponds to a stroke distancecomparable to the length of the bridging expansion 134 of the microfluidic chip 100, which improves trapping efficiency. A consistent trend emerges across all bead sizes: below a criticalQ' Qfvalue of — — , trapping efficiency remains constant. The influence of the — — ratio can beQ interpreted in terms of steady flow velocity. When — —rincreases, trapping efficiency tends to Vi / ii decrease. This may be attributed to the requirement of a certain oscillatory velocity per steady flow velocity for effective bead trapping. When Fsfsignificantly exceeds V , the oscillatory velocity is not large enough in comparison to the steady flow velocity, and the beads do not get trapped.

[0160] FIGs. 6B-1 to 6B-3 are a series of plots of trapping efficiency dimensional analysis versus Womersley number squared for 10 micron, 20 micron, and 40 micron beads. FIG. 6B-1 is a plot of trapping efficiency versus Womersley number squared for 10 micron beads, FIG. 6B-2 is a plot of trapping efficiency versus Womersley number squared for 20 micron beads, and FIG. 6B-3 is a plot of trapping efficiency versus Womersley number squared for 40 micron beads.

[0161] FIGs. 6B-1 to 6B-3 highlight the importance of the Womersley number a2=xa>p]p as well as the importance of the oscillatory velocity. Womersley number characterizes unsteady, oscillatory flow. Elevated Womersley numbers reflect that the oscillatory flow begins to lag the applied pressure more and more due to inertia. This leads to stronger asymmetry, particularly during the forward stroke where high peak velocity increases the lag of flow to pressure.Combining high a and high -7- lead to increased lag between flow and pressure, accentuating the MOAT phenomenon. At low values of a2and of - -, trapping efficiencies higher than 60%are rarely reached, and when they are, it occurs at very low forward bias flow rate. However, increasing Womersley number, even at low oscillatory velocities, increases the trapping efficiency per flow rate. Also, increasing values whilst keeping low Womersley numbersleads to higher trapping efficiencies at higher flow rates. Finally, the combination of both Womersley and - - numbers at highest values leads to the best achieved trapping efficiencies.

[0162] As shown in FIGs. 6B-1 to 6B-3, a significantly higher Womersley number was reached for all three additional experiments. Most importantly, these Womersley numbers have led to the highest trapping efficiencies at highest flow rates observed. This helps support the importance of the Womersley number in the MOAT phenomenon, when in combination with significantKeeping values of - - in the same range, increasing the Womersley number has a significant, CO / li positive impact, on trapping efficiency. Moreover, for the same Womersley numbers, a higher value of leads to higher trapping efficiency at higher flow rates, showing the benefit of having a higher oscillatory velocity on successful trapping.

[0163] FIGs. 6C-1 to 6C-3 are a series of plots of robustness dimensional analysis versus particleReynolds number for 10 micron, 20 micron, and 40 micron beads. FIG. 6C-1 is a plot of robustness versus particle Reynolds number for 10 micron beads, FIG. 6C-2 is a plot of robustness versus particle Reynolds number for 20 micron beads, and FIG. 6C-3 is a plot of robustness versus particle Reynolds number for 40 micron beads.

[0164] To gain insight into the influence of different pi-terms and parameters on the strength of the trap in retaining particles, the data was plotted using pi-terms. FIGs. 6C-1 to 6C-3 illustrate this representation, with one plot dedicated to each bead size. The x-axis represents the particleReynolds numberpV]a, while the y-axis corresponds to the ratio of Both axes are displayed coh' Q on a loglO scale. The-z axis represents different values of the ratior

[0165] Upon examination of FIGs. 6C-1 to 6C-3, it becomes evident that a higher trap strength is achieved at higher particle Reynolds numbers. This suggests that increased inertial lift forces contribute to enhanced resistance of the beads within the trap against increasing flow rates.Furthermore, there is an optimal value of— where the trap strength is maximized. This am-optimum is observed for values of the -7- ratio ranging between 2 and 3. Notably, this range corresponds to a stroke distance comparable to the length of the bridging expansion 134 of the microfluidic chip 100, indicating the importance of this parameter in determining trap strength.

[0166] These plots reveal specific conditions where only certain beads remain trapped. For instance, at a particle Reynolds number of 2 X 10-2and a -7- of 3, only 10 pm beads remain trapped while 20 pm and 40 pm do not. This was apparent experimentally: 20 pm and 40 pm beads left the microfluidic chip 100, but 10 pm beads remained trapped. This observation suggests the possibility of size fractionation within the MOAT phenomenon, including trapping smaller particles while larger particles pass by, adding uniquely tunable functionality as compared to the way a static filter operates. Moreover, filters often pass deformable particles due to extended contact time, absent in the MOAT, enabling trapping of deformable particles based on their unstressed shape.

[0167] Example ID - Additional Experiments and Discussion

[0168] FIGs. 7A and 7B include images depicting a timelapse of HeLa cells trapped in a device as described herein. FIG. 7A shows a timelapse of HeLa cells trapped in the device at a flowrate of lOnL / s and a frequency of 75 Hz, FIG. 7B shows a timelapse of 20pm beads trapped in the same device as the HeLa cells, at a flowrate of lOnL / s and a frequency of 75 Hz. Particles can be seen oscillating as they are trapped in the device.

[0169] FIG. 7C is a series of timelapse images depicting trapping of 20 micron beads in fluid seeded with 2 micron particles, in a curved channel as described herein. Oscillation frequency was set to 50 Hz, net steady flowrate was set to 2 pL / min, and direction indicated by arrow on first image. Inner radius of the curvature is 500 pm IR, channel is 3 mm wide and 100 pm high. Circled particles show 2 pm particles moving upstream, despite the net flowrate going in the other direction.

[0170] It is important to note the surprising ubiquity of the MOAT phenomenon. As can be seen in FIGs. 7A and 7B, experiments were performed using particles other than beads, such as blood, diluted blood, and HeLa cells. Remarkably, the MOAT phenomenon occurred with all three types of samples, demonstrating that factors such as the viscosity of blood, the softness of cells, and particle size do not impede the functioning of the MOAT.

[0171] The presence of bubbles in the device was found to influence particle trapping. When rooted to the channel, bubbles trapped particles in their vicinity, suggesting that the asymmetry provided by the bubbles contributes to the trapping mechanism, though at much lower frequencies than the typical > 10 kHz for acoustofluidic trapping involving bubbles. Moreover, when small fabrication defects, such as scratches, stuck beads, or dust, were present in the regions of the device, particles tended to accumulate around these defects, further indicating the sensitivity of particle trapping to local variations in the device geometry. As mentioned beforehand, the phenomenon occurs in various density and viscosity media.

[0172] Taken together, these experimental examples demonstrated the wide spectrum of conditions under which the phenomenon can occur, underscoring its robust nature and versatility. Its potential applications span diverse domains such as water treatment and cell culture.

[0173] It was established that particle trapping occurred in PDMS / glass microfluidic fdters, using standard soft lithography, where particles did not exit the filter though remaining suspended. This implicated either expansion / contraction of the designed channels, inflation / collapse of the channels due to the oscillating inlet pressure / deformability of PDMS, or particle contact with the walls, to impart asymmetry, e.g. deterministic lateral displacement, albeit in an oscillatory flow. A series of targeted experiments was conducted to control for these various factors.

[0174] It was further established that trapping can occur in rigid filters of comparable design. To control for particle-wall contact (or near-contact), simple PDMS devices were examined with either expansion or contraction as the required asymmetry. These larger channels demonstrated that trapping occurred without particle contact to walls; however, channels were again deformable, subject to inflation / collapse during the sinewave oscillatory pressure. To examine expansion and contraction by channel design, not by happenstance of the properties of PDMS, pseudo-2D 3D-printed devices were created as described in FIGs. 3A and 3B. These rigid devices revealed that trapping could occur with expansion or contraction. Thus, cyclical inflation / deflation was not required in the absence of particle contact to the walls. Trapping in constant-cross-section curving channels, in rigid plastic, was also examined in FIG. 7C, finding that curvature was sufficient as an asymmetry in the absence of expansion or contraction and without particle contact to the walls. Therefore, trapping can occur whenever the channelgeometry changes along the direction of steady flow, whether by its cross-sectional shape or overall direction of flow.

[0175] Whether and where trapping will occur depends first on the fluid velocity distribution as it evolves over time (oscillatory flow) and space (channel asymmetry along the flow direction), which can be computed numerically. Secondly, trapping depends on the drifting equilibrium positions for inertial focusing along the length of the channel, and the speed with which particles migrate from their current streamline into their changing equilibrium focusing positions all along the oscillatory path (in response to local lift forces). It is important to note that overall changes in fluid velocity induce a “lag” of the particle to the flow, as embodied in the Stokes number, Stk = pa2v / (18jUL), where p is the particle density, a is the particle diameter, v is the fluid velocity, L is the characteristic dimension, and p is the fluid dynamic viscosity (and not-withstanding the no-slip condition at the particle surface). Along a trapping loop, the particle is most often slightly out of equilibrium to the lift and drag forces pushing it towards equilibrium, leading to its acceleration by Newton’s second law. Trapping relies partially upon the particle migrating into faster streamlines (relative to its current streamline) during the backstroke, but slower streamlines during the forward stroke, on average through a cycle. By crossing toward the faster flow in the upstream direction, then slower flow in the downstream direction, particles can remain trapped despite that the fluid does not. As the bias flow increases, there comes a point where the differential travel upstream by the particle is insufficient to hold a zero net velocity in the loop, causing a breakdown in trapping.

[0176] In a simplified MATLAB model, it was confirmed that particle “lag” to the flow was sufficient in and of itself to trap particles in a channel contraction, in the absence of inertial lift forces, though this is a weaker effect. It is worth pointing out however that in principle an overall change in channel cross-section would be sufficient for trapping, even without significant lift forces, as might occur in a much larger cross-section pipe with « 1, where D is the diameterof the pipe.

[0177] Interestingly, it was observed that trapping also occurred in curved channels with constant cross sections. The effect may be attributed to inertial focusing, which manifests by directing particles towards distinct preferred streamlines. The flow profile within the curved channel section exhibits notable asymmetry before and after flow reversal, imparting significant influence over the particle’s position along particular streamlines. Particles will cross streamlineswhilst being subjected to a unidirectional flow during the curvature of the channel and will also cross streamlines once the flow reverses. The particle therefore migrates across streamlines during forward and reverse strokes, modulated by the changing channel shape, which compensates for the bias flow rate in the forward direction. Indeed, the behavior of particles is notable when they transition to faster streamlines during flow reversal, increasing their upstream migration rate. If these particles subsequently move to slower streamlines during flow directions that align with the bias flow downstream, the cumulative upstream movement effectively counterbalances the bias flow's effect. Particle migration due to inertial focusing can eliminate a large majority of accessible streamlines for a particle in the trap, any of which may be more or less effective at net migration upstream in the flow. Even when particles become stably trapped, inertial focusing causes cross-stream migration towards the preferred focusing streamlines all along the changing channel geometry at the trap, sometimes pushing the particles further downstream or upstream as a result according to the detailed path taken by a given particle. Thus, inertial focusing is superimposed upon the MOAT, becoming one of multiple sources of particle migration asymmetry.

[0178] Another factor contributing to trapping of particles in channels with constant cross section is the lag of the flow to the pressure that can create areas of net local upstream flow, near the walls. This can be observed for large values of Womersley number: a2= h2ip / .. These areas of net upstream flow can occur as a result of the downstream stroke being faster than the upstream stroke, owing to the bias flow. In other words, the core of the flow lags more when turning around from downstream to upstream flow. To match the bias flow enforced by the syringe pump, the slower parts of the flow must therefore compensate for this lag imbalance, by exhibiting net upstream flow near the walls.

[0179] Besides filtration of particles by size, particle trapping by asymmetry has been achieved previously in steady flow using multiple fixed geometrical expansions and contractions in series. This vortex method relies on inertial migration of large particles (and cells) across streamlines and into zones of recirculation created at sudden expansions. In contrast, the MOAT effect occurs in an oscillatory flow, with or without vorticity, and with or without significant inertial migration, requiring only that particles traverse forward and reverse strokes differently. Within the realm of oscillatory flow, acoustics uses vibration to create standing pressure waves in microchannels, with or without bias flow, driving particle migration towards either nodes orantinodes depending on particle and fluid properties. However, acoustic focusing involves typically sub-micron fluid displacements in the megahertz range owing to the scale of channels and speed of sound in water. In contrast, the MOAT effect occurred around 100 Hz in the experiments, using large displacements on the order of a millimeter to around 100 microns. Further, though altered trapping near expanding / contracting bubbles was observed in the experiments, traditional acoustic trapping near oscillating bubbles differs from the MOAT in its reliance again on resonance at much higher frequencies and on acoustic streaming to generate trailing vortices into which particles can become trapped. The findings and understandings of the MOAT presented herein are of practical significance to particle and cell-based microfluidics.

[0180] Example 2 - Use of MOAT in Single-Cell RNA Sequencing

[0181] Example 2 provides an application of MOAT to Single-Cell RNA Sequencing using the microfluidic chip 100 of FIG. 8-1 and the microfluidic system 10 of FIG. 10A.

[0182] The application of MOAT in multiomics, especially in approaches like CITE-seq (Cellular Indexing of Transcriptomes and Epitopes by Sequencing), revolutionized the study of complex biological systems by simultaneously integrating diverse datasets, such as transcriptomics, proteomics, and epigenomics. This comprehensive approach revealed intricate cellular heterogeneity, regulatory mechanisms, and novel cell types within tissues, providing deeper insights into health, disease, and therapeutic development. Although single-cell RNA sequencing (scRNA-seq) primarily focuses on RNA, it leaves out important information about protein expression. CITE-seq overcomes this limitation by enabling simultaneous measurement of both RNA and surface protein levels in the same single cell. This dual-layered approach provides a more complete picture of cellular function, making it particularly valuable for studying complex systems like the immune response or cancer.

[0183] Despite its potential, one of the significant challenges in CITE-seq is the washing process to eliminate free-floating bar-coded antibodies. These unbound antibodies can interfere with the sequencing process, leading to background noise and significantly increasing the overall cost. While many computational tools have been developed to address this noise, the high sequencing costs remain and hinder the broader adoption of this technology.

[0184] Increasing the number of washes by centrifugation can help reduce the interference from free antibodies, but this comes with its own set of problems. More washing steps lead to cell loss,which is especially problematic when working with rare cells, like circulating tumor cells. Additionally, each washing step can negatively impact cell viability and retention, making it critical to minimize the number of centrifugation cycles to preserve the integrity of the samples.

[0185] The MOAT phenomenon is able to provide contactless washing. In contrast to a fdter, which often loses cells as they squeeze through pores over time, becomes clogged early in the filter stages, and requires much smaller apertures, MOAT devices can hold particles much smaller than the open areas, increasing capacity, reducing shear stress, and ensuring cell removal after washing without sticking to the walls as in a filter. These specially designed MOAT device patterns serve as high-capacity contactless cell washers, ideal for applications requiring minimal cell loss. The innovative design allows for the preservation of roughly 40,000 cells even in the prototypes, with many possibilities for scaling up further, which is more than sufficient for the cell input requirements of many single-cell technologies, such as 10X Genomics or BD Rhapsody. By minimizing the need for centrifugation-based washing steps, these patterns help maintain cell viability and retention, addressing a key challenge in workflows like CITE-seq.

[0186] As shown in FIG. 8-1, the unit cell is designed with two distinct zones to ensure maximum cell capacity and minimize cell loss within the microfluidic chip 100. Within the first zone, microstructures 158 are strategically placed in the shape of two opposing L-shaped islands 158-1 and 158-2. Each microstructure 158 in the design has a length of 300 pm and a width of 200 pm. The spacing between each set of the opposing microstructures 158 is 50 pm. The space 159 (or “trapping region) between the two opposing L-shaped microstructures 158, with an area of roughly 12855 pm2, similar to a circle with an effective diameter of 128 pm, is designed specially to trap cells owing to its high degree of asymmetry (expansion / contraction) and stroke distance of similar length to the circular cavities. Additionally, the straight microchannel 157-1 and 157-2 between complementary L-shaped microstructures 158 has 50 pm width. This spacing ensures an optimal stroke distance to maintain cells in position within the microchannel 157. The stroke distance is precisely calibrated: it is not high enough for cells to escape from the traps, yet not too low to prevent effective trapping of the cells (cells should oscillate through a significant asymmetry. This balance is crucial for ensuring that cells remain securely confined within the trapping regions 159.

[0187] Net flow rate is another decisive factor in the design of this system of microchannels 157. A very low flow rate can compromise the functionality of the microfluidic chip 100, making itless effective in washing cells in a reasonable time. Conversely, high flow rates can reduce the capacity of the traps to hold cells securely, leading to potential cell loss. To strike the right balance, a flow rate of 10 pL / min was selected as the optimal rate for cell washing in the CITE- seq application (the dead volume of the device is 20-30 microliters, meaning washing can occur in a few minutes). This flow rate ensures that the cells remain trapped effectively within the trap regions while allowing for efficient media exchange, providing the right conditions for successful cell washing to remove free floating antibodies without compromising cell retention. The net flow rate will of course change according to the detailed design and needs of the washing application.

[0188] Once the oscillation is initiated, two counter-rotating zones of recirculation can be generated between the complementary L-shaped obstacles in the microchannel. These zones of recirculation are not in themselves required for MOAT operation, but can enhance the strength of cell trapping in these regions over what will be the case from other sources of asymmetry alone. As the cells enter these zones of recirculation, they rotate in the direction of the circular flow, moving in a controlled circular pattern. Additionally, each end of the L-shaped obstacle is rounded with a 50 pm curvature, specifically optimized to ensure sufficient space for effective cell trapping at those curved regions due to the channel asymmetry there, increasing overall cell capacity. This design adds an extra layer of security to the system, ensuring that even if a cell escapes from one trapping region, it is immediately captured in another. The combination of recirculation generation and asymmetrical obstacle design ensures that there is minimal to zero cell loss, providing a highly reliable solution for applications requiring delicate cell handling and retention.

[0189] Finally, the network 152-2 of outlet microchannels 154-2 was designed with ultra-high- capacity structure 154-2 (or island) locations that act as secondary zones for cell trapping. If cells happen to escape from the primary trapping regions 159 during the washing process, they can still be captured at these structure 154-2 locations. This strategic design minimizes the chance of cell loss, potentially addressing a significant issue in single-cell washing steps, where typically 15% to 70% of cells are lost during centrifugation as the primary alternative to MOAT washing. The combination of these secondary traps, along with the L-shaped microstructures 158, ensures that there is minimal to zero cell loss, providing a highly reliable solution for applications requiring delicate cell handling and retention. In addition, the media used for the CITE-seqapplication is free of free-floating antibodies, which dramatically reduces the experimental cost by approximately 85%. This cost reduction makes this dual-purpose single-cell technology more accessible to researchers worldwide, enabling broader adoption and advancing studies that rely on precise single-cell analysis.

[0190] FIGs. 8-2A to 8-2D are a series of images of experiments on the microfluidic chip 100 of FIG. 8-1. FIG. 8-2A shows a snapshot of 10 pm particles being trapped at flow rate 10 pm and frequency of 75 Hz. FIG. 8-2Bshows a trajectory of 10 pm particles at flow rate 10 pm, frequency 75 HZ. While the particles remain motile within the trap locations, they do not escape from the traps or exit the microchannel 157, effectively confirming the reliability of the design. FIG. 8-2C shows a snapshot of particles trapped at a net flow rate of 10 pL / min and a frequency of 75 HZ. FIG. 8-2D shows a timelapse of trajectories of particles being trapped at same conditions. Here, the trapping yield is maximum since particles occupy both trapping regions at the center of circular cavities between the L-shaped microstructure 158 and the curving part of the microstructures 158. This dual trapping capacity maximizes the trapping efficiency, ensuring that particles are securely held in place within multiple trapping regions 159 of the microfluidic chip 100.

[0191] FIGs. 8-3 A and 8-3B are a pair of images of experiments on the microfluidic chip 100 of FIG. 8-1 with increasing particle load size. FIG. 8-3A shows a snapshot of particles being partially trapped at a flow rate of 10 pL / min and 50 Hz frequency. FIG. 8-3B shows a timelapse of trajectories of particles at same conditions. The lower frequency leads to a high stroke distance, causing particles to leave the trapping regions 159, resulting in lower system capacity and less stable trapping conditions.

[0192] FIG. 8-4 includes an image of an experiment on the microfluidic chip 100 of FIG. 8-1 for performing stable and effective trapping of CTC cancer cell line (MGH-BRX-142) at 10 pL / min and 75 Hz oscillation frequency. The image represents loading of few cells to enable each to be clearly seen. This cell line is described in Jordan NV, et al. “HER2 expression identifies dynamic functional states within circulating breast cancer cells,” Nature (2016) Sep 1 ;537(7618): 102- 106.

[0193] Example 3 - Use of MOAT for Culturing Circulating Tumor Cells (CTCs)

[0194] Example 3 provides an application of MOAT to Culturing CTCs using the microfluidic chip 100 of FIG. 9-1 and the microfluidic system 10 of FIG. 10A.

[0195] A platform for culture circulating tumor cells (CTCs) is crucial for advancing cancer research and personalized medicine. CTCs, which are shed from primary tumors into the bloodstream, provide valuable insights into cancer metastasis and tumor heterogeneity. Culturing CTCs allows for detailed studies on their biology, drug resistance / sensitivity, and genetic mutations, which can lead to the development of more targeted therapies. Furthermore, such platforms enable the expansion of rare CTCs, making it possible to perform various downstream analyses that would otherwise be limited due to their scarcity. This can ultimately enhance our ability to monitor disease progression and tailor treatments to individual patients, improving outcomes in cancer care.

[0196] Culturing CTCs presents several significant challenges. First, CTCs are extremely rare in the bloodstream, often occurring at a concentration of just a few cells per milliliter of blood, making their isolation and expansion difficult and the isolated product often has impurities (blood cells). Additionally, CTCs are highly heterogeneous, with diverse phenotypes and genotypes, which complicates the establishment of consistent culture conditions. Another major challenge is that CTCs tend to have a limited viability and proliferative capacity outside their native tumor environment, which makes sustaining long-term cultures difficult. Finally, mimicking the complex tumor microenvironment in vitro to maintain the physiological relevance of CTCs remains a hurdle, as the interactions between CTCs and their surrounding cells, extracellular matrix, and mechanical forces are difficult to replicate in a culture system.

[0197] Besides as a platform for suspension cell culture in general, the contactless MOAT enables experiments on continuous flow CTC culturing, providing a stable platform for establishing cancer cell lines. The system allows for media to be perfused into the channel at a flow rate as low as about 1 pL / min (which can effectively replenish the medium in an hour, compared to daily or less often cell passaging), eliminating the need for equipment like syringe pumps or pressure supplies. The perfusion of fresh media acts as a continuous washing step, effectively removing debris or extracellular vesicles shed by the cells and keep providing fresh media.

[0198] To achieve this, MOAT traps were designed to ensure low-capacity trapping, where only a single cell is confined at each site. This helps minimize unwanted cell-cell interactions, especially in scenarios where CTC samples may not be completely pure, such as when residual white blood cells (WBCs) are present after isolation from blood. Additionally, the design canprevent multiple cells from being trapped together at the same specific point in space, which could lead to cell aggregates or clusters — an undesirable outcome for clonal CTC culturing applications, where individual growth of CTC clones is preferred. We selected an array of square obstacles with a length and height of 100 pm between identically sized square islands to optimize the trapping mechanism by inducing wall effects. This size also ensures that the traps are small enough to accommodate a higher number of single-cell traps within a designated footprint, maximizing efficiency. The spacing between the squares was also set at 100 pm to provide adequate separation between each cell, preventing unwanted interactions. To address the issue of unwanted vortices that could form at the comers of the squares, the comers were rounded with a 5 pm radius.

[0199] Cells are efficiently trapped between two squares, approximately 50 pm from each, where they reach an equilibrium position due to balanced forces within the system. The optimal frequency for the oscillatory trap was found to be 75 Hz, which, combined with low flow rates, ensures that cells remain securely trapped. This design is crucial for maintaining individual cell trapping.

[0200] Similar to the L-shaped island structures 158, there is a high-capacity region designed at the outlet of the microchannel. This region acts as a secondary safeguard, ensuring that if any cells do not become trapped along the way in the rectangular array, they will be captured at the outlet. This design feature provides an additional layer of security, minimizing the risk of cell loss. By integrating this high-capacity region, even cells that might escape the initial traps are retained, enhancing the overall efficiency and reliability of the system for continuous CTC culturing.

[0201] FIGs. 9-2 to 9-5 are a series of images of experiments on the microfluidic chip of FIG. 9- 1. FIG. 9-2 shows individual particles between arrays of square-shaped microstructures 158 at flow rate 10 pL / min and frequency 75 Hz. FIG. 9-3 shows individual cells being trapped for the CTC culture application between arrays of square-shaped microstructures 158 at a flow rate of 10 pL / min and frequency of 75 Hz. FIG. 9-3 includes a 40X photograph of cells trapped between two square-shaped microstructures 158 at net flow rate of 10 pL / min and frequency of 75 Hz. Note that this device had 50 pm wide, 110 pm tall channels with 200 pm square-shaped microstructures 158 between them. FIG. 9-4 includes a 40X photograph of cells trapped between two square-shaped microstructures 158 at net flow rate of 10 pL / min and frequency of 75 HZ.Note that this microfluidic chip 100 had 50 pm wide, 1 10 pm tall intermediate microchannels 157 with 200 pm square-shaped microstructures 158 between them. Two cells are trapped in central cross region within the array, showing they do not leave the trap.OTHER EMBODIMENTS

[0202] While the subject matter has been described with reference to example embodiments, those of ordinary skill in the art will appreciate that certain substitutions, alterations, and / or omissions may be made to any aspect or embodiment, whether or not specifically described herein, without departing from the spirit and scope of the subject matter. Accordingly, the foregoing description is meant by way of example only and is not intended, and should not be utilized, to limit the scope of the subject matter.

Claims

What is claimed is:CLAIMS1. An oscillatory microfluidic system for trapping particles contained in a fluid flowing within a channel, the oscillatory microfluidic system comprising: the channel to conduct the fluid, wherein the channel comprises a longitudinal axis and one or more geometric features that provide at least one asymmetry along the longitudinal axis; a source of pressure or flow to move the fluid through the channel; a fluid oscillator to provide an oscillating pressure on the fluid within the channel; and a controller arranged and configured to transmit control signals to the fluid oscillator to generate a repeating oscillation flow profile of the fluid within the channel, wherein the repeating oscillation flow profile includes at least one step in a direction of net flow parallel to the longitudinal axis and at least one step in a direction opposite to the direction of net flow, such that fluid step lengths have a magnitude similar in size to a size of one of the one or more geometric features, thereby trapping the particles in one or more zones centered on the one or more geometric features within the channel.

2. The oscillatory microfluidic system of claim 1, wherein: the control signals to generate the repeating oscillation flow profile are determined by performing a simulation of an oscillatory flow of the fluid within the channel, and the simulation establishes that the fluid step lengths are of a magnitude that is about the same as the size of the geometric features if, in the simulation, the following constraints are satisfied: one or more fluid particle paths exist within the channel during the oscillatory flow of the fluid; and for each fluid particle path: a time-averaged magnitude of a relative acceleration along the fluid particle path, multiplied by a stroke duration of a cycle along the fluid particle path, is 10% or more of a time-averaged magnitude of a velocity along the fluid particle path,wherein the relative acceleration along the fluid particle is defined as a total acceleration of the fluid minus a transient rate of change of the velocity along the fluid particle path.

3. The oscillatory microfluidic system of claim 1, wherein the longitudinal axis is straight, and the one or more geometric features comprise at least an expansion or a contraction of the channel along the longitudinal axis.

4. The oscillatory microfluidic system of claim 1, wherein the longitudinal axis is curved, the one or more geometric features comprise a curve of the channel along the longitudinal axis, and the channel has a constant cross-section along the longitudinal axis.

5. The oscillatory microfluidic system of claim 1, wherein the longitudinal axis is straight, and the one or more geometric features comprise an array of polygonal microstructures, e.g., L- shaped, rectangular, or square microstructures, arranged within the channel along the longitudinal axis.

6. The oscillatory microfluidic system of any one of claims 1-5, wherein the source comprises a syringe pump or a hydrostatic pressure system.

7. The oscillatory microfluidic system of any one of claims 1 to 7, wherein the fluid oscillator further comprises a pulse generator.

8. The oscillatory microfluidic system of any one of the preceding claims, wherein the magnitude of the fluid step lengths is between 1 and 5 times, e.g., between 2 and 3 times, the size of one of the one or more geometric features.

9. The oscillatory microfluidic system of any one of the preceding claims, wherein the dimensions of the channel are configured and the flow rate of the fluid within the channel is controlled such that a particle Reynolds number of the particles within the channel is from 0.01 to 10, e.g., from 0.1 to 1.

10. The oscillatory microfluidic system of any one of the preceding claims, wherein the dimensions of the channel are configured and the flow rate of the fluid within the channel is controlled such that Womersley number within the channel is from 0.1 to 10, e.g., from 1 to 3.

11. The oscillatory microfluidic system of any one of the preceding claims, wherein a frequency of the oscillating pressure is from 0.01 Hertz to 800 Hertz, e.g., 0.1 Hertz to 500 Hertz, or 1.0 Hertz to 150 Hertz.

12. A microfluidic chip, comprising: a planar surface; and a superstate disposed on the planar surface, the superstate and planar surface defining a microfluidic structure comprising: a first port and a second port; and a fluidic lumen extending from the first port to the second port along a longitudinal axis parallel to the planar surface, the fluidic lumen comprising one or more geometric features that provide at least one asymmetry along the longitudinal axis, wherein the one or more geometric features within the fluidic lumen comprise: a first channel extending from the first port along the longitudinal axis, the first channel having a first height from the planar surface; a second channel extending to the second port along the longitudinal axis, the second channel having a second height from the planar surface that is greater than the first height; and a bridging expansion between the first and second channels, the bridging expansion having a third height from the planar surface that increases from the first height to the second height along the longitudinal axis.

13. The microfluidic chip of claim 12, wherein the third height increases linearly from the first height to the second height at an acute angle from the planar surface.

14. The microfluidic chip of claim 12, wherein the third height increases from the first height to the second height in a plurality of discrete steps having increasingly greater heights from the planar surface.

15. The microfluidic chip of any one of claims 12-14, wherein the first and second channels each extend linearly along the longitudinal axis.

16. The microfluidic chip of any one of claims 12-15, wherein the fluidic lumen has a width in a direction parallel to the planar surface and orthogonal to the longitudinal axis, and the width is greater than both the first height and the second height.

17. A microfluidic chip, comprising: a planar surface; and a superstate disposed on the planar surface, the superstate and planar surface defining a microfluidic structure comprising: a first port and a second port; and a channel extending from the first port to the second port along a longitudinal axis parallel to the planar surface, wherein the channel comprises a plurality of geometric features in the form of an array of polygonal microstructures arranged along the longitudinal axis to provide a plurality of asymmetries within the channel along the longitudinal axis.

18. The microfluidic chip of claim 17, wherein each polygonal microstructure in the array is an L-shaped, rectangular, or square microstructure, arranged within the channel along the longitudinal axis.

19. The microfluidic chip of any one of claims 12-18, further comprising a substrate having the planar surface, e.g., wherein the substrate is transparent, e.g., wherein the substrate is a glass slide.

20. The microfluidic chip of any one of claims 12-19, wherein the superstrate is 3D-printed.21 . An oscillatory microfluidic system, comprising: the microfluidic chip of any one of claims 12-20; a first tube connected to the first port of the microfluidic chip; a second tube connected to the second port of the microfluidic chip; a source of pressure or flow to move a fluid comprising particles through the one or more channels of the microfluidic chip; a fluid oscillatory system to provide an oscillating pressure on the fluid within the one or more channels; and a controller arranged and configured to transmit control signals to the fluid oscillatory system to generate a repeating oscillation flow profile of the fluid within the one or more channels, wherein the repeating oscillation flow profile includes at least one step in a direction of net flow parallel to the longitudinal axis and at least one step in a direction opposite to the direction of net flow, such that fluid step lengths have a magnitude similar in size to a size of one of the one or more geometric features, thereby trapping the particles in one or more zones centered on the one or more geometric features within the channel.

22. The oscillatory microfluidic system of claim 21, wherein the fluid oscillatory system is mechanically coupled to any one or more of the first tube, the second tube, or the microfluidic chip.

23. The oscillatory microfluidic system of claim 22, wherein the fluid oscillatory system comprises one or more speakers.

24. A method for implementing a microfluidic oscillatory asymmetrical trap (MOAT), the method comprising: providing the microfluidic chip of any one of claims 12-20; moving a fluid comprising particles between the first and second ports of the microfluidic chip; and imparting oscillations to the fluid flowing within the one or more channels within the microfluidic chip.

25. The method of claim 24, wherein moving the fluid between the first and second ports of the microfluidic chip comprises applying a pressure via a syringe pump or a hydrostatic pressure system.

26. The method of claim 24, wherein moving the fluid between the first and second ports of the microfluidic chip comprises: attaching a first tube to the first port of the microfluidic chip; attaching a second tube to the second port of the microfluidic chip; moving the fluid into the first or second tube; and applying a source of pressure or flow to the first or second tube to move the fluid between the first and second tubes.

27. The method of any one of claims 24-26, wherein imparting the oscillations to the fluid comprises coupling a fluid oscillatory system to any one or more of a length of the first tube, a length of the second tube, or the microfluidic chip, and activating the fluid oscillatory system to impart the oscillations to the fluid in the first tube, the second tube, or the microfluidic chip.

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