Hydrodynamic separator with ideal micro-channel length

Description

1 / 37 “HYDRODYNAMIC SEPARATOR WITH IDEAL MICROCHANNEL LENGTH” Technology Field

[001] The present disclosure relates generally to hydrodynamic separators. More particularly, the present disclosure relates to hydrodynamic separators with an ideal microchannel length. Background

[002] Hydrodynamic separators are used in a variety of industries for the concentration and / or separation of particles in fluid streams, such as hydrocarbon liquids, beverages, aqueous solutions, and the like. Particles suspended in the fluid can cause problems in system processes (such as, for example, in fuel or hydraulic systems), may be generally undesirable for consumers (e.g., pulp in orange juice or impurities in beer or wine), or may be subjected to processing steps different from the fluid (such as in wastewater treatment). It may be desirable to design such hydrodynamic separators to achieve adequate particle separation with minimal pressure drop to improve particle separation and efficiency in terms of both energy expenditure and time. Summary

[003] Some embodiments of the technology disclosed in this document relate to a hydrodynamic separator. The hydrodynamic separator is configured to separate a liquid that has dispersed particles having a diameter (a). The hydrodynamic separator has a substrate and a liquid channel defined by the substrate. The liquid channel has an inlet and an outlet. The liquid channel is configured to receive a liquid that has a Reynolds number (Re) within the channel. The liquid channel is curved to define an inner radius (Rc) and has a liquid channel length (Ld) along the curve. The liquid channel has a Petition 870230043709, dated 05 / 24 / 2023, page 11 / 59 2 / 37 rectangular cross-section along the length of the curve, and the rectangular cross-section has a height, a width (w), and a hydraulic diameter (Dh). The liquid channel length (Ld) is greater than or equal to a linear focusing length (Lf), where Lf = 1598.8η^τ + 6.4·

[004] In several embodiments, such a system is configured to have a Dean number (De) between 5 and 25. Additionally or alternatively, the particle diameter (a) is greater than 8% of the hydraulic diameter (Dh). Additionally or alternatively, the liquid channel length (Ld) is not more than 40% greater than the linear focusing length (Lf). Additionally or alternatively, the liquid channel length (Ld) is not more than 30% greater than the linear focusing length (Lf). Additionally or alternatively, the particles are up to three times denser than the liquid. Additionally or alternatively, the outlet comprises a first outlet and a second outlet. Additionally or alternatively, the liquid channel is one among a plurality of identical liquid channels.Alternatively, the liquid channel has a first region with a first channel width and a second region with a second channel width, and a tapered region extending from the first channel width to the second channel width.

[005] Some embodiments disclosed in this document relate to a hydrodynamic separator configured to separate a liquid that has dispersed particles. The hydrodynamic separator has a substrate and a liquid channel defined by the substrate, wherein the liquid channel has an inlet and an outlet. The liquid channel is configured to receive a liquid that has a Reynolds number (Re) within the channel. The liquid channel is curved to define an inner radius (Rc) and has a liquid channel length (Ld) along the curve. The liquid channel has a rectangular cross-section along the length of the curve, wherein the rectangular cross-section has a height, a width (w), and a hydraulic diameter (Dh). Petition 870230043709, dated 05 / 24 / 2023, page 12 / 59 3 / 37 The liquid channel length (Ld) is greater than or equal to a linear focusing length (Lf), where Lf = 156.2 ^^(^H~) + 24.3.

[006] In several embodiments, such a system is configured to have a Dean number (De) between 5 and 25. Additionally or alternatively, the particle diameter (a) is greater than 8% of the hydraulic diameter (Dh). Additionally or alternatively, the liquid channel length (Ld) is not more than 40% greater than the linear focusing length (Lf). Additionally or alternatively, the liquid channel length (Ld) is not more than 30% greater than the linear focusing length (Lf). Additionally or alternatively, the particles are up to three times denser than the liquid. Additionally or alternatively, the outlet comprises a first outlet and a second outlet. Additionally or alternatively, the liquid channel is one among a plurality of identical liquid channels.Alternatively, the liquid channel has a first region with a first channel width and a second region with a second channel width, and a tapered region extending from the first channel width to the second channel width.

[007] Some embodiments refer to a hydrodynamic separator configured to separate a liquid that has dispersed particles that have a diameter (a). The hydrodynamic separator has a substrate and a liquid channel defined by the substrate, wherein the liquid channel is configured to receive a liquid that has a Reynolds number (Re) within the channel. The liquid channel has an inlet and an outlet, and the liquid channel is curved to define an inner radius (Rc) and has a liquid channel length (Ld) along the curve. The liquid channel has a rectangular cross-section along the length of the curve. The rectangular cross-section has a height, a width (w), and a hydraulic diameter (Dh). The liquid channel length (Ld) is greater than or equal to a linear focusing length (Lf), and Lf = ---h 24.3. 8 8 dh Petition 870230043709, dated 05 / 24 / 2023, page 13 / 59 4 / 37

[008] In several embodiments, such a system is configured to have a Dean number (De) between 5 and 25. Additionally or alternatively, the particle diameter (a) is greater than 8% of the hydraulic diameter (Dh). Additionally or alternatively, the liquid channel length (Ld) is not more than 40% greater than the linear focusing length (Lf). Additionally or alternatively, the liquid channel length (Ld) is not more than 30% greater than the linear focusing length (Lf). Additionally or alternatively, the particles are up to three times denser than the liquid. Additionally or alternatively, the outlet comprises a first outlet and a second outlet. Additionally or alternatively, the liquid channel is one among a plurality of identical liquid channels.Alternatively, the liquid channel has a first region with a first channel width and a second region with a second channel width, and a tapered region extending from the first channel width to the second channel width.

[009] Some embodiments refer to a hydrodynamic separator configured to separate a liquid that has dispersed particles having a particle diameter (a). The hydrodynamic separator has a substrate and a liquid channel defined by the substrate. The liquid channel is configured to receive a liquid that has a Reynolds number (Re) within the channel, and the liquid channel has an inlet and an outlet. The liquid channel is curved to define an inner radius (Rc) and has a liquid channel length (Ld) along the curve around a central geometric axis. The liquid channel has a rectangular cross-section along the length of the curve, wherein the rectangular cross-section has a height, a width (w), and a hydraulic diameter (Dh). The liquid channel has a focusing angle (α) around the central geometric axis, wherein α = 265.6823+ 45.1. The liquid channel extends circumferentially around the central geometric axis to an arc measurement greater than or equal to the focusing angle α. Petition 870230043709, dated 05 / 24 / 2023, p. 14 / 59 5 / 37

[010] In several embodiments, such a system is configured to have a Dean number (De) between 5 and 25. Additionally or alternatively, the particle diameter (a) is greater than 8% of the hydraulic diameter (Dh). Additionally or alternatively, the arc measurement is no more than 40% greater than the focusing angle. Additionally or alternatively, the arc measurement is greater than 360 degrees, and the liquid channel defines a helix. Additionally or alternatively, the arc measurement is less than 360 degrees. 12. Additionally or alternatively, the particles are up to three times denser than the liquid. Additionally or alternatively, the outlet comprises a first outlet and a second outlet. Additionally or alternatively, the liquid channel is one among a plurality of identical liquid channels.Alternatively, the liquid channel has a first region with a first channel width and a second region with a second channel width, and a tapered region extending from the first channel width to the second channel width.

[011] Some embodiments refer to a hydrodynamic separator configured to separate a liquid that has dispersed particles that have a diameter (a). The separator has a substrate and a liquid channel defined by the substrate. The liquid channel is configured to receive a liquid that has a Reynolds number (Re) within the channel. The liquid channel has an inlet and an outlet. The liquid channel has a curved inner wall that defines an inner radius (Rc) and a curved outer wall that defines an outer radius. The liquid channel has a liquid channel length (Ld) along the curved inner wall. The liquid channel has a rectangular cross-section along the liquid channel length. The rectangular cross-section has a channel width (w) between the inner wall and the outer wall, where the channel has a tapered region in which the channel width tapers between the inlet and the outlet.

[012] In some such modes, the channel width increases towards Petition 870230043709, dated 05 / 24 / 2023, page 15 / 59 6 / 37 at the outlet. Alternatively, the channel width increases at a constant rate between the inlet and the outlet. Alternatively, the channel width decreases towards the outlet. Alternatively, the inner radius is constant from inlet to outlet. Alternatively, the outer radius tapers outwards between inlet and outlet. Alternatively, the liquid channel has: a first region that has a first channel width and a first liquid channel length, a second region that has a second channel width and a second liquid channel length, and the tapered region that has a tapered region length extending from the first region to the second region. In some such embodiments, the first region has a greater length than the second region.

[013] Alternatively, the system is configured to have a Dean number (De) between 5 and 25 in the first region and in the second region. Alternatively, the particles are up to three times denser than the liquid. Alternatively, the outlet has a first outlet and a second outlet. Alternatively, the liquid channel is one among a plurality of identical liquid channels. Alternatively, the particle diameter (a) is greater than 8% of the hydraulic diameter (Dh) of the first region and the hydraulic diameter of the second region.

[014] The above summary is not intended to describe each embodiment or all implementations. Instead, a fuller understanding of the illustrative embodiments will be made more evident and understood with reference to the following Detailed Description of Exemplary Embodiments and claims in view of the accompanying figures of the drawings. Brief Description of the Drawings

[015] Figure 1 is a schematic representation of an exemplary hydrodynamic separator system consistent with the embodiments. Petition 870230043709, dated 05 / 24 / 2023, page 16 / 59 7 / 37

[016] Figure 2 is a cross-sectional view of the liquid channel in Figure 1.

[017] Figure 3 is a plot representing the focusing of particles along the length of a liquid channel.

[018] Figure 4 is a plot of typical radial flow profiles for different Dean numbers consistent with a liquid channel.

[019] Figure 5 is a plot of experimental results against an equation from the prior art that defines the radial flow velocity.

[020] Figure 6 is a plot of experimental results against a new equation that defines radial flow velocity.

[021] Figure 7 is a plot of experimental results against a first equation that defines the focusing length of particles.

[022] Figure 8 is a plot of experimental results against a second equation that defines the focusing length of particles, where the second equation takes particle size into account.

[023] Figure 9 is a plot of experimental results against a third equation that defines the arc measurement of the liquid channel.

[024] Figure 10 is a schematic diagram representing an exemplary hydrodynamic separator with a helical liquid channel.

[025] Figure 11 is a front view of the exemplary hydrodynamic separator of Figure 10.

[026] Figure 12 is another illustrative system consistent with the modalities.

[027] The present technology can be more fully understood and observed by considering the following detailed description of various embodiments in connection with the attached drawings.

[028] The figures are presented primarily for clarity and, as Petition 870230043709, dated 05 / 24 / 2023, page 17 / 59 8 / 37 result, are not necessarily drawn to scale. Furthermore, various structures / components, including but not limited to fasteners, electrical components (wiring, cables, etc.), and the like, may be shown diagrammatically or removed from some or all views to better illustrate aspects of the embodiments represented, or when the inclusion of such structures / components is not necessary for understanding the various exemplary embodiments described in this document. The lack of illustration / description of such structures / components in a particular figure, however, should not be interpreted as limiting the scope of the various embodiments in any way. Detailed description

[029] Hydrodynamic separators are microfluidic devices capable of focusing particles within a fluid stream based solely on the forces due to internal fluid flow. Particles can be separated from a portion of the fluid stream and / or separated from particles of other sizes within the fluid stream. The hydrodynamic separator generally defines a fluid channel that has an inlet and an outlet with at least two flow branches. Particles within a particle size range can be focused, or concentrated, in one of the two flow branches. For example, particles exceeding a limiting size range are focused in one of the two flow branches. The concentrated portion of the fluid stream can be removed from the system or retained for further processing. Any remaining particles can flow through at least two flow branches.

[030] Figure 1 is a schematic representation of an exemplary system 10 consistent with some implementations of the technology disclosed in this document. System 10 is a hydrodynamic separator system that is configured to focus particles that are suspended in a fluid stream. System 10 has a hydrodynamic separator 100 that has an inlet 122 Petition 870230043709, dated 05 / 24 / 2023, page 18 / 59 9 / 37 and an outlet 124. A fluid pump 30 creates a fluid communication between a fluid source 20 and the hydrodynamic separator 100. In particular, the fluid pump 30 is configured to pump fluid from the fluid source 20 through an inlet flow channel 40 to the inlet 122 of the hydrodynamic separator 100. The fluid is configured to flow through a liquid channel 120 of the hydrodynamic separator 100 to the outlet 124. A first outlet branch 50 and a second outlet branch 52 may lead from the outlet 124 to other systems or system components. In some embodiments, the fluid flowing through the first outlet branch 50 is configured to have a higher concentration of particles within a particular size range compared to the fluid flowing through the second outlet branch 52.

[031] The hydrodynamic separator consistent with the technology disclosed herein is generally constructed from a substrate 110. The substrate 110 defines the liquid channel 120 therein. The substrate may be constructed from a variety of different materials and combinations of materials. The substrate may be polymeric in some embodiments. In some examples, the substrate is polydimethylsiloxane (PDMS). In some embodiments, the substrate may include glass. In some embodiments, the substrate may include a non-reactive metal. In some embodiments, the substrate may include one or more adhesive layers, such as a pressure-sensitive adhesive. In some embodiments, the substrate may be two or more materials, so that the channel walls may be two or more materials.

[032] Liquid channel 120 is generally configured to accommodate liquid flow. Liquid channel 120 defines inlet 122 and outlet 124. Liquid channel 120 defines a channel length Ld from inlet 122 to outlet 124. Liquid channel 120 is generally curved to define an inner radius Rc around a central geometric axis x. Thus, liquid channel 120 extends Petition 870230043709, dated 05 / 24 / 2023, page 19 / 59 10 / 37 circumferentially around the central geometric axis x to define a channel arc measure. In the current example, the 120 liquid channel extends approximately 180° around the central geometric axis x. In the current example, the inner radius Rc is substantially constant along the channel length, but in some other examples, the inner radius Rc may vary.

[033] Liquid channel 120 generally has a rectangular cross-section along the channel length, which is visible in Figure 2. The cross-section of liquid channel 120 is generally perpendicular to the direction of fluid flow through channel 120. Channel 120 has a height (h) which is visible in Figure 2, and a width (w) which is visible in both Figures 1 and 2. Channel 120 also has a hydraulic diameter (Dh). The following equation is used to calculate the hydraulic diameter of a microfluidic channel that has a rectangular cross-section: x height x width

[034] The liquid channel 120 can be formed on the substrate 110 through molding, photolithography, and 3D printing operations, as examples. In some examples, the liquid channel 120 is formed on the substrate 110 through injection molding or embossing of plastics. Other approaches can also be used to form the liquid channel 120. In several embodiments, the hydrodynamic separator 100 defines a plurality of liquid channels 120 that are configured to operate in parallel. In several embodiments, the hydrodynamic separator 100 has at least 10 liquid channels. In several embodiments, the hydrodynamic separator 100 has at least 50 liquid channels or at least 100 liquid channels.

[035] In some embodiments where the hydrodynamic separator 100 has a plurality of liquid channels, a liquid channel 120 may be defined within a single substrate layer. In some such embodiments, multiple substrate layers may be arranged in a stacked configuration, such that each of the plurality of liquid channels 120 defined for each layer Petition 870230043709, dated 05 / 24 / 2023, page 20 / 59 11 / 37 of the substrate is also in a stacked configuration. The stacked layers of substrate and the liquid channels 120 form the hydrodynamic separator 100. The hydrodynamic separator 100 can define the inlet flow channel 40 upstream of and in direct fluid communication with each of the microfluidic channel inlets (such as inlet 122). The inlet flow channel 40 will generally have a hydraulic diameter that is larger than the hydraulic diameter of each of the liquid channels 120. The hydrodynamic separator 100 can define the first outlet branch 50 and the second outlet branch 52, which are both positioned downstream of and in direct fluid communication with each outlet 124. Each of the first outlet branch 50 and the second outlet branch 52 will generally have a diameter that is larger than the hydraulic diameter of each of the liquid channels. Such a configuration can advantageously equalize the flow through the channels.

[036] Liquid channel 120 is configured to receive a liquid that has a Reynolds number (Re) within the liquid channel. Fluid flow within a curved channel is described by two dimensionless numbers, the Reynolds number and the Dean number. The Reynolds number describes the ratio between inertial forces and viscous forces and is defined as follows: DpUDHRe =---P where ρ is the fluid density, U is the average fluid velocity, and μ is the dynamic viscosity of the fluid. In hydrodynamic separators, the Reynolds number is typically small (<1000), meaning the flow profile is laminar. In several embodiments, the system is configured to have a Dean number (De) between 5 and 25. In several embodiments, the system is configured to have a Dean number between 5 and 20. The Dean number describes the behavior of fluids in a curved tube and considers inertial forces, centripetal forces, and viscous forces acting on the fluid. The Dean number is defined as follows: Petition 870230043709, dated 05 / 24 / 2023, p. 21 / 59 12 / 37 De = Re 1^22 R<

[037] The hydrodynamic system 10 is generally configured to focus particles in the liquid channel 120. As used in this document, the term “particle” refers to a discrete quantity of material that is dispersed in a fluid. Non-limiting examples of material that can be formed particles include dirt, metal, cells, air bubbles, and water droplets. In one specific example, water droplets can be dispersed in a hydrocarbon fluid, such as gasoline or diesel fuel, to form an emulsion. In another example, air bubbles can be dispersed in a hydraulic fluid. In yet another example, cells can be dispersed in an aqueous fluid. In still other examples, particles can be pulp in orange juice, fat in milk, and impurities in beer or wine.

[038] In several implementations, the hydrodynamic separator 100 is configured to focus particles that have a diameter greater than 8% of the hydraulic diameter of the liquid channel 120. Particles whose diameter is greater than 8% of the hydraulic channel diameter are generally focused towards the inner wall when the Dean number is in the range of 5 to 25. The hydrodynamic separator is generally configured to focus particles that have a diameter that is less than or equal to 50% of the channel height. In several examples, for the purposes of calculations provided in this document, the particles have a sphericity greater than 0.5. For non-spherical particles, for the purposes of calculations provided in this document, the particle diameter is considered to be the equivalent spherical diameter.In various embodiments, hydrodynamic separators consistent with the technology disclosed in this document are configured to focus particles that have a density up to three times greater than the liquid in liquid channel 120.

[039] Particle focusing occurs in two distinct stages. The first Petition 870230043709, dated 05 / 24 / 2023, p. 22 / 59 Stage 13 / 37 is a particle migration stage in which suspended particles migrate through the liquid channel 120 to the edges of the liquid channel 120. The particle migration stage generally begins at the liquid channel inlet 122 and extends for a particle migration length Lo of the liquid channel 120 to define the particle migration region 126 of the liquid channel 120. In this region, no further focusing on the inner wall 121 of the liquid channel 120 is observed. The second region is a linear focusing region 128 in which the amount of focusing on the inner wall 121 increases linearly along the channel length. Focusing continues until maximum particle focusing is achieved. No further focusing is observed after maximum particle focusing is achieved.The linear focusing region 128 has a linear focusing length Lf, which is the length required to achieve maximum particle focusing. The linear focusing region 128 generally extends from the particle migration region 126 towards the channel outlet 124.

[040] The length of the liquid channel 120 after the linear focusing region 128 is termed the fully focused region 130. The fully focused region 130 has a width that extends from the linear focusing region 128 to the outlet 124. In various implementations, it may be desirable to limit or eliminate the fully focused region 130 in order to decrease the system's energy requirements by reducing the pressure drop across the liquid channel 120 while still achieving maximum particle focusing.

[041] Figure 3 is a graph showing representative focusing behavior demonstrating the three stages of particle focusing along the length of the curved liquid channel. The particle migration region 126 represents approximately the first 16 mm of the channel length, and the linear focusing region 128 follows. In this example, the focusing region Petition 870230043709, dated 05 / 24 / 2023, page 23 / 59 The 14 / 37 linear 128 achieves maximum particle focusing at approximately 114 mm along the length of the liquid channel. Once the maximum particle orientation value is reached, the particle orientation can remain approximately constant. This region of the device is considered the fully focused region 130. In this example, the maximum focusing percentage in the fully focused region is approximately 90% (i.e., 90% of the particles are focused).

[042] Mathematically, the length of the linear focusing region required to achieve maximum particle focusing in a curved channel (such as that shown in Figure 1) is a linear function based on the radial component of the particle velocity through the channel. According to the existing literature (see, for example, Di Carlo, D., Irimia, D., Tompkins, RG, Toner, M.; Continuous Inertial Focusing, Ordering, and Separation of Particles in Microchannels. Proceedings of the National Academy of Sciences of the USA, Nov. 2007, Volume 104, No. 4, 18892-7.), the magnitude of the radial component of Dean's flow profile, or the linear focusing ratio Ud, is as follows: De2μ PDh

[043] This relationship was tested in rectangular channels using computational fluid dynamics in STAR-CCM+ software by Siemens PLM Software based in Plano, Texas. To measure the radial flow component, a function probe was inserted at the center of the virtual fluid domain, aligned with the channel depth (in the Z direction) at distinct radial positions along the primary fluid flow direction. An exemplary series of typical radial flow profiles is shown in Figure 4, where the radial velocity is a function of the depth through the center of the channel. The flow profiles shown are of a single device geometry and fluid combination through varying Dean numbers, but with constant channel height h (150 pm), width w (500 pm), and inner radius Rc (20 mm). In this Petition 870230043709, dated 05 / 24 / 2023, page 24 / 59 15 / 37 coordinate system, positive flow velocities indicate that the fluid is moving towards the outer wall of the device, while negative flow velocities indicate that the fluid is moving towards the inner wall of the device. At the center of the channel depth, the maximum radial flow component is observed. This corresponds to the maximum velocity towards the outer wall due to the fluid's inertia. There are two minimum radial flow components, symmetrically observed above and below the center of the channel depth. These flow components are the recirculation flow towards the inner wall, which are ultimately responsible for passively moving the particles to the final focusing position.

[044] The minimum radial flow velocities for different liquid channel widths at four different Dean numbers (De = 5, 10, 15, 20) were plotted against the literature equation for the magnitude of the radial component of the Dean flow profile, which is reflected in Figure 5. As can be seen, the equation does not define a linear relationship across different liquid channel widths and thus is not an accurate predictor of radial velocity. Over the course of further testing and analysis, the following relationship was found for the linear focusing rate Ud: De2μ UD--Z pw

[045] This equation was plotted against the minimum radial velocity, and the results are reflected in Figure 6. As can be seen, the data from devices with different liquid channel widths collapse into a single linear curve. This relationship remains true when the device geometry (width, height, and Rc) and fluid properties (viscosity and density) are changed within the range of Dean numbers relevant for hydrodynamic separators (5 <De< 25). Especificamente, a velocidade radial mínima mostrou ser a seguinte: UD= -0.02597 *^-^- 1.107 * 10 ~4pw where μ is in cP, w is in microns, p is g / cm3 and Ud is in m / s. Petition 870230043709, dated 05 / 24 / 2023, page 25 / 59 16 / 37

[046] Based on the minimum radial velocity, an equation to determine the length of the linear focusing region to obtain maximum particle focusing can be derived. The velocity through the width of the liquid channel is nearly constant, thus the time a particle takes to travel the width of the liquid channel to the inner wall is: ww 2p ix — = —z— UDDe2p

[047] Thus, the length of the linear focusing region is: w2pl>*w=d£1Uem where U is the average downstream velocity of the fluid. Substitution in Reu 11=-^PDh produces: Re w22RC / w \2Lf k5^2 1H = ^^(^Hi)e, more specifically, Rr(w \2L'=156·2«CG^+ 243

[048] The linear focusing region is generally shorter at a higher Dean number, and, due to the fact that the operating range for a hydrodynamic separator consistent with the technology disclosed herein is a Dean number in the range of 5 to 25, the linear focusing length Lf will generally be a minimum of Rew2L'=— '243

[049] Using the particle focusing ratio (i.e., the slope of the linear focusing region), the length required to focus an additional 80% of the particles was calculated. An additional 80% of particles being focused could lead to a focusing efficiency of over 90% due to the fact that, at the device entrance, 10-20% of the particles are already in the focusing position. The observed focusing length associated with the results Petition 870230043709, dated 05 / 24 / 2023, page 26 / 59 17 / 37 experimental data was plotted against the focusing length equation Lf above, which is reflected in Figure 7. The error bars correspond to the standard error based on the uncertainty in the slope of the linear focusing region. This fit shows a clear trend, dominated by changes in device width and radius of curvature. Closer observation of the data suggests that the focusing length Lf depends on particle size. Specifically, smaller particles focus faster than larger particles. In fact, particles of different sizes experienced different lifting forces, and thus traverse the width of the device at different heights. It was found that considering the linear focusing length Lf and multiplying it by the particle confinement (a / Dh) produces Rcaw2 Lfk-----=fReD2e, more specifically, Rraw2Lf= 1598.8c, + 6.4fReD2, which is plotted against the observed experimental focusing lengths as reflected in Figure 8. The data collapsed into a linear fit yield an R2 value greater than 0.95.

[050] Instead of being described in terms of the length of the linear focusing region Lf, the linear focusing region can also be described in terms of the focusing angle (α), which is the arc measure of the linear focusing region 128 around the central geometric axis x: aw2nReDH3, or more specifically, α = 265.682 aw + 45.1 nReDH3, which is plotted against the experimental data in Figure 9. As demonstrated, several liquid channels consistent with the technology revealed in Petition 870230043709, dated 05 / 24 / 2023, page 27 / 59 18 / 37 of this document require a focusing angle greater than 360 degrees, indicating that complete focusing cannot occur with a “simple” hydrodynamic separator, where a “simple” hydrodynamic separator is one in which the liquid channel is less than a complete revolution around the central geometric axis x. Liquid channels that completely focus particles within one revolution around the central geometric axis x generally have a small width, a high Reynolds number, and a large hydraulic diameter.

[051] A series of experiments was conducted that measured the actual particle migration length L0 and the particle focusing length Lf of various hydrodynamic systems consistent with the technology disclosed in this document. Hydrodynamic separators of varying device heights and widths were created from PDMS and glass slides using standard methods. Fluorescently labeled particle solutions were introduced into the hydrodynamic separator channel at known flow rates within Dean numbers of 5–25. Images were taken at various locations along the hydrodynamic separator using a CMOS camera. Image processing was used to identify particle concentration as a function of channel position and length. The particle focusing length Lf was also calculated in accordance with the equations provided above. The results are reflected in Table 1 below.___________________________________. No. Experimental Lo (mm) Experimental Lf (mm) (Lo / (Lo+Lf )) Experimental Lo / Lf Lf 156.2 ^(^-}2 Re\Dh) + 24.3 Lf - □□ a ' 2 1598.8 □ , □ □□□ + 6, 4 1 13 381 3.30 % 3.4 % 395 370 2 0 87 0 % 0 % 82 110 3 13.5 140 8.70 % 9.6 % 145 148 4 16.5 138 10.70 % 12.0 % 105 101 5 20.7 286 6.70% 7.2% 271 297 6 5.9% 58 9.10% 10.2% 62 69 7 19.4% 68 22.30% 28.5% 50 48 8% 7% 222 3.10% 3.2% 161 188 Petition 870230043709, dated 05 / 24 / 2023, page 28 / 59 19 / 37 9 16.5 133 11.00% 12.4% 136 155 10 5.2 133 3.80% 3.9% 99 105 11 18.9 65 22.50% 29.1% 77 76 12 12.6 61 17.20% 20.7% 64 59 13 16.9 62 21.50% 27.3% 103 76 14 18.5 47 28.20% 39.4% 77 53 15 12.6 44 22.30% 28.6% 64 41 16 30.8 138 18.30% 22.3% 174 168 Table 1

[052] Through experimental results, the particle focusing length Lf was greater than the particle migration length Lo. The particle migration length Lo ranged from 0% of the total liquid channel length Ld to 28.2% of the total liquid channel length Ld. Furthermore, the particle migration length L0 ranged from 0% of the particle migration length Lf to 39.4% of the particle migration length Lf. Thus, in some embodiments, liquid channels consistent with the technology disclosed herein will have a liquid channel length Ld that is approximately equal to the particle migration length Lf. In several embodiments, liquid channels consistent with the technology disclosed herein will have a liquid channel length Ld that is greater than the particle migration length Lf.Based on the data collected, it appears that, in many embodiments, the liquid channel length Ld is less than 40% greater than the particle migration length Lf. The liquid channel length Ld may be less than or equal to 30% greater than the particle migration length Lf. The liquid channel length Ld may be less than or equal to 20% greater than the particle migration length Lf. In some embodiments, the liquid channel length Ld may be 3% to 20% greater than the particle migration length Lf.

[053] Figures 10 and 11 show a schematic view of another exemplary hydrodynamic separator 200 consistent with some embodiments. Figure 10 Petition 870230043709, dated 05 / 24 / 2023, page 29 / 59 Figure 20 / 37 is a schematic perspective view, and Figure 11 is a schematic front view of the inlet side of the hydrodynamic separator, wherein the liquid channel 220 is represented by dashed lines. The hydrodynamic separator 200 is generally consistent with the descriptions above, except where contradictory. The hydrodynamic separator 200 is configured to focus particles that are dispersed in a liquid stream. The hydrodynamic separator 200 is constructed from a substrate 210. The substrate 210 defines a liquid channel 220 that has an inlet 222 and an outlet 224. The liquid is configured to flow through the liquid channel 220 of the hydrodynamic separator 200 from inlet 222 to outlet 224.

[054] Liquid channel 220 defines a channel length Ld from inlet 222 to outlet 224. Liquid channel 220 is generally curved to define an inner radius Rc around a central geometric axis x. Thus, liquid channel 220 extends circumferentially around the central geometric axis x to define a channel arc measure. In the present example, liquid channel 220 extends approximately 810° around the central geometric axis x. In the present example, the inner radius Rc is substantially constant along the channel length. In the present example, liquid channel 220 forms a helix around the central geometric axis x. The helical arrangement of liquid channel 220 accommodates both a constant inner radius Rc and multiple revolutions around the central geometric axis x. In some embodiments, however, the inner radius is not constant.

[055] Liquid channel 220 generally has a rectangular cross-section along the channel length, which is visible in Figure 11 at inlet 222. The cross-section of liquid channel 220 is generally perpendicular to the direction of fluid flow through channel 220. Channel 220 has a height (h) which is visible in Figure 2, and a width (w) which is visible in Figure 11. Channel 220 also has a hydraulic diameter (Dh) as revealed.

[056] Similar to the examples discussed above, focusing on Petition 870230043709, dated 05 / 24 / 2023, page 30 / 59 21 / 37 particles can occur in two distinct stages. To optimize the liquid channel length Ld, a completely focused region must be avoided, so that the entire length of the liquid channel is the particle migration length Lo and the particle focusing length Lf. The optimization of the liquid channel length Ld and / or the arc measurement should generally be consistent with the discussion above.

[057] In several embodiments, such as those consistent with the examples in Figures 1-2 and 10-11, the liquid channel dimensions, such as height h, width w, and inner radius Rc, are substantially constant along the length of the liquid channel, meaning that such dimensions do not vary beyond 5% of the weighted average value of the dimension along the length of the liquid channel. The equations provided in this document are, in general, for optimizing a length of liquid channel where the liquid channel has a substantially constant inner radius Rc. In some embodiments, the channel width w is not substantially constant along the length of the channel. In such embodiments, the weighted average of the channel width w along the channel length can be used in the equations provided in this document for optimizing the length of the liquid channel.In several examples, the optimized channel length can be based on the weighted average of the channel dimensions within the focusing region.

[058] Figure 12 is a schematic representation of yet another exemplary hydrodynamic separator system consistent with some embodiments. The system has a fluid source 20, a pump, an inlet flow channel 40 and outlet flow branches 50, 52 as discussed above with reference to Figure 1. The system has a hydrodynamic separator 300 which is, in general, consistent with the descriptions above, except where contradictory. The hydrodynamic separator 300 is configured to focus particles that are dispersed in a Petition 870230043709, dated 05 / 24 / 2023, page 31 / 59 22 / 37 liquid stream. The hydrodynamic separator 300 is constructed from a substrate 310. The substrate 310 defines a liquid channel 320 that has an inlet 322 and an outlet 324. The liquid is configured to flow through the liquid channel 320 of the hydrodynamic separator 300 from inlet 322 to outlet 324.

[059] Liquid channel 320 defines a channel length Ld from inlet 322 to outlet 324. Liquid channel 320 is generally curved to define an inner radius Rc around a central geometric axis x. Thus, liquid channel 320 extends circumferentially around the central geometric axis x to define a channel arc measure. In the present example, liquid channel 320 extends approximately 180° around the central geometric axis x. In the present example, the inner radius Rc is substantially constant along the channel length, but in some other embodiments, the inner radius is not constant.

[060] Liquid channel 320 generally has a rectangular cross-section along the channel length, which is not currently visible. Liquid channel 320 has a height (h) that is not currently visible, and a first channel width wi and a second channel width W2 that is visible in Figure 12. In this particular example, liquid channel 320 does not have a constant width. The channel width tapers between the inlet and outlet. Specifically, a first region 326 of liquid channel 320 defines a first width wi, a second region 328 of liquid channel 320 defines a second width W2, and a tapered region 327 extends between the first width wi and the second width W2 to provide a smooth transition from the first width wi to the second width w2.The term "tapering" is used in this document to mean a relatively gradual expansion / contraction that excludes an abrupt transition, such as a stepped transition, between the first width wi and the second width w2. Tapering can be linear, parabolic, or exponential, as examples. Other tapering shapes are also possible, including combinations of... Petition 870230043709, dated 05 / 24 / 2023, page 32 / 59 23 / 37 tapered shapes along the length of the tapered region.

[061] In some embodiments, the first region 326 and the second region 328 may have approximately equal lengths, but in the present embodiment, the first region 326 is shorter than the second region 328. In some embodiments, the first region 326 has a greater length than the second region 328. In some embodiments, the tapered region 327 is longer than one or both of the first region 326 or the second region 328. In the present example, only the outer wall radius 323 of the liquid channel 320 tapers between the first region 326 and the second region 328. In some other embodiments, the outer wall radius 323 and the inner wall radius 321 taper between the first region 326 and the second region 328. In still other embodiments, only the inner wall radius 321 tapers between the first region 326 and the second region 328.

[062] Liquid channel designs in which narrowing from a smaller width to a larger width may be desirable in some implementations. The smaller the width of a liquid channel 320, the shorter the path for particles to focus towards the inner wall 321. The larger the width of a liquid channel 320, the smaller the pressure drop along the channel 320, which reduces the energy required to pump liquid through the channel 320. Thus, it may be desirable in some implementations to have a liquid channel width that increases along at least a portion of the length of the liquid channel 320.

[063] In some implementations, the ideal channel length can be approximated using the weighted average of the width along the length of the liquid channel 320 in such calculations. In some implementations consistent with Figure 12, to achieve maximum focusing, the following is true: < ^w1+^w2Lf(w 1) ^f(w 2) where Lw1 and Lw2 are the actual lengths of the first region 326 (which has Petition 870230043709, dated 05 / 24 / 2023, page 33 / 59 24 / 37 the first width w1) and the second region 328 (which has the second width w2) of the channel, respectively. Lf(w1) and Lf(w2) are the theoretical linear focusing lengths of a channel consistent with the first region 326 and a channel consistent with the second region 328, respectively. In the case where the length of the tapering region 327 is relatively small compared to Lw1 and Lw2, the linear focusing length (Lf) could be as follows: £ / = aLf(w 1) +(1 -a)Lf(w2)

[064] Where a = — e corresponds to the percentage of focusing that Lf(w 1) occurs within the first region 326 and where (1 - a) =Lw2e corresponds to the additional percentage of focusing that occurs within the second region 328. Relatively small means that the tapering region 327 is less than 30%, 20% or even less than 10% of the combined length of the first region 326 and the second region 328.

[065] In some other implementations, for the purpose of calculating the total length of the focusing region, a first portion of the tapered region may be considered part of the length of the first region 326 and a second portion of the tapered region may be considered part of the length of the second region 328. For example, half the length of the tapered region 327 may be considered part of the length of the first region 326 and the other half of the length of the tapered region 327 may be considered part of the length of the second region 328. Other approaches may also be used. Examples Example A (25 pm particles in water)

[066] A hydrodynamic separator is designed to focus 25 µm particles in water. The main parameters are in Table 2. The flow rate range in which the particles focus is approximately 1.3 ml / min to 6.5 ml / min (Dean number = 5.1 to 25.3). The linear focusing region length is calculated for Petition 870230043709, dated 05 / 24 / 2023, page 34 / 59 25 / 37 these flow rates as shown in Table 3. The system pressure drop is an estimated pressure drop based on straight channel calculations and does not include minor losses or secondary flow effects. Fluid density (g / ml) 0.998 Channel height (pm) 150 Channel width (pm) 500 Hydraulic dimension (pm) 231 Viscosity (Pa-s (cP)) 10-3 (1) Radius of curvature (mm) 20 Particle confinement 0.11 Table 2 156.2 ^£(^)2 + 24.3 Re\DhJ Rr aw 2 1598.8 c , + 6.4 ReDH Flow rate (ml / min) Dean number (De) Lf (mm) System pressure drop (mbar) Lf (mm) System pressure drop (mbar) 0.95 5.1 245 415 250 423 1.90 10.1 135 456 128 434 2.85 15.2 98 498 87 442 3.80 20.2 79 535 67 448 4.75 25.3 68 575 55 465 Table 3 Example B (10 pm particles in fuel, variable radius of curvature)

[067] A hydrodynamic separator is designed to focus 10 µm particles in a fluid. The main parameters are in Table 4. The linear focusing region length and estimated pressure drop can be calculated for different hydrodynamic separator radii at a constant Dean number (De = 10). These data are shown in Table 5. The system pressure drop is an estimated pressure drop based on straight channel calculations and does not include minor losses or secondary flow effects. At larger radii of curvature, the flow rate through the channel increases, but with the disadvantage of increased pressure drop._____________________________________________ Fluid density (g / ml) 0.85 Channel height (pm) 100 Petition 870230043709, dated 05 / 24 / 2023, page 35 / 59 26 / 37 Channel width (pm) 150 Hydraulic dimension (pm) 120 Viscosity (Pa-s (cP)) 3x10-3 (3) Particle confinement 0.08 Table 4 156.2 7Γ 02 + 24.3 Rg \Dfj / Rr aw 2 1598.8 c , + 6.4 ReD2 Radius of curvature (mm) Flow rate (ml / min) Dean number Lf (mm) System pressure drop (mbar) Lf (mm) System pressure drop (mbar) 10 3.4 10 43.3 10633 21.6 5304 20 4.8 10 51.2 17749 28.4 9828 30 5.9 10 57.1 24331 33.4 14228 40 6.8 10 62.3 30596 37.8 18570 Table 5 Example C (8-12 pm particles in wine)

[068] A hydrodynamic separator is designed to focus 8-12 µm particles in wine. This represents the process of removing yeast from beer or wine during clarification. The main parameters are in Table 6. The length of the linear focusing region is calculated for different flow rates as shown in Table 7. The largest particle size (12 µm) is used for this calculation. The system pressure drop is an estimated pressure drop based on straight channel calculations and does not include minor losses or secondary flow effects. Fluid density (g / ml) 1.05 Channel height (pm) 75 Channel width (pm) 150 Hydraulic dimension (pm) 100 Fluid viscosity (Pa-s (cP)) 1.8x10-3 (1.8) Radius of curvature (mm) 20 Particle confinement (8 pm) 0.08 Particle confinement (12 0.12 Petition 870230043709, dated 05 / 24 / 2023, page 36 / 59 27 / 37 pm) Table 6 156.2 -^(^)2 + 24.3 Re \DH1 Rc aw 2 1598.8 c , + 6.4 ReDH Flow rate (ml / min) Dean number (De) Lf (mm) System pressure drop (mbar) Lf (mm) System pressure drop (mbar) 1.16 5 94 9070 63 6040 2.32 10 59 11390 49 9300 3.48 15 48 13900 34 9940 4.64 20 42 16210 27 10440 Table 7 Example D (Device with two widths)

[069] A hydrodynamic separator is configured to focus 8-12 µm particles in wine. In some implementations, such a separator can be used to remove yeast from beer or wine during clarification. The hydrodynamic separator has two regions of different widths, wi and W2, and a relatively smaller transition region that has a width of 1 mm or less. The flow rate is 3.48 ml / min. The main parameters are in Table 8. The separator is configured to perform α% of the focusing in the first region, and (1 - α)% of the focusing in the second region, so that the particles are completely focused at the end of the second region. The length of each region, Lwi and Lw2, and the total focusing length, Lf, are calculated in Table 9. Fluid density (g / ml) 1.05 Fluid flow rate (ml / min) 3.48 Channel height (pm) 75 Region 1 channel width (pm) 100 Region 2 channel width (pm) 150 Region 1 hydraulic dimension (pm) 86 Region 2 hydraulic dimension (pm) 100 Fluid viscosity (Pa-s (cP)) 1.8x10-3 (1.8) Petition 870230043709, dated 05 / 24 / 2023, pp. 37 / 59 28 / 37 Radius of curvature (mm) 20 Particle confinement region 1 (8 pm) 0.09 Particle confinement region 1 (12 pm) 0.14 Particle confinement region 2 (8 pm) 0.08 Particle confinement region 2 (12 pm) 0.12 Table 8 156.2 pi^i + 24.3 Rg \Dfj / Rr aw 2 1598.8 c , + 6.4 ReD2 Focusing region 1 (α) Focusing region 2 (1 — α) Lw1 (mm) Lw2 (mm) Lf (mm) Lw1 (mm) Lw2 (mm) Lf (mm) 0 % 100 % 0 48 48 0 34 34 25 % 75 % 9 36 45 5 26 31 50 % 50 % 18 24 42 11 17 28 75 % 25 % 26 12 38 16 9 25 100 % 0 % 35 0 35 21 0 21 Table 9

[070] Although it can be observed, in general, that by increasing the focusing percentage in the narrower channel (region 1), the overall focusing length can be decreased, this will occur at the cost of increased pressure drop due to the smaller channel dimensions. An ideal design will depend on the application requirements. Examples of Modalities Embodiment 1. A hydrodynamic separator configured to separate a liquid that has dispersed particles having a diameter (a) comprising: a substrate; A liquid channel defined by the substrate, wherein the liquid channel is configured to receive a liquid that has a Reynolds number (Re) within the channel, wherein the liquid channel has an inlet and an outlet, in which: The liquid channel is curved to define an inner radius (Rc) and has a liquid channel length (Ld) along the curve. Petition 870230043709, dated 05 / 24 / 2023, pp. 38 / 59 29 / 37 The liquid channel has a rectangular cross-section along the length of the curve, the rectangular cross-section has a height, a width (w) and a hydraulic diameter (Dh), the liquid channel length (Ld) is greater than or equal to a linear focusing length (Lf), and Lf = 1598.8Rcaw3+ 6.4. J' ReDfa Embodiment 2. The hydrodynamic separator of any of the modalities 1 and 3-9, where the system is configured to have a Dean number (De) between 5 and 25. Embodiment 3. The hydrodynamic separator of any of the embodiments 1-2 and 4-9, in which the particle diameter (a) is greater than 8% of the hydraulic diameter (Dh). Embodiment 4. The hydrodynamic separator of any of the embodiments 1-3 and 5-9, wherein the liquid channel length (Ld) is no more than 40% greater than the linear focusing length (Lf). Embodiment 5. The hydrodynamic separator of any of the embodiments 1-4 and 6-9, wherein the liquid channel length (Ld) is no more than 30% greater than the linear focusing length (Lf). Embodiment 6. The hydrodynamic separator of any of the 1-5 and 7-9 embodiments, where the particles are up to three times denser than the liquid. Embodiment 7. The hydrodynamic separator of any of the 1-6 and 8-9 embodiments, wherein the outlet comprises a first outlet and a second outlet. Embodiment 8. The hydrodynamic separator of any of the embodiments 1-7 and 9, wherein the liquid channel is one among a plurality of identical liquid channels. Petition 870230043709, dated 05 / 24 / 2023, pp. 39 / 59 30 / 37 Embodiment 9. The hydrodynamic separator of any of the embodiments 1-8, wherein the liquid channel has a first region that has a first channel width and a second region that has a second channel width, and a tapered region that extends from the first channel width to the second channel width. Embodiment 10. A hydrodynamic separator configured to separate a liquid that has dispersed particles, comprising: a substrate; A liquid channel defined by the substrate, wherein the liquid channel is configured to receive a liquid that has a Reynolds number (Re) within the channel, wherein the liquid channel has an inlet and an outlet, in which: The liquid channel is curved to define an inner radius (Rc) and has a liquid channel length (Ld) along the curve. The liquid channel has a rectangular cross-section along the length of the curve. The rectangular cross-section has a height, a width (w), and a hydraulic diameter (Dh). The liquid channel length (Ld) is greater than or equal to a linear focusing length (Lf), and Lf = 156.2 ^^(^~) + 24.3. Embodiment 11. The hydrodynamic separator of any of the embodiments 10 and 12-18, in which the system is configured to have a Dean number (De) between 5 and 25. Embodiment 12. The hydrodynamic separator of any of the embodiments 10-11 and 13-18, in which the particle diameter (a) is greater than 8% of the hydraulic diameter (Dh). Embodiment 13. The hydrodynamic separator of any of the embodiments 10-12 and 14-18, in which the length of the liquid channel (Ld) is not Petition 870230043709, dated 05 / 24 / 2023, pp. 40 / 59 31 / 37 more than 40% greater than the linear focusing length (Lf). Embodiment 14. The hydrodynamic separator of any of the embodiments 10-13 and 15-18, wherein the liquid channel length (Ld) is no more than 30% greater than the linear focusing length (Lf). Embodiment 15. The hydrodynamic separator of either of the 10-14 and 16-18 embodiments, where the particles are up to three times denser than the liquid. Embodiment 16. The hydrodynamic separator of any of the modalities 10-15 and 17-18, where the outlet comprises a first outlet and a second outlet. Embodiment 17. The hydrodynamic separator of any of the embodiments 10-16 and 18, wherein the liquid channel is one among a plurality of identical liquid channels. Embodiment 18. The hydrodynamic separator of any of the embodiments 10-17, in which the liquid channel has a first region that has a first channel width and a second region that has a second channel width, and a tapered region that extends from the first channel width to the second channel width. Embodiment 19. A hydrodynamic separator configured to separate a liquid that has dispersed particles comprising: a substrate; A liquid channel defined by the substrate, wherein the liquid channel is configured to receive a liquid that has a Reynolds number (Re) within the channel, wherein the liquid channel has an inlet and an outlet, in which: The liquid channel is curved to define an inner radius (Rc) and has a liquid channel length (Ld) along the curve; the liquid channel has a rectangular cross-section along the Petition 870230043709, dated 05 / 24 / 2023, pp. 41 / 59 32 / 37 length of the curve, the rectangular cross-section has a height, a width (w) and a hydraulic diameter (Dh), where the length of the liquid channel (Ld) is greater than or equal to a n,-.ii>2 linear focusing length (Lf), and Lf= --h 24,3. 8 dh Embodiment 20. The hydrodynamic separator of any of the embodiments 19 and 21-27, where the system is configured to have a Dean number (De) between 5 and 25. Embodiment 21. The hydrodynamic separator of any of the embodiments 19-20 and 22-27, in which the particle diameter (a) is greater than 8% of the hydraulic diameter (Dh). Embodiment 22. The hydrodynamic separator of any of the embodiments 19-21 and 23-27, in which the liquid channel length (Ld) is no more than 40% greater than the linear focusing length (Lf). Embodiment 23. The hydrodynamic separator of any of the embodiments 19-22 and 24-27, in which the liquid channel length (Ld) is no more than 30% greater than the linear focusing length (Lf). Embodiment 24. The hydrodynamic separator of any of the embodiments 19-23 and 25-27, where the particles are up to three times denser than the liquid. Embodiment 25. The hydrodynamic separator of any of the embodiments 19-24 and 26-27, in which the outlet comprises a first outlet and a second outlet. Embodiment 26. The hydrodynamic separator of any of the embodiments 19-25 and 27, wherein the liquid channel is one among a plurality of identical liquid channels. Embodiment 27. The hydrodynamic separator of any of the embodiments 19-26, in which the liquid channel has a first region that has a Petition 870230043709, dated 05 / 24 / 2023, pp. 42 / 59 33 / 37 first channel width and a second region that has a second channel width, and a tapered region that extends from the first channel width to the second channel width. Embodiment 28. A hydrodynamic separator configured to separate a liquid that has dispersed particles having a particle diameter (a) comprising: a substrate; A liquid channel defined by the substrate, wherein the liquid channel is configured to receive a liquid that has a Reynolds number (Re) within the channel, wherein the liquid channel has an inlet and an outlet, in which: The liquid channel is curved to define an inner radius (Rc) and has a liquid channel length (Ld) along the curve around a central geometric axis. The liquid channel has a rectangular cross-section along the length of the curve. The rectangular cross-section has a height, a width (w), and a hydraulic diameter (Dh). The liquid channel has a focusing angle (α) around the central geometric axis, where the focusing angle α = 265.682aw3 + 45.1, and the liquid channel extends circumferentially around the central geometric axis to an arc measure greater than or equal to the focusing angle α. Embodiment 29. The hydrodynamic separator of any of the embodiments 28 and 30-37, in which the system is configured to have a Dean number (De) between 5 and 25. Embodiment 30. The hydrodynamic separator of any of the embodiments 28-29 and 31-37, in which the particle diameter (a) is greater than 8% of the hydraulic diameter (Dh). Petition 870230043709, dated 05 / 24 / 2023, pp. 43 / 59 34 / 37 Embodiment 31. The hydrodynamic separator of any of the 28-30 and 32-37 modalities, in which the arc measurement is no more than 40% greater than the focusing angle. Embodiment 32. The hydrodynamic separator of any of the embodiments 28-31 and 33-37, in which the arc measurement is greater than 360 degrees, and the liquid channel defines a helix. Embodiment 33. The hydrodynamic separator of any of the modalities 28-32 and 34-37, in which the arc measurement is less than 360 degrees. Embodiment 34. The hydrodynamic separator of any of the 28-33 and 35-37 embodiments, where the particles are up to three times denser than the liquid. Embodiment 35. The hydrodynamic separator of any of the modalities 28-34 and 36-37, in which the outlet comprises a first outlet and a second outlet. Embodiment 36. The hydrodynamic separator of any of the embodiments 28-35 and 37, wherein the liquid channel is one among a plurality of identical liquid channels. Embodiment 37. The hydrodynamic separator of any of the embodiments 28-36, wherein the liquid channel has a first region having a first channel width and a second region having a second channel width, and a conical region extending from the first channel width to the second channel width. Embodiment 38. A hydrodynamic separator configured to separate a liquid having dispersed particles having a diameter (a) comprising: a substrate; a liquid channel defined by the substrate, where the liquid channel is configured to receive a liquid that has a Reynolds number (Re) within the Petition 870230043709, dated 05 / 24 / 2023, pp. 44 / 59 35 / 37 channel, in which the liquid channel has one inlet and one outlet, where: The liquid channel has a curved inner wall that defines an inner radius (Rc) and a curved outer wall that defines an outer radius. The liquid channel has a liquid channel length (Ld) along the curved inner wall. The liquid channel has a rectangular cross-section along the liquid channel length, and the rectangular cross-section has a channel width (w) between the inner wall and the outer wall, where the channel has a tapered region in which the channel width narrows between the inlet and the outlet. Embodiment 39. The hydrodynamic separator of any of the 38 and 40-50 modalities, in which the width increases towards the outlet. Embodiment 40. The hydrodynamic separator, of either of the 38-39 and 41-50 embodiments, in which the channel width increases at a constant rate between the inlet and outlet. Embodiment 41. The hydrodynamic separator of either of the 38-40 and 42-50 models, where the width decreases towards the outlet. Embodiment 42. The hydrodynamic separator of any of the 38-41 and 43-50 modalities, where the internal radius is constant from inlet to outlet. Embodiment 43. The hydrodynamic separator of any of the 38-42 and 44-50 embodiments, in which the outer radius tapers outwards between the inlet and outlet. Embodiment 44. The hydrodynamic separator of any of the embodiments 38-43 and 45-50, wherein the liquid channel has a first region having a first channel width and a first liquid channel length, a second region having a second channel width and a second liquid channel length, and the tapered region having a length of Petition 870230043709, dated 05 / 24 / 2023, pages 45 / 59 36 / 37 funnel-shaped region that extends from the first region to the second region. Embodiment 45. The hydrodynamic separator of modality 44, in which the first region has a greater length than the second region. Embodiment 46. The hydrodynamic separator of either of the 38-45 and 47-50 embodiments, wherein the system is configured to have a Dean number (De) between 5 and 25 in the first region and in the second region. Embodiment 47. The hydrodynamic separator of either of the 38-46 and 48-50 embodiments, where the particles are up to three times denser than the liquid. Embodiment 48. The hydrodynamic separator of any of the 38-47 and 49-50 configurations, where the outlet comprises a first outlet and a second outlet. Embodiment 49. The hydrodynamic separator of any of the embodiments 38-48 and 50, wherein the liquid channel is one among a plurality of identical liquid channels. Embodiment 50. The hydrodynamic separator of any of the embodiments 38-49, in which the particle diameter (a) is greater than 8% of the hydraulic diameter (Dh) of the first region and the hydraulic diameter of the second region.

[071] It should also be noted that, as used in this descriptive report and the accompanying claims, the term “configured” describes a system, apparatus or other structure that is built or configured to perform a particular task or adopt a particular configuration. The term configured may be used interchangeably with similar terms such as arranged, constructed, manufactured and the like.

[072] All publications and patent applications in this descriptive report are indicative of the common skill level in the art to which this technology belongs. All publications and patent applications are incorporated herein. Petition 870230043709, dated 05 / 24 / 2023, pp. 46 / 59 37 / 37 as a reference to the same extent as if each individual publication or patent application were specifically and individually cited as a reference. If there is any inconsistency between the disclosure of this application and the disclosure (or disclosures) of any document incorporated herein by reference, the disclosure of this application shall prevail.

[073] This application is intended to cover adaptations or variations of the present subject matter. It should be understood that the above description is intended to be illustrative and not restrictive, and the claims are not limited to the illustrative embodiments as presented in this document. Petition 870230043709, dated 05 / 24 / 2023, pp. 47 / 59

Claims

1 / 2 CLAIMS 1. Hydrodynamic separator configured to separate a liquid that has dispersed particles having a diameter (a) CHARACTERIZED in that it comprises: a substrate (110, 210, 310); a liquid channel (120, 220, 320) defined by the substrate (110, 210, 310), the liquid channel (120, 220, 320) configured to receive a liquid that has a Reynolds number (Re) within the channel, the liquid channel (120, 220, 320) having an inlet (122, 222, 322) and an outlet (124, 224, 324), wherein: the liquid channel (120, 220, 320) is generally curved, has a curved inner wall (321) that defines an inner radius (Rc) and a curved outer wall (323) that defines an outer radius, wherein the inner radius (Rc) is constant from the inlet (122, 222, 322) to the outlet (124, 224, 324), the liquid channel (120, 220, 320) has a liquid channel length (Ld) along the inner wall (321) curve, the liquid channel (120, 220,320) has a rectangular cross-section along the length of the liquid channel, and the rectangular cross-section has a channel width (w) between the inner wall (321) and the outer wall (323), where the channel (120, 220, 320) has a tapered region (327) in which the channel width (w) tapers between the inlet (122, 222, 322) and the outlet (124, 224, 324), additionally where the channel width (w) increases towards the outlet (124, 224, 324).

2. Hydrodynamic separator, according to claim 1, CHARACTERIZED in that the channel width (w) increases at a constant rate between the inlet (122, 222, 322) and the outlet (124, 224, 324).

3. Hydrodynamic separator, according to claim 1 or 2, CHARACTERIZED in that the outer radius tapers outward between the inlet Petition 870250120618, dated 12 / 29 / 2025, page 14 / 18 2 / 2 (122, 222, 322) and the outlet (124, 224, 324).

4. Hydrodynamic separator, according to any one of claims 1 to 3, CHARACTERIZED in that the liquid channel (120, 220, 320) has a first region (326) having a first channel width (wi) and a first liquid channel length (Lw1), a second region (328) having a second channel width (w2) and a second liquid channel length (Lw2), and a tapered region (327) having a tapered region length extending from the first region (326) to the second region (328).

5. Hydrodynamic separator, according to claim 4, CHARACTERIZED in that the first region (326) has a greater length than the second region (328). Petition 870250120618, dated 12 / 29 / 2025, page 15 / 18

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