Hydrodynamic separator with a tapered microfluidic channel

Abstract

The technology disclosed in this specification relates to a hydrodynamic separator. The hydrodynamic separator can be configured to separate a liquid having dispersed particles with a diameter. The hydrodynamic separator has a substrate and a liquid channel at least partially defined by the substrate. The liquid channel is configured to receive liquid therein. The liquid channel has an inlet and an outlet. The outlet has a first outlet branch and a second outlet branch. The liquid channel has an inner wall defining an inner radius around a central axis and an outer wall defining an outer radius around the central axis. The liquid channel has a liquid channel length along the inner wall from the inlet to the outlet. The liquid channel has a channel width between the inner wall and the outer wall, and the channel has a tapered region where the channel width increases towards the outlet.

Description

Technical Field

[0001] Related Applications This application claims priority to U.S. Provisional Application No. 63 / 347,915, filed Jun. 1, 2022, which is incorporated herein by reference in its entirety.

[0002] This disclosure generally relates to hydrodynamic separators. More specifically, this disclosure relates to hydrodynamic separators having tapered microfluidic channels.

Background Art

[0003] Hydrodynamic separators are used in various industries for the concentration and / or separation of particles in fluid streams such as hydrocarbon liquids, beverages, aqueous solutions, etc. Particles suspended in a fluid can cause problems in a system process (e.g., in a fuel or hydraulic system), may generally be undesirable to a consumer (e.g., pulp in orange juice, or impurities in beer or wine), or may be subject to a different processing step (such as in wastewater treatment). It may be desirable to design such hydrodynamic separators to achieve proper particle separation with a minimum pressure drop and improve particle separation and efficiency from both an energy consumption and time perspective.

Summary of the Invention

[0004] Some embodiments of the technology disclosed herein relate to a hydrodynamic separator configured to separate a liquid having dispersed particles with a diameter (a). The hydrodynamic separator has a substrate. The hydrodynamic separator has a liquid channel defined by the substrate. The liquid channel is configured to receive liquid therein. The liquid channel has an inlet and an outlet. The liquid channel has an inner wall defining an inner radius around a central axis and an outer wall defining an outer radius around the central axis. The liquid channel has a liquid channel length along the inner wall from the inlet to the outlet. The liquid channel has a rectangular cross-section along the liquid channel length. The rectangular cross-section has a channel width between the inner wall and the outer wall, and the channel has a tapered region where the channel width increases at a constant rate between 0.00 mm and 0.01 mm per mm of the liquid channel length towards the outlet.

[0005] In some such embodiments, the tapered region extends from the inlet to the outlet. Additionally or alternatively, the inner radius is constant from the inlet to the outlet. Additionally or alternatively, the outer radius tapers outwards between the inlet and the outlet. Additionally or alternatively, 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 a tapered region having a tapered region length extending from the first region to the second region. Additionally or alternatively, the first region has a length longer than that of the second region. Additionally or alternatively, the separator is configured to have a Dean number (De) between 5 and 25 in the first and second regions. Additionally or alternatively, the particle diameter (a) is greater than at least 8% of the hydraulic diameter (D H ) in the first region. Additionally or alternatively, the separator is configured to separate particles with a density up to three times that of the liquid. Additionally or alternatively, the outlet has a first outlet and a second outlet. Additionally or alternatively, the liquid channel is one of a plurality of identical liquid channels.

[0006] Some embodiments of the technology disclosed herein relate to hydrodynamic separators. The hydrodynamic separator can be configured to separate a liquid having dispersed particles with a diameter (a). The hydrodynamic separator has a substrate and a liquid channel at least partially defined by the substrate. The liquid channel is configured to receive liquid therein. The liquid channel has an inlet and an outlet. The outlet has a first outlet branch and a second outlet branch. The liquid channel has an inner wall defining an inner radius around a central axis and an outer wall defining an outer radius around the central axis. The liquid channel has a liquid channel length along the inner wall from the inlet to the outlet. The liquid channel has a channel width between the inner wall and the outer wall, and the channel has a tapered region where the channel width increases towards the outlet.

[0007] In some such embodiments, the tapered region extends from the inlet to the outlet. Additionally or alternatively, the inner radius is constant from the inlet to the outlet. Additionally or alternatively, the outer radius is tapered outwardly between the inlet and the outlet. Additionally or alternatively, 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 a tapered region having a tapered region length extending from the first region to the second region. Additionally or alternatively, the first region has a length that is longer than the second region. Additionally or alternatively, the separator is configured to have a Dean number (De) between 5 and 25 in the first and second regions. Additionally or alternatively, the particle diameter (a) is greater than at least 8% of the hydraulic diameter (D H ) in the first region.

[0008] Additionally or alternatively, the separator is configured to separate particles with a density up to three times that of the liquid. Additionally or alternatively, the inner radius is from 10 mm to 100 mm. Additionally or alternatively, the liquid channel is one of a plurality of identical liquid channels defined by a substrate. Additionally or alternatively, the liquid channel has a width in the range from 400 μm to 1000 μm. Additionally or alternatively, the liquid channel has a height in the range from 100 μm to 500 μm. Additionally or alternatively, the liquid channel has a polygonal cross-section along the liquid channel length. Additionally or alternatively, the liquid channel has a rectangular cross-section along the liquid channel length.

[0009] Additionally or alternatively, the channel width of the liquid channel does not vary by more than 10 mm per mm of the liquid channel length along the liquid channel. Additionally or alternatively, the channel width increases at a constant rate in the tapered region. Additionally or alternatively, the liquid channel has a first region with a first channel width and a tapered region with an increasing channel width from the first region to the outlet. Additionally or alternatively, the liquid channel has a plurality of tapered regions, each having an increasing channel width towards the outlet. Additionally or alternatively, the liquid channel is a microfluidic channel.

[0010] The above summary is not intended to describe every embodiment or all implementations. Rather, a more complete understanding of the exemplary embodiments will become apparent and understood by reference to the detailed description of the following exemplary aspects and the claims, in consideration of the accompanying drawings.

Brief Description of the Drawings

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[0024] The present technology can be more fully understood and evaluated by considering the following detailed description of various embodiments related to the accompanying drawings.

[0025] The figures are drawn primarily for clarity and, as a result, are not necessarily drawn to scale. Further, various structures / components, including but not limited to fasteners, electrical components (wiring, cables, etc.), may be shown schematically or removed from part or all of the figures to better illustrate the aspects of the illustrated embodiments or if such structures / components are not necessary to understand the various exemplary embodiments described herein. However, the absence of illustration / explanation of such structures / components in a particular figure should not be construed as limiting the scope of the various embodiments in any way.

DETAILED DESCRIPTION OF THE INVENTION

[0026] A hydrodynamic separator consistent with the present disclosure is a microfluidic device that can focus particles within a fluid stream relying only on forces from the internal fluid flow. The particles can be separated from a portion of the fluid stream and / or from other sized particles within the fluid stream. The hydrodynamic separator generally defines a fluid channel having an inlet and an outlet with at least two flow branches. Particles within a particular size range can be focused or concentrated into one of the two flow branches. For example, particles exceeding a threshold size range are focused into 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.

[0027] FIG. 1 is a schematic diagram of an exemplary system 10 that conforms to some implementations of the technology disclosed herein. System 10 is a hydrodynamic separator system configured to focus particles suspended in a fluid stream. System 10 includes a hydrodynamic separator 100 having a liquid channel 120 with an inlet 122 and an outlet 124. A fluid pump 30 forms a fluid communication between a fluid source 20 and the hydrodynamic separator 100. Specifically, 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 the liquid channel 120 of the hydrodynamic separator 100 to the outlet 124. The outlet 124 has a first outlet branch 50 and a second outlet branch 52 that can lead from the liquid channel 120 to another system or another system component. In some embodiments, the fluid flowing through the first outlet branch 50 is configured to have a higher concentration of particles within a specific size range compared to the fluid flowing through the second outlet branch 52.

[0028] A hydrodynamic separator that conforms to the technology disclosed herein generally consists of a substrate 110. The substrate 110 at least partially defines the liquid channel 120 therein. The substrate 110 can be composed of various different materials and combinations of materials. In some embodiments, the substrate can be polymeric. In some examples, the substrate includes acrylic. In some examples, the substrate includes polycarbonate. In some examples, the substrate includes polydimethylsiloxane (PDMS). In some embodiments, the substrate can include glass. In some embodiments, the substrate can include a non-reactive metal. In some embodiments, the substrate can include one or more adhesive layers such as a pressure-sensitive adhesive. In some embodiments, the substrate can be composed of two or more materials so that the walls of the channel can be two or more materials.

[0029] The liquid channel 120 is generally configured to accommodate the flow of liquid. The liquid channel 120 defines an inlet 122 and an outlet 124. The liquid channel 120 has a channel length L from the inlet 122 to the outlet 124. D defines it. The liquid channel 120 is generally curved to define an inner radius R around the central axis x. C In this way, the liquid channel 120 extends circumferentially around the central axis x to define a channel arc dimension. In this example, the liquid channel 120 extends approximately 180° around the central axis x. In this example, the inner radius R C is substantially constant along the length of the channel, although in some other examples, the inner radius R C can vary. In some implementations, the inner radius R C is 5 mm, 10 mm, or 15 mm or more. In some implementations, the inner radius R C is 100 mm, 60 mm, 50 mm, or 30 mm or less.

[0030] In various embodiments, the liquid channel 120 of the hydrodynamic separator is a microfluidic channel, where the term "microfluidic channel" refers to a channel having at least one dimension less than 1 millimeter (1000 micrometers). A microfluidic channel can have a channel width less than 1000 micrometers, a channel height (or depth) less than 1000 micrometers, or both. In some embodiments, for higher flow rate applications, at least one dimension of the microfluidic channel may be greater than 1 millimeter. In some embodiments, at least one dimension of the microfluidic channel is 1, 2, 3, 4, 5, 6, 7, 8, 9, or 10 millimeters or more, or 10, 9, 8, 7, 6, 5, 4, 3, or 2 millimeters or less. Generally, the channel can have any suitable length to provide appropriate particle focusing and a balanced appropriate pressure drop.

[0031] Microfluidic channels can be described by their cross-sectional area. The cross-section of the liquid channel 120 as used herein is substantially perpendicular to the direction of fluid flow through the channel 120. In some embodiments, the cross-sectional area of the microfluidic channel can be less than 10, 9, 8, 7, 6, 5, 4, 3, or 2 square millimeters (mm 2 ).

[0032] The liquid channel 120 can generally have a cross-section of any shape along the channel length, which is a closed loop around the liquid channel 120. In some embodiments, the liquid channel 120 has a curved cross-section such as a circular or oval cross-section. In some embodiments, the liquid channel 120 has a polygonal cross-section. In some embodiments, the liquid channel 120 has an irregular cross-section. In the example of FIG. 2, the liquid channel 120 has a rectangular cross-section along the channel length. The term "rectangular" as used herein includes squares. The channel 120 has a height (h) shown in FIG. 2 and a width (w) shown in both FIGS. 1 and 2. For liquid channels having a curved and / or irregular shaped cross-section, the width and height are generally the maximum width and maximum height in the cross-section.

[0033] Microfluidic channels can also be described by their hydraulic diameter. The channel 120 also has a hydraulic diameter (D H ). To calculate the hydraulic diameter of a microfluidic channel, the following equation is used:

Equation

Equation

[0034] The liquid channel 120 can be formed in the substrate 110, for example, by a molding operation, laser cutting, micromachining, photolithography, and 3D printing. In some examples, the liquid channel 120 is formed in the substrate 110 by injection molding or embossing of plastic. Other approaches can also be used to form the liquid channel 120. In various embodiments, the hydrodynamic separator 100 defines a plurality of identical liquid channels 120 configured to operate in parallel. In various embodiments, the hydrodynamic separator 100 has at least 10 liquid channels. In various embodiments, the hydrodynamic separator 100 has at least 50 liquid channels or at least 100 liquid channels.

[0035] In some embodiments where the hydrodynamic separator 100 has a plurality of identical liquid channels, one liquid channel 120 can be defined within a single substrate layer. In some other embodiments, a single substrate layer can define a plurality of liquid channels 120. The liquid channels within the substrate layer can be configured to operate in parallel. In various embodiments, a plurality of substrate layers can be laminated in a stacked configuration such that the liquid channel(s) 120 defined by each substrate layer are also in a stacked configuration. The stacked layers of the substrate and the liquid channels 120 form the hydrodynamic separator 100. The hydrodynamic separator 100 can define an inlet flow channel 40 that is upstream of and in direct fluid communication with each of the microfluidic channel inlets (such as inlet 122). The inlet channel 40 generally has a fluid diameter that is larger than the fluid diameter of each of the liquid channels 120. The hydrodynamic separator 100 can define a first outlet branch 50 and a second outlet branch 52 that are both downstream of the outlet 124 and in direct fluid communication with the outlet. Each of the first outlet branch 50 and the second outlet branch 52 generally has a hydraulic diameter that is larger than the hydraulic diameter of each liquid channel. Such a configuration can advantageously equalize the flow through the channels.

[0036] The liquid channel 120 is configured to receive a liquid having a Reynolds number (Re) within the liquid channel. The 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 of inertial forces to viscous forces and is defined as follows: [Number] Here, ρ is the fluid density, U is the average fluid velocity, and μ is the kinematic viscosity of the fluid. In a hydrodynamic separator, the Reynolds number is generally small (<1000), which means the flow profile is laminar. In various embodiments, the system is configured to have a Dean number (De) between 5 and 25. In various embodiments, the system is configured to have a Dean number between 5 and 20. The Dean number describes the fluid behavior in a curved pipe and accounts for the inertial, centrifugal, and viscous forces acting on the fluid. The Dean number is defined as follows: [Number]

[0037] The hydrodynamic system 10 is generally configured to focus particles within the liquid channel 120. As used herein, the term "particle" refers to a discrete amount of material dispersed in a fluid. Non-limiting examples of materials that can form particles include mud, metal, cells, bubbles, fat, and water droplets. In one particular example, water droplets can be dispersed in a hydrocarbon fluid such as gasoline or diesel fuel to form an emulsion. In another example, bubbles can be dispersed in a hydraulic fluid. In another example, cells can be dispersed in an aqueous fluid. In yet another example, the particles can be pulp in orange juice, fat in milk, and impurities in beer or wine.

[0038] In various implementations, the hydrodynamic separator 100 is configured to agglomerate particles having a diameter greater than 8% of the hydraulic diameter of the liquid channel 120. Particles with a diameter greater than 8% of the channel hydraulic diameter generally agglomerate towards the inner wall when the Dean number is in the range of 5 to 25. The hydrodynamic separator is generally configured to agglomerate particles having a diameter of 50% or less of the channel height. In various examples, for the purposes of the calculations provided herein, the particles have a sphericity greater than 0.5. For non-spherical particles, for the purposes of the calculations provided herein, the particle diameter is considered to be the volume equivalent spherical diameter. In various embodiments, a hydrodynamic separator consistent with the techniques disclosed herein is configured to agglomerate particles having a density up to three times that of the liquid within the liquid channel 120.

[0039] The agglomeration of the particles occurs in two different stages. The first stage is the particle movement stage in which the suspended particles move across the liquid channel 120 to the upper and lower ends of the liquid channel 120. The particle movement stage generally begins at the liquid channel inlet 122 and extends for the particle movement length L of the liquid channel 120 o and defines the particle movement region 126 of the liquid channel 120. In this region, no additional agglomeration towards the inner wall 121 of the liquid channel 120 is observed. The second region is the linear agglomeration region 128 where the amount of agglomeration towards the inner wall 121 increases linearly along the channel length. The agglomeration continues until maximum particle agglomeration is reached. After reaching maximum particle agglomeration, no further agglomeration is observed. The linear agglomeration region 128 has a linear agglomeration length L which is the length required to achieve maximum particle agglomeration. f The linear agglomeration region 128 generally extends from the particle movement region 126 towards the channel outlet 124.

[0040] The length of the liquid channel 120 after the linear agglomeration region 128 is called the complete agglomeration region 130. The complete agglomeration region 130 extends for a length L from the linear agglomeration region 128 to the outlet 124. ffIt has. In various implementations, it may be desirable to limit or eliminate the fully focused region 130 in order to reduce the energy requirements of the system by reducing the pressure drop across the liquid channel 120 while achieving maximum particle focusing.

[0041] Figure 3 is a graph showing representative focusing behavior that shows three stages of particle focusing along the length of a curved liquid channel. The particle transport region 126 occupies the first approximately 16 mm of the channel length, followed by the linear focusing region 128. In this example, the linear focusing region 128 achieves maximum particle focusing at approximately 114 mm along the length of the liquid channel. Once the maximum value of particle focusing is reached, the particle focusing can remain approximately constant. This region of the device is considered the fully focused region 130 described above. In this example, it shows that the maximum focusing percentage in the fully focused region is approximately 90% (i.e., 90% of the particles are focused).

[0042] Mathematically, the length of the linear focusing region required to achieve maximum particle focusing in a curved channel (such as shown in FIG. 1) is a linear function based on the radial component of the particle velocity through the channel. According to existing literature (see, for example, Di Carlo, D., Irimia, D., Tompkins, R. G., Toner, M.; Continuous Inertial Focusing, Ordering, and Separation of Particles in Microchannels. Proceedings of the National Academy of Sciences of the U.S.A., Nov. 2007, Vol. 104, No. 4, 18892-7), the magnitude of the radial component of the Dean flow profile, or the linear focusing rate U D is as follows:

Equation

[0043] This relationship was tested in a rectangular channel using the computational fluid dynamics of the STAR-CCM+ software by Siemens PLM Software, headquartered in Plano, Texas. To measure the radial flow component, function probes were inserted at discrete radial positions along the primary fluid flow direction, at the center of a virtual fluid region aligned with the depth of the channel (Z direction). An example of a series of typical radial flow profiles is shown in Figure 4. Here, the radial velocity is a function of the depth passing through the center of the channel. The flow profiles shown are for the geometry of a single device and combinations of fluids over a range of Dean numbers, but the channel height h (150 μm), width w (500 μm), and inner radius R C (20 mm) are constant. In this coordinate system, a positive flow velocity indicates that the fluid is moving towards the outer wall of the device, and a negative flow velocity indicates 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 fluid inertia. There are two minimum radial flow components observed symmetrically above and below the center of the channel depth. These flow components are recirculation flows towards the inner wall that ultimately cause the particles to be passively moved to the final focusing position.

[0044] The minimum radial flow velocity for different liquid channel widths at four different Dean numbers (De = 5, 10, 15, 20) was plotted against the magnitude of the radial component of the Dean flow profile reflected in Figure 5, according to the literature equation. As is clear, this equation does not define a linear relationship over different liquid channel widths and is therefore not an accurate predictor of the radial velocity. During further testing and analysis, the following relationship was discovered for the linear focusing velocity U D :

Number

[0045] This equation is plotted against the minimum radial velocity, and the results are reflected in Figure 6. As is evident, data from devices with different liquid channel widths fall on a single straight line. This relationship holds when varying the device's geometric shape (width, height, R C ) and fluid properties (viscosity and density) over the range of Dean numbers relevant to hydrodynamic separators (5 < De < 25). Specifically, it was found that the minimum radial velocity is as follows:

Number

[0046] Based on the minimum radial velocity, an equation can be derived to determine the length of the linear focusing region for obtaining maximum particle focusing. Since the velocity across the width of the liquid channel is approximately constant, the time it takes for a particle to pass across the width of the liquid channel to the inner wall is as follows:

Number

[0047] In such a case, the length of the linear focusing region is as follows:

Number

Number

Number

Number

[0048] The linear focusing region generally becomes shorter as the Dean number increases, and since the operating range of the hydrodynamic separator consistent with the technology disclosed herein is a Dean number in the range of 5 to 25, the linear focusing length L f is generally at least the following:

Number

[0049] Using the particle focusing velocity (i.e., the gradient of the linear focusing region), the length required to further focus 80% of the particles was calculated. When 80% of the particles are further focused, the focusing efficiency becomes 90% or more. This is because at the inlet of the device, 10 - 20% of the particles are already at the focusing position. The observed focusing length related to the experimental results is the above-mentioned focusing length L f plotted against the equation and reflected in FIG. 7. The error bars correspond to the standard error based on the uncertainty of the gradient of the linear focusing region. This fit shows a distinct trend dominated by changes in the width and radius of curvature of the device. Looking at the data in more detail, the focusing length L f is suggested to be dependent on the particle size. Specifically, smaller particles focus faster than larger particles. In fact, particles of different sizes experience different lift forces and pass through the width of the device at different heights. The linear focusing length L f was obtained and it was found that multiplying it by the particle confinement (a / Dh) gives the following:

Number

Number

[0050] The length L of the linear focusing region fRather than being described with respect to, the linear focusing region can also be described with respect to the focusing angle (α), which is the arc dimension (degrees) of the linear focusing region 128 around the central axis x:

Number

Number

[0051] A series of experiments were conducted to measure the actual particle migration length L 0 and the particle focusing length L f for various hydrodynamic systems consistent with the technology disclosed herein. Hydrodynamic separators of various device heights and widths were fabricated from PDMS and glass slides using standard methods. A solution of fluorescently labeled particles was introduced into the hydrodynamic separator channels at known flow rates within the range of Dean numbers 5 - 25. Images were taken at various positions along the hydrodynamic separator using a CMOS camera. Image processing was used to identify the particle concentration as a function of channel position and length. The particle focusing length L f was also calculated according to the above formula. The results are shown in Table 1 below.

Table 1

[0052] Through the experimental results, the particle focusing length L f was greater than the particle migration length L 0 The particle migration length L 0 was in the range from 0% to 28.2% of the total liquid channel length L D Furthermore, the particle migration length L D was in the range from 0% to 28.2% of the total liquid channel length L 0is the particle migration length L f ranged from 0% of the particle migration length L f to 39.4% of the particle migration length L. Thus, in some embodiments, the liquid channel that is consistent with the technology disclosed herein has a liquid channel length L f that is approximately equal to the particle migration length L D . In various embodiments, the liquid channel that is consistent with the technology disclosed herein has a liquid channel length L f that is greater than the particle migration length L D . Based on the collected data, in many embodiments, the liquid channel length L D appears to be less than 40% greater than the particle migration length L f . The liquid channel length L D may be less than or equal to 30% greater than the particle migration length L f . The liquid channel length L D may be less than or equal to 20% greater than the particle migration length L f . In some embodiments, the liquid channel length L D may be 3% to 20% greater than the particle migration length L f .

[0053] FIGS. 10 and 11 show schematic views of another example hydrodynamic separator 200 that is consistent with some embodiments. FIG. 10 is a schematic perspective view, and FIG. 11 is a schematic front view of the inlet side of the hydrodynamic separator, where the liquid channel 220 is represented by a dotted line. The hydrodynamic separator 200 generally conforms to the above description, except where there are contradictions. The hydrodynamic separator 200 is configured to focus particles dispersed in a liquid flow. The hydrodynamic separator 200 is composed of a substrate 210. The substrate 210 defines a liquid channel 220 having an inlet 222 and an outlet 224. The liquid is configured to flow through the liquid channel 220 of the hydrodynamic separator 200 from the inlet 222 to the outlet 224. Although not shown here, it should be noted that, as described above with reference to FIG. 1, a first outlet branch and a second outlet branch can extend outward from the outlet 224.

[0054] The liquid channel 220 has a channel length L from the inlet 222 to the outlet 224D defines. The liquid channel 220 has an inner radius R centered on the central axis x C is generally curved so as to define. In this way, the liquid channel 220 extends circumferentially about the central axis x and defines a channel arc dimension. In this example, the liquid channel 220 extends about 810° about the central axis x. In this example, the inner radius R C is substantially constant along the length of the channel. In this example, the liquid channel 220 forms a helix about the central axis x. The helical arrangement of the liquid channel 220 corresponds to both a constant inner radius R C and a plurality of rotations about the central axis x. However, in some embodiments, the inner radius is not constant.

[0055] In some embodiments, the liquid channel 220 can have a rectangular cross-section along the channel length, as shown in FIG. 11 at the inlet 222. The cross-section of the liquid channel 220 is substantially perpendicular to the direction of fluid flow through the channel 220. The channel 220 has a height (h) shown in FIG. 2 and a width (w) shown in FIG. 11. The channel 220 also has a hydraulic diameter (D H ) as disclosed.

[0056] Similar to the above embodiments, particle focusing can occur in two different stages. To optimize the liquid channel length L D , the region of complete focusing is avoided such that the total length of the liquid channel is the particle travel length L 0 and the particle focusing length L f . The optimization of the liquid channel length L D and / or the arc dimension generally agrees with the above discussion.

[0057] In various embodiments, such as embodiments consistent with the examples of FIGS. 1-2 and 10-11, the height h, width w, and inner radius R CLiquid channel dimensions such as these are substantially constant along the length of the liquid channel, meaning that such dimensions do not vary by more than 5% of the weighted average value of the dimensions along the length of the liquid channel. The equations provided herein generally assume that the liquid channel has a substantially constant inner radius R C for the optimization of the liquid channel length. 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 herein for the optimization of the liquid channel length. In various examples, the optimized channel length can be based on the weighted average of the channel dimensions within the focusing region.

[0058] In some embodiments of the techniques disclosed herein, the hydrodynamic separator system has a liquid channel width that is tapered for at least a portion of the length of the liquid channel. The term "tapered" is used herein to mean a relatively gradual expansion / contraction that excludes a sharp transition such as a stepwise transition between a first width w 1 and a second width w 2 . By way of example, the taper can be linear, parabolic, or exponential. Other taper shapes are also possible, including combinations of taper shapes along the length of the taper region. The tapered liquid channel can advantageously reduce the focusing length of the channel, which has been found to advantageously reduce the length of the channel required to achieve the desired separation efficiency. From a practical perspective, the smaller the width of the liquid channel, the shorter the path for the particles to converge towards the inner wall, which allows the system to have a smaller size. On the other hand, the larger the width of the liquid channel, the smaller the pressure drop along the channel, which reduces the energy required to pump the liquid through the channel. Additionally, the relatively large width of the liquid channel at the outlet can advantageously facilitate the separation of the portion of the fluid flow having the focused particles from the rest of the fluid flow. Tapered the liquid channel can advantageously balance these and other factors while achieving the desired separation efficiency.

[0059] FIG. 12 is a schematic diagram of yet another exemplary hydrodynamic separator system that conforms to some embodiments. The system has a fluid source 20, a pump 30, an inlet flow channel 40, and outlet flow branches 50, 52, as described above with reference to FIG. 1. The system has a hydrodynamic separator 300 that generally conforms to the above description, except where inconsistent. The hydrodynamic separator 300 is configured to focus particles dispersed in a liquid stream. The hydrodynamic separator 300 is composed of a substrate 310. The substrate 310 defines a liquid channel 320 having an inlet 322 and an outlet 324. The liquid is configured to flow through the liquid channel 320 of the hydrodynamic separator 300 from the inlet 322 to the outlet 324.

[0060] The liquid channel 320 defines a channel length L from the inlet 322 to the outlet 324. D The liquid channel 320 is generally curved so as to define an inner radius R about a central axis x. C Thus, the liquid channel 320 extends circumferentially about the central axis x and defines a channel arc dimension. In this example, the liquid channel 320 extends about 180° about the central axis x. In this example, the inner radius R C is substantially constant along the length of the channel, although in some other embodiments the inner radius is not constant.

[0061] The liquid channel 320 may have a rectangular cross-section along the channel length, which is not visible here, although the liquid channel 320 may have a cross-section forming other shapes described above. The liquid channel 320 has a height (h) that is not visible here and a first channel width w 1 and a second channel width w 2 visible in FIG. 12. In this particular example, the liquid channel 320 does not have a constant width. The channel width is tapered between the inlet and the outlet. Specifically, a first region 326 of the liquid channel 320 defines a first width w 1 and a second region 328 of the liquid channel 320 defines a second width w 2is defined, and the tapered region 327 has a first width w 1 to a second width w 2 To provide a smooth transition to, the first width w 1 and the second width w 2 extends between. In this example, the width of the liquid channel tapers from a smaller width to a larger width. More specifically, the liquid channel width increases along at least a portion of the length of the liquid channel 320.

[0062] The relatively large channel width at the outlet 324 can advantageously improve the separation of the focused particles from the remaining fluid flow, based simply on the physical constraints associated with the relative distance between the focused particles (generally disposed towards the inner wall 321) and the fluid lacking the focused particles (towards the outer wall 323). The smaller the channel width, the higher the chance that some of the focused particles will exit into the second outlet flow branch 52 rather than the first outlet flow branch 50, simply because the first outlet flow branch 50 and the second outlet flow branch 52 are closer. Further, at a relatively wide channel width, the focused particles can advantageously converge at a relatively small percentage of the total channel width, further reducing the chance that the particles will inadvertently exit through the second outlet branch 52.

[0063] In some embodiments, the first region 326 and the second region 328 can have substantially equal lengths, but in this embodiment, the first region 326 is shorter than the second region 328. In some embodiments, the first region 326 has a length longer 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 this example, only the radius of the outer wall 323 of the liquid channel 320 tapers between the first region 326 and the second region 328. In some other embodiments, the radius of the outer wall 323 and the radius of the inner wall 321 taper between the first region 326 and the second region 328. In yet other embodiments, only the radius of the inner wall 321 tapers between the first region 326 and the second region 328.

[0064] In this example, there is a single tapered region along the length of the liquid channel 320, but it will be understood that the liquid channel 320 may have a plurality of tapered regions 327 along the channel length.

[0065] In some implementations, the optimal channel length can be approximated by using a weighted average of the widths along the length of the liquid channel 320 in such calculations. In some implementations consistent with FIG. 12, for achieving maximum focusing, the following is true:

Number

Number

Number

Number

[0066] In some other implementations, for the purpose of calculating the overall length of the focusing region, the first portion of the tapered region can be considered as part of the length of the first region 326, and the second portion of the tapered region can be considered as part of the length of the second region 328. For example, half of the length of the tapered region 327 can be considered as part of the length of the first region 326, and the other half of the length of the tapered region 327 can be considered as part of the length of the second region 328. Other approaches can also be used.

[0067] FIG. 13 is a schematic diagram of yet another exemplary hydrodynamic separator system consistent with some embodiments. The system has a fluid source 20, a pump 30, an inlet flow channel 40, and outlet flow branches 50, 52 as described above with reference to FIG. 1. The system has a hydrodynamic separator 400 that generally conforms to the above description except where inconsistent with the discussion herein. The hydrodynamic separator 400 is configured to focus particles dispersed in a liquid stream. The hydrodynamic separator 400 is composed of a substrate 410. The substrate 410 defines a liquid channel 420 having an inlet 422 and an outlet 424. The liquid is configured to flow through the liquid channel 420 of the hydrodynamic separator 400 from the inlet 422 to the outlet 424.

[0068] The liquid channel 420 defines a channel length L from the inlet 422 to the outlet 424. D The liquid channel 420 is generally curved so as to define an inner radius R about a central axis x. C The liquid channel 420 extends circumferentially about the central axis x and defines a channel arc dimension. In this example, the liquid channel 420 extends about 180° about the central axis x. In this example, the inner radius R C is substantially constant along the length of the channel, although in some other embodiments the inner radius is not constant.

[0069] The liquid channel 420 may have a rectangular or alternative cross-section along the channel length, which, although not visible here, may be similar to that shown in FIG. 2 or the description elsewhere in this specification. The liquid channel 420 has a height (h) (see FIG. 2), a first channel width w 1 and a second channel width w 2 . In this particular example, the liquid channel 420 does not have a constant width. The channel width tapers between the inlet 422 and the outlet 424. Unlike the above example, in this example, the channel width tapers from the inlet 422 to the outlet 424. However, in some other examples, a part of the length of the channel 420 can have a constant width, and another part of the length of the channel 420 can have a tapered width.

[0070] In this example, only the radius of the outer wall 423 of the liquid channel 420 tapers between the inlet 422 and the outlet 424. In some other embodiments, the radius of the outer wall 423 and the radius of the inner wall 421 each taper between the inlet 422 and the outlet 424. In yet other embodiments, only the radius of the inner wall 421 tapers between the inlet 422 and the outlet 424.

[0071] In this example, the width of the liquid channel tapers from a small width to a large width. More specifically, the liquid channel width increases along at least a part of the length of the liquid channel 420.

[0072] Note that channels that taper from a large width to a small width from the inlet to the outlet may not be desirable in some implementations. For example, a relatively small channel outlet 424 may pose practical problems when separating a portion of the fluid having particles focused from the rest of the fluid via the first outlet branch 50 and the second outlet branch 52.

[0073] Example Example A (25 μm particles in water)

[0074] The hydrodynamic separator is designed to agglomerate 25-μm particles in water. The main parameters are shown in Table 2. The flow rate range in which the particles agglomerate is from about 1.3 mL / min to 6.5 mL / min (Dean number = 5.1 to 25.3). The linear agglomeration region length is calculated for these flow rates as shown in Table 3. The system pressure drop is the estimated pressure drop based on straight channel calculations and does not include the effects of minor losses or secondary flows.

[0075]

Table 2

Table 3

[0076] Example B (10-μm particles in fuel, various radii of curvature)

[0077] The hydrodynamic separator is designed to agglomerate 10-μm particles in a fluid. The main parameters are shown in Table 4. The length of the linear agglomeration region and the estimated pressure drop can be calculated for different hydrodynamic separator radii at a constant Dean number (De = 10). This data is shown in Table 5. The system pressure drop is the estimated pressure drop based on straight channel calculations and does not include the effects of minor losses or secondary flows. As the radius of curvature increases, the flow rate through the channel increases, but there is a drawback that the pressure drop increases.

Table 4

Table 5

[0078] Example C (8-12-μm particles in wine)

[0079] The hydrodynamic separator is designed to agglomerate 8 - 12μm particles in wine. This represents the process of removing yeast from beer or wine during clarification. The main parameters are shown in Table 6. The linear agglomeration region length is calculated for different flow rates as shown in Table 7. The maximum particle size (12μm) is used in this calculation. The system pressure drop is an estimated pressure drop based on straight channel calculations and does not include minor losses or the effects of secondary flow.

Table 6

Table 7

[0080] Example D (Device with two widths)

[0081] The hydrodynamic separator is configured to agglomerate 8 - 12μm 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 w 1 and w 2 and a relatively small transition region with a length of 1 mm or less. The flow rate is 3.48 mL / min. The main parameters are shown in Table 8. The separator is configured to achieve α% agglomeration in the first region and (1 - α)% agglomeration in the second region such that the particles are fully agglomerated at the end of the second region. The lengths L w1 and L w2 of each region, and the total agglomeration length L f are calculated in Table 9.

Table 8

Table 9

[0082] Generally, it can be observed that by increasing the percentage of focusing in a narrower channel (region 1), the overall focusing length can be decreased, which occurs at the expense of an increased pressure drop due to the smaller channel dimensions. The optimal design depends on the application requirements.

[0083] Example E (Channel with Tapered Width)

[0084] Compare two microfluidic channels and use the theoretical calculations identified herein to identify the effect of the taper of the channel width of the microfluidic channel on the focusing length. The baseline microfluidic channel has a constant width of 628.4 μm from the channel inlet to the channel outlet, and the comparative microfluidic channel has a channel width at the inlet of 500 μm and a channel width at the outlet of 628.4 μm. The channel width of the comparative microfluidic channel has a taper from the channel inlet to the channel outlet at a constant rate k of 0.001 mm of the channel width per mm of the channel length (mm / mm). In the taper design, the inner wall maintains a constant radius of curvature, and the outer wall has a taper towards the outside.

[0085] The baseline microfluidic channel and the comparative microfluidic channel each had an inner wall with a constant channel height of 150 μm and a constant inner radius of curvature of 25 mm. Further, the flow rate of the liquid through each channel was equal.

[0086] It was assumed that the lateral movement of the particles due to the focusing of the particles is proportional to the radial component of the Dean flow at the position x along the length of the liquid channel:

Equation

[0087] In a tapered channel where the inner wall has a constant radius and the outer wall tapers outward, the fluid flowing through the channel spreads outward to fill the channel. As a result, the particles in the channel move outward (i.e., away from the inner wall and towards the outer wall), which can be approximated by the following equation: [Number] where U M (x) is the outward movement of the particle, p(x) is the distance from the particle to the channel inner wall, U(x) is the average velocity of the fluid, k is the outward taper rate per unit length, and w(x) is the channel width at position x. The lateral movement of the particle outward due to channel expansion cancels out the focusing of the particle. Therefore, the lateral movement U DM (x) of the particle in a channel tapered outward is approximated by the following equation: [Number] Or [Number]

[0088] A numerical integration was developed to approximate the time (focusing time) required for the particle to move laterally from the outer wall to the inner wall of the channel: [Number] where w0 is the initial width of the channel. The focusing length L of the tapered channel, which is the channel length required for the particles to move laterally from the outer wall to the inner wall of the channel f,tapered is as follows:

Number

[0089] The following table shows the above two design examples, which indicate the reduction in the required focusing length due to the addition of the taper. Note that the final width and the linear fluid velocity are the same in the two designs - thus, the flow rates are equal, making the designs comparable.

Table 10

[0090] In particular, the outward particle movement U M (x) due to channel expansion and the inward particle movement U D (x) due to particle focusing. If the former is greater than the latter, the particles in the fluid may never converge, and some particles will ultimately be pulled outward rather than inward. Therefore, it is desirable to limit the rate of expansion of the width of channel k, which limits the outward particle movement U D (x) with respect to the inward particle movement U M (x) due to particle focusing.

[0091] The following Table 11 shows the influence of the taper ratio k on the focusing length L f . In this example, the fluid is water. The channel height is constant at 150 μm between the inlet and the outlet, and the initial channel width w 0 is 500 μm. The channel has an inner wall with a constant radius of curvature of 25 mm. The initial flow velocity of the water through the channel is 1 m / s.

Table 11

[0092] As k increases, the focusing length L fIt should be noted that it increases significantly. Various datasets were considered according to the operating conditions of the microfluidic channel to approximate the convergence length L f and k generally seems to be less than 0.01 mm / mm. In some embodiments, k is less than 0.007 mm / mm. In some embodiments, k is 0.005 mm / mm or less, or 0.004 mm / mm or less. When a taper is incorporated into the microfluidic channel, the taper is generally greater than 0 mm / mm.

[0093] The above-reported data regarding the tapered channel relates to a channel having a taper from the channel inlet to the channel outlet. In some implementations, the rate of taper k can be greater than 0.004 mm / mm, 0.005 mm / mm, 0.007 mm / mm, 0.01 mm / mm, or 0.016 mm / mm, such as when the channel tapers towards the outlet from an intermediate point along the channel (between the channel inlet and the channel outlet). In implementations where the taper starts towards the end of the channel, many particles may already be converging towards the inner wall, and thus it is predicted that the taper rate can be increased relatively because they may not move significantly outward by the fluid filling the expanding channel.

[0094] Example F

[0095] Table 12 below shows the results of comparing a channel having certain dimensions (height 150 μm, width 500 μm, radius of curvature 25 mm) with a tapered channel having the same height and radius of curvature but a width that doubles from 500 μm to 1000 μm (1 mm) in the last quarter of the length of the channel. The channels have a fairly consistent (13 / 87 vs 15 / 85) total fluid volume flow rate split, but a fairly significant increase (from 59% to 79%) in particle retention in the internal channel as a result of the taper was observed.

Table 12

[0096] Exemplary embodiments

[0097] Aspect 1 A hydrodynamic separator configured to separate a liquid having dispersed particles with a diameter (a), comprising: a substrate; and a liquid channel defined by the substrate, the liquid channel being configured to receive liquid therein, the liquid channel having an inlet and an outlet: the liquid channel having an inner wall defining an inner radius around a central axis and an outer wall defining an outer radius around the central axis, the liquid channel having a liquid channel length along the inner wall from the inlet to the outlet, the liquid channel having a rectangular cross-section along the liquid channel length, the rectangular cross-section having a channel width between the inner wall and the outer wall, the channel having a tapered region where the channel width increases at a constant rate between 0.00 mm and 0.01 mm per mm of the liquid channel length towards the outlet, having the liquid channel, the hydrodynamic separator.

[0098] Aspect 2 The hydrodynamic separator according to any one of Aspects 1 and 3-11, wherein the tapered region extends from the inlet to the outlet.

[0099] Aspect 3 The hydrodynamic separator according to any one of Aspects 1-2 and 4-11, wherein the inner radius is constant from the inlet to the outlet.

[0100] Aspect 4 The hydrodynamic separation device according to any one of Aspects 1-3 and 5-11, wherein the outer radius tapers outwardly between the inlet and the outlet.

[0101] Aspect 5 The hydrodynamic separation device according to any one of Aspects 1-4 and 6-11, 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 a tapered region having a tapered region length extending from the first region to the second region.

[0102] Aspect 6. The hydrodynamic separator according to any one of Aspects 1-5 and 7-11, wherein the first region has a length longer than that of the second region.

[0103] Aspect 7. The hydrodynamic separator according to any one of Aspects 1-6 and 8-11, wherein the separator is configured to have a Dean number (De) between 5 and 25 in the first region and the second region.

[0104] Aspect 8. The hydrodynamic separator according to any one of Aspects 1-7 and 9-11, wherein the particle diameter (a) is larger than 8% of the hydraulic diameter (D H ) at least in the first region.

[0105] Aspect 9. The hydrodynamic separator according to any one of Aspects 1-8 and 10-11, wherein the separator is configured to separate particles with a density up to three times that of the liquid.

[0106] Aspect 10. The hydrodynamic separator according to any one of Aspects 1-9 and 11, wherein the outlet has a first outlet and a second outlet.

[0107] Aspect 11. The hydrodynamic separator according to any one of Aspects 1-10, wherein the liquid channel is one of a plurality of identical liquid channels.

[0108] Aspect 12. A hydrodynamic separator configured to separate a liquid having dispersed particles with a diameter (a), comprising: a substrate; and a liquid channel at least partially defined by the substrate, the liquid channel being configured to receive the liquid therein, the liquid channel having an inlet and an outlet including a first outlet branch and a second outlet branch: the liquid channel has an inner wall defining an inner radius around a central axis and an outer wall defining an outer radius around the central axis, the liquid channel has a liquid channel length along the inner wall from the inlet to the outlet, The liquid channel has a channel width between an inner wall and an outer wall, and the channel has a tapered region where the channel width increases towards the outlet. having a liquid channel a hydrodynamic separator.

[0109] Aspect 13 The hydrodynamic separator according to any one of Aspects 12 - 31, wherein the tapered region extends from the inlet to the outlet.

[0110] Aspect 14 The hydrodynamic separator according to any one of Aspects 12 - 13 and 15 - 31, wherein the inner radius is constant from the inlet to the outlet.

[0111] Aspect 15 The hydrodynamic separator according to any one of Aspects 12 - 14 and 16 - 31, wherein the outer radius is tapered outwardly between the inlet and the outlet.

[0112] Aspect 16 The hydrodynamic separator according to any one of Aspects 12 - 15 and 17 - 31, 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 a tapered region having a tapered region length extending from the first region to the second region.

[0113] Aspect 17 The hydrodynamic separator according to any one of Aspects 12 - 16 and 18 - 31, wherein the first region has a length longer than that of the second region.

[0114] Aspect 18 The hydrodynamic separator according to any one of Aspects 12 - 17 and 19 - 31, wherein the separator is configured to have a Dean number (De) between 5 and 25 in the first region and the second region.

[0115] Aspect 19 The hydrodynamic separator according to any one of Aspects 12 - 18 and 20 - 31, wherein the particle diameter (a) is greater than at least 8% of the hydraulic diameter (D H ) in the first region.

[0116] Aspect 20: The separator is the hydrodynamic separator according to any one of Aspects 12-19 and 21-31, configured to separate particles with a density up to three times that of the liquid.

[0117] Aspect 21: The hydrodynamic separator according to any one of Aspects 12-20 and 22-31, wherein the inner radius is 10 mm or more and 100 mm or less.

[0118] Aspect 22: The hydrodynamic separator according to any one of Aspects 12-21 and 23-31, wherein the liquid channel is one of a plurality of identical liquid channels defined by a substrate.

[0119] Aspect 23: The hydrodynamic separator according to any one of Aspects 12-22 and 24-31, wherein the liquid channel has a width in the range of 400 μm to 1000 μm.

[0120] Aspect 24: The hydrodynamic separator according to any one of Aspects 12-23 and 25-31, wherein the liquid channel has a height in the range of 100 μm to 500 μm.

[0121] Aspect 25: The hydrodynamic separator according to any one of Aspects 12-24 and 26-31, wherein the liquid channel has a polygonal cross-section along the length of the liquid channel.

[0122] Aspect 26: The hydrodynamic separator according to any one of Aspects 12-25 and 27-31, wherein the liquid channel has a rectangular cross-section along the length of the liquid channel.

[0123] Aspect 27: The hydrodynamic separator according to any one of Aspects 12-26 and 28-31, wherein the channel width of the liquid channel does not change by more than 10 mm per mm of the liquid channel length along the liquid channel.

[0124] Aspect 28: The hydrodynamic separator according to any one of Aspects 12-27 and 29-31, wherein the channel width increases at a constant rate in the tapered region.

[0125] Aspect 29. The hydrodynamic separator according to any one of Aspects 12 - 28 and 30 - 31, wherein the liquid channel has a first region having a first channel width and a tapered region having a channel width that increases from the first region to the outlet.

[0126] Aspect 30. The hydrodynamic separator according to any one of Aspects 12 - 29 and 31, wherein the liquid channel has a plurality of tapered regions, each having a channel width that increases towards the outlet.

[0127] Aspect 31. The hydrodynamic separator according to any one of Aspects 12 - 30, wherein the liquid channel is a microfluidic channel.

[0128] It should also be noted that, as used in this specification and the appended claims, the phrase "configured to" describes a system, device, or other structure that is constructed to perform a particular task or to adopt a particular configuration. The term "configured to" can be used interchangeably with similar terms such as "arranged to", "constructed to", "manufactured to", etc.

[0129] All publications and patent applications herein are indicative of the level of those skilled in the art to which this technology pertains. All publications and patent applications are incorporated herein by reference as if each individual publication or patent application were specifically and individually indicated to be incorporated by reference. In case of any conflict between the disclosure of this application and the disclosure(s) of any document(s) incorporated herein by reference, the disclosure of this application shall apply.

[0130] This application is intended to cover adaptations or variations of the subject matter. It is to be understood that the above description is illustrative and not restrictive, and that the claims are not limited to the exemplary embodiments described herein.

Claims

1. 1. A hydrodynamic separator configured to separate a liquid having dispersed particles having a diameter (a), comprising: a substrate; and a liquid channel defined at least in part by the substrate, the liquid channel configured to receive a liquid therein, the liquid channel having an inlet and an outlet having a first outlet branch and a second outlet branch; the liquid channel has an inner wall defining an inner radius about a central axis and an outer wall defining an outer radius about the central axis; the liquid channel has a liquid channel length along the inner wall from the inlet to the outlet; the liquid channel has a channel width between the inner wall and the outer wall, the channel having a tapered region where the channel width increases toward the outlet. Hydrodynamic separator.

2. the tapered region extends from the inlet to the outlet; 10. The hydrodynamic separator of claim 1.

3. the inner radius is constant from the inlet to the outlet; 3. A hydrodynamic separator according to any one of claims 1 and 2.

4. the outer radius tapers outwardly between the inlet and the outlet.

3. A hydrodynamic separator according to any one of claims 1 and 2.

5. the liquid channel having 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 a tapered region having a tapered region length extending from the first region to the second region; 3. A hydrodynamic separator according to any one of claims 1 and 2.

6. The first region has a longer length than the second region.

6. The hydrodynamic separator of claim 5.

7. the separator is configured to have a Dean number (De) between 5 and 25 in the first region and the second region; 6. The hydrodynamic separator of claim 5.

8. The diameter (a) of the particle is a hydraulic diameter (D Ｈ ) is greater than 8% of 6. The hydrodynamic separator of claim 5.

9. the separator is configured to separate particles up to three times the density of the liquid; 3. A hydrodynamic separator according to any one of claims 1 and 2.

10. The inner radius is equal to or greater than 10 mm and equal to or less than 100 mm.

3. A hydrodynamic separator according to any one of claims 1 and 2.

11. the liquid channel is one of a plurality of identical liquid channels defined by the substrate; 3. A hydrodynamic separator according to any one of claims 1 and 2.

12. The liquid channel has a width in the range of 400 μm to 1000 μm.

3. A hydrodynamic separator according to any one of claims 1 and 2.

13. The liquid channel has a height in the range of 100 μm to 500 μm.

3. A hydrodynamic separator according to any one of claims 1 and 2.

14. the liquid channel has a polygonal cross section along the length of the liquid channel; 3. A hydrodynamic separator according to any one of claims 1 and 2.

15. the liquid channel has a rectangular cross section along the length of the liquid channel; 3. A hydrodynamic separator according to any one of claims 1 and 2.

16. the channel width of the liquid channel does not vary by more than 10 mm per mm of liquid channel length along the liquid channel; 3. A hydrodynamic separator according to any one of claims 1 and 2.

17. the channel width increases at a constant rate in the tapered region; 3. A hydrodynamic separator according to any one of claims 1 and 2.

18. the liquid channel having a first region having a first channel width and a tapered region having an increasing channel width from the first region to the outlet; 3. A hydrodynamic separator according to any one of claims 1 and 2.

19. the liquid channel having a plurality of tapered regions, each having an increasing channel width toward the outlet; 3. A hydrodynamic separator according to any one of claims 1 and 2.

20. the liquid channel is a microfluidic channel; 3. A hydrodynamic separator according to any one of claims 1 and 2.

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