A self-cleaning micro-fluidic chip biospired by the filtering system of manta rays

Abstract

Size-based particle filtration has become indispensable in numerous biomedical and environmental applications. In this study, bioinspired by the filter-feeding mechanism (lobe filtration) of manta rays, we designed a U-shaped biomimetic gill rake filter that combined lobe filtration and Dean flow to filter monodisperse suspensions, bi-disperse suspensions and yeast cells. Compared with other equipment using the inertial focusing technology, our equipment can perform high-throughput (up to 8 mL min⁻¹) and high-efficiency filtration of particles (maximum filtration efficiencies of 96.08% and 97.14% for 10 and 15 μm monodisperse suspensions at the optimum flow rate of 6 mL min⁻¹). The complex velocity field of the micro-fluidic flow within the filter is numerically simulated, and in combination with experiments, a threshold for the flow rate is identified. When the inlet flow rate exceeds the threshold value, the efficiency of particle filtration is increased rapidly. Afterwards, by analysing the filtration mechanism, we develop three novel filtration processes. The equilibrium positions of the particles and yeast cells in the main channel are close to the outer wall at high flow rate, which diminishes the likelihood of particles and yeast cells entering the side channel. This configuration establishes a self-cleaning mechanism, ensuring prolonged and efficient operation of the filter with high-throughput processing. Furthermore, the influence of the filter lobe angle and channel width on the filtration efficiency and outlet flow rate ratio are explored, and an optimisation plan is prepared.

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1. Introduction

The ability to separate biological cells or micrometre-scale particles is important in micrometer-scale manufacturing,¹ particle counting,² and bio-molecular analysis.³ Conventional separation methods, such as sieving,⁴ centrifugation,⁵ and cross-flow filtration⁶ can effectively separate particles. However, these separation techniques are limited by low throughput (1–1000 μL), particle size restrictions, highly skilled operator requirements, clogging and fouling or extended processing times.^7,8 In recent years, researchers have detected the presence of 100 nm to 5 mm micro-plastics (MPs), in the human circulatory system and breast milk. The potential hazards associated with these particles have garnered widespread attention.^9,10 Leslie et al.¹¹ measured micro-plastic particles in human whole blood collected from 22 healthy volunteers. The overall measured concentration of the MPs was 1.6 μg mL⁻¹. In a pilot study conducted in Italy, the MP concentrations in 34 samples of breast milk were between 0 and 2.72 MP g⁻¹.¹² The accumulation of MPs in human body is mainly related to their size, which should not exceed 10–15 μm.¹³ Therefore, small-particle separation at high-flow rates has become a focus of attention.

Micro-fluidic techniques, which can efficiently and flexibly manipulate particles in small-sized (micro-metre-scale) channels,^14,15 have been widely applied to separate particles. They can be divided into two categories: sheath-flow-assisted techniques and sheathless techniques.¹⁶ The sheath-flow-assisted technique achieves particle separation by co-flowing the sample fluid with a sheath flow.¹⁷ However, the sheath flow significantly reduces sample flow flux.^18,19 Sheathless techniques, such as dielectrophoresis,²⁰ magnetophoresis,²¹ acoustophoresis,²² and optical tweezing,²³ have been rapidly developed in recent years to increase the sample throughput. However, in most cases, the increased sample throughput is still at the level of μL h⁻¹ and is dependent on complex external field generators or high-precision micro-structures, which impede the application in large-volume sample processing.

Inertial micro-fluidics has garnered significant attention because of its ability to achieve extremely high throughput continuously without depending on external forces. It has been used to precisely manipulate micro-particles based on the equilibrium positions of different-sized particles.²⁴ The inertial migration of particles in a straight tube was first reported by Segre and Siberberg.²⁵ The changes that occurred in the particle equilibrium positions with flow conditions were complicated. Four or eight particle equilibrium positions have been reported in a square channel at various Reynolds numbers (Re_c) and particle sizes.²⁶ Because of the high dependence of the inertial lift force on fluid flow rates, excessive flow rates will cause particle defocusing. Consequently, the channels in micro-fluidic chips need to be long enough to meet the particle focusing requirements.²⁷ The flow rates of these channels typically remain at μL min⁻¹ level, limiting their further development.

To increase the throughput and reduce the chip size, various channel geometries have been designed, such as spiral,²⁸ serpentine,²⁹ contraction-expansion³⁰ and non-rectangular cross-sectional channels.^31,32 The overall curvature of the channel and the design of channel cross-section will determine the Dean flow into the forces exerted on the particles within a straight channel.^33,34 They will increase the complexity of particle migration physics and reduce the number of particle equilibrium positions.³⁵ Yeh et al.³⁶ introduced a passive micro-fluidic device with a spiral micro-channel geometry and successfully separated different-sized particles at a flow rate of 0.4 mL min⁻¹. Cha et al.³⁷ systematically investigated the effects of concave and convex obstacles on inertial focusing and separation in sinusoidal channels. When two sinusoidal channels were connected at a high throughput of 1 mL min⁻¹, the recovery ratio of 15 μm particles was ∼92.43%.

Biomimicry has already provided new ideas and principles for scientific and technological innovation. It has long been believed that fish typically acquired food through a simple curved filtration process although anatomical studies revealed that their mechanisms for obtaining food were more complex than sieving.^38,39 Manta rays feed by opening their mouths as they swim, catching tiny plankton while simultaneously expelling water through their gills. How their filtering apparatus allow the capturing of food that is smaller than their filter pore sizes, particularly without being clogged, remains elusive. Recently, Divi et al.⁴⁰ examined the particle suspension flow around the filter-feeding mouth of a manta ray using physical and computational modelling. Flow separation occurred behind the leading edge of each filter lobe, generating large vortex flows within each pore (340 μm). The filtration efficiency was increased when the particle size exceeded ∼200 μm, which was smaller than the pore size. Contact forces caused particles to “ricochet” away from the filter pores, thereby leading to a non-clogging filtration mechanism. Clark & San-Miguel⁴¹ designed a straight channel filter based on this filtration mechanism, where 25 μm particles achieved high efficiencies with the maximum efficiency of ∼99%. However, the filter offered moderate filtration efficiencies (75%) for 15 μm particles at flow rate >6 mL min⁻¹. The authors noted that lobe filtration using a micro-fluidic device capable of filtering small particles (∼10 μm) with high efficiencies could be challenging.

In this study, we designed and manufactured a U-shaped biomimetic gill rake filter that combined lobe filtration with Dean side flow to achieve size-based particle filtration. We first explored the effects of critical operational parameters, such as the inlet flow rate, on particle filtration. By using ANSYS Fluent, we revealed the intricate velocity distribution of the fluid flow within micro-channels and proposed three novel filtration process models. The effect of particle size on lobe filtration efficiency and flow rate ratio was then further examined. Furthermore, the variation patterns of the filtration efficiency and flow rate ratio as the changes of the filter lobe angle and channel width were compared. Finally, the separation of bi-disperse suspensions and yeast cells validated the capability of the filter to handle complex particle size samples and biological samples. The chip offers a promising solution for applications requiring the swift processing of substantial quantities of sample solutions with small particles.

2. Theory

The inertial effect of a fluid is often described using the dimensionless Reynolds number, Re_c (ref. 42) (Re_c = ρU_fD_h/μ, where ρ is the fluid density, U_f = Q/A is the average fluid velocity, Q is the fluid volume flow rate, A is the channel cross-sectional area and μ is the dynamic fluid viscosity, D_h = 2hw/(h + w) is the hydraulic channel diameter, h and w are the channel height and width, respectively). As shown in Fig. 1C, the Reynolds numbers for the main and side channels are defined as Re_m and Re_d, respectively. The larger the Reynolds number, the more pronounced the inertial effects. When particles move in a Newtonian fluid, in addition to experiencing drag forces exerted by the fluid to make the particles to move at the same velocity as the surrounding fluid, they also encounter an inertial lift force (F_L) acting perpendicular to the main flow direction due to inertial effects. The F_L is essentially the resultant force of two components: the shear-induced inertial lift force (F_LS) and the wall-induced inertial lift force (F_LW).⁴³ The inertial lift force on a particle varies with the position of the particle in the channel. When F_LS and F_LW become equal, the particle is at an equilibrium position. An accurate lift and drag model is a popular and difficult research topic. Only the force at different positions of the channel cross-section is analysed and the empirical formulas is obtained in a straight microchannel under the limitation of low Reynolds number (Re_c < 100).^43–45 We introduce classic lift forces and attempts to explain the mechanism of particle motion from a theoretical perspective. Di Carlo et al.²⁷ derived an expression describing the magnitude of the lift forces as a function of the particle position across the channel cross-section, the F_L can be expressed as:where a_p is the particle diameter, f_L is the dimensionless lift coefficient, which is dependent on the channel Reynolds number (Re_c) and the particle position within the channel cross-section (X_p).

Fig. 1 (A) Manta ray feeding behaviour and gill raker. (B) Photograph of the completed PDMS micro-fluidic device (the channel was filled with red ink to enable its visualisation). The scale bar is 1 cm. (C) Schematic diagram of the biomimetic micro-fluidic structure. Dimensions of the main channels are shown in the inset image.

When the fluid flow in a curved micro-channel, the fluid near the outer wall will be squeezed and will flow back along the upper and lower walls. This flow results in the formation of two symmetric vortices in the cross-section of the channel. This phenomenon is commonly referred to as Dean flow or secondary flow.⁴⁶ The flow intensity of the Dean flow is characterised by a dimensionless Dean number (De), which is given as⁴⁷

where R is the radius of curvature of the channel. Due to the presence of the cross-sectional Dean flow in a curved microchannel, the particles experience not only the F_L, but also the Dean drag force (F_D).⁴⁸ The F_D applied by this side flow further alters the transverse positions of the flowing particles. The expression for the classical Dean drag force experienced by the particle in microchannel can be arrived as²⁷

It should be noted that the ratio of particle diameter (a_p) to the hydraulic diameter (D_h) should satisfy the condition a_p/D_h ≥ 0.07 to ensure effective particle focusing; otherwise, the particle focusing will not obvious.⁴⁹

A flow rate in the range of 0.25–8 ml min⁻¹ was used in this study, and the corresponding Reynolds numbers and Dean numbers were listed in Tables S1–S4.† From the tables, it can be seen that the Dean number increases with the increase in inlet flow rate and curvature radius, decreases with the increase in aspect ratio. The change in the Dean number will affect the strength of the Dean secondary flow, consequently affecting the equilibrium positon and filtration efficiency of the particles.

3. Materials and methods

3.1. Design and fabrication of micro-fluidic devices

Bioinspiration is based on the unique filter-feeding mechanism of manta rays: these massive creatures have evolved in the regular arrangements (Fig. 1A). While swimming, the manta rays open their mouths to capture planktonic organisms smaller than the gaps between their gill rakers and simultaneously expel water through their gills. Besides, the gill in most fishes form the curve shapes, thus the curved channel is also introduced to optimal the filtration efficiency.

Accordingly, based on the filter-feeding mechanism of manta rays, we designed a biomimetic filter as shown in Fig. 1B and C. By employing an equidistant filter lobe array (53 filter lobe structures), the U-shaped micro-channel is divided into a main channel and a side channel. The micro-channel features one sample inlet (named as inlet) and two sample outlets (named as outlet 1 and outlet 2). The inner wall radius of the micro-channel is 4.50 mm, and its outer wall radius is 5.24 mm. The aspect ratios (AR = h/w, where h is the channel height, and w is the channel width) of channel cross-sections have two values, namely 200 μm (AR = 3 : 10) and 300 μm (AR = 1 : 5), for studying the effects of channel width variations on filtration efficiency. The angle between the filter lobe and the horizontal line, defined as α, can have three values: 13°, 17°, and 21°, to enable the analysis of the effects of the filter lobe angles on filtration efficiency. A photograph of the finished device is shown in Fig. 1B. The small overall size (∼2.5 cm²) and the simple planar nature of the device enable its flexible integration with the existing lab-on-a-chip units.

The chip fabrication followed standard procedure described in the literature.^50,51 Briefly, the wafer was spin-coated with a layer of negative photoresist (SU-8 3050, MicroChem) with a thickness of 60 μm. After baking, the mask was covered on the silicon wafer using UV light exposure. Then it was placed in SU-8 developer (Macklin) for removing the uncured photoresist to obtain the master mold with patterned channel structures. Then, the polydimethylsiloxane (PDMS, Sylgard 184, Dow Corning) with the ratio of base to curing agent of 10 : 1 was poured onto the master mold. After cooling, the PDMS channel was peeled from the wafer, cut into shape, perforated with a 1 mm diameter hole at the inlet and outlets, and bonded to glass after surface activation with oxygen plasma (PDC-32G-2, Harrick Plasma). The chip was then placed in the oven at 65 °C for 2 hours to allow it to irreversibly bond to the slide glass. Finally, a quality check was conducted before each experiment.

3.2. Polystyrene particle sample preparation

Fluorescent polystyrene particles (Jiangsu Zhichuan Technology Co., Ltd), 5, 10, 15 and 20 μm in diameter (Red, Ex: 532 nm, Em: 580 nm) were used in the feasibility experiments. All micro-particles had a density of 1.05 g cm⁻³. In a monodisperse particle suspension, four types of particles with different sizes were suspended in deionised water (DI) with 0.5 wt% Tween 20 (Sigma-Aldrich) to avoid particle aggregation. The 5, 10, 15 and 20 μm particle concentrations were all diluted to 1.0 × 10⁶ particles per mL. Particle suspensions were mixed for 10 minutes by using a vortex mixer prior.

To evaluate the capability of the filtration device in processing complex samples with different particle sizes, two types of bi-disperse suspensions were also prepared. Particle sizes were 10 and 15 μm, and 10 and 20 μm respectively. Two different sizes of particles were suspended in deionised water (DI) with 0.5 wt% Tween 20 (Sigma-Aldrich). The concentration of both particle sizes in each bi-disperse suspension was kept the same as 1.0 × 10⁶ particles per mL.

3.3. Yeast cells preparation

Before the separation experiment, yeast cells were cultured on YPD agar plates (prepared with 1000 mL of deionised water, 10 g of Bacto Yeast Extract, 20 g of BactoPeptone, 20 g of dextrose, and 20 g of agar) at 20 °C. During the experiment, cells in the logarithmic growth phase were transferred to YPD liquid medium. After disintegration of larger clusters by vortexing and centrifugation, the supernatant was removed, and the remaining cells were dispensed in phosphate-buffered saline (PBS, Sigma-Aldrich) at a cell concentration of 1.0 × 10⁶ cells per mL for evaluating the filtration performance.

3.4. Experimental setup and data analysis

The fabricated micro-fluidic device was mounted on the platform of an inverted microscope (Elipse Ti, Nikon) with a ×2 objective lens. Before injecting the suspension into the bionic filter, the chip was primed with deionised water for several minutes to remove air bubbles. The liquid mixture containing fluorescent polystyrene particles was injected into the micro-channel using a syringe pump (dLSP 510, Longer). A total of three experiments were conducted, and the average of the collected experimental data was used to draw the required graphs. The error bar in the graphs represented the relevant standard deviation. A CCD camera (Ds-qi1mc, Nikon) was used to record the particle dynamics in both the fluorescence and bright field modes. The images were processed using the software ImageJ (National Institutes of Health, USA): the time-series images (0–50 images) were stacked using sum slices z projection provided in ImageJ. The fluorescence intensity across the micro-channel width was measured by applying the plot profile function of ImageJ. The dimensionless equilibrium positions of the particles in the channel are as follows:where w_L is the distance of the main equilibrium position of particle from the left wall of channel and w is the channel width.

The micro-channel wall positions in the dark fluorescence spectrum were precisely determined by stacking each image and its bright field image. The particle concentration at both outlets was obtained using a hemocytometer. Filtration experiments using different particle sizes were conducted by obtaining the total number of particles from both outlets for each experimental parameter. The filtration efficiency is calculated as:

where N₁ is the total number of particles coming out from outlet 1, and N is the total number of particles entering the inlet.

For each set of experiments, we collected samples from two outlets to obtain outlet 1 flow rate ratio, which can be calculated as:

where Q₁ is the flow rate at the outlet 1 and Q is the flow rate at the inlet.

3.5. Simulation of velocity distribution in the micro-channel

To guide the experimental setup, we used numerical simulations to quantitatively investigate the velocity distribution in the micro-fluidic chip by using the ANSYS Fluent 18.0 computational fluid dynamics simulation software. The momentum conservation equation (eqn (7)) and continuity equation (eqn (8)) were used to calculate the laminar flow of an incompressible fluid.⁵²

∇·u = 0 (8)

where u is the velocity vector, t is the time, p is the total pressure and I is the identity matrix.

Steady state simulations (with 2000 iterations) were performed using standard water properties for the fluid and laminar flow modelling using the SIMPLE solver. No slip condition was used as the boundary condition at the solid walls. A residual convergence criterion of 10⁻⁵ was used. Velocity inlet boundary conditions were used (0.25–8 ml min⁻¹), and the zerogauge pressure is applied at the outlets, which is consistent well with the experimental conditions.

A mesh independence study was conducted by plotting the mass flow rate at outlet 1 vs. flow rate at the inlet to ensure mesh performance (Fig. S1A†). We observe that the flow rate ratio of outlet 1 in the experiment is slightly lower than the numerical simulation results at high flow rates (Fig. S1B and C†) with a relative small deviation (<5%), which is acceptable. The comparison further confirms that the numerical velocity distribution in the micro-fluidic chip align well with the experiments.

4. Results and discussion

4.1. Effect of the flow rate

The biomimetic filter, characterised by w = 200 μm and α = 13°, is initially utilized. The 10 μm particle suspension (a_p/D_h = 0.11 > 0.07) is pumped into the biomimetic filter at an inlet flow rate ranging between 0.25 and 8 mL min⁻¹ (Re_c = 32–1021). The filtration efficiency of the filter is categorised as low (40–60%), medium (20–40% and 60–80%) and high (0–20% and 80–100%) filtration efficiencies. These low, medium and high filtration efficiencies are represented in Fig. 2C and in the subsequent figures by red, yellow and green backgrounds.

Fig. 2 (A) Fluorescent stream images illustrating the particle trajectories of the 10 μm particles at different flow rates. The first image is a photograph of the entrance section at 0.25 mL min⁻¹. The white dotted lines in the images mark the channel walls, and the scale bar is 100 μm. The green arrows indicate the locations of the backflow regions between the filtering lobes. (B) The normalised fluorescent intensity distributions of the 10 μm particle on the yellow line at different flow rates. (C) The two columns display the dimensionless lateral equilibrium positions and filtration efficiency of the 10 μm particles in the main and side channels at different inlet flow rates. (D) Microscopic images sampled at the inlet and the two outlets at 6 mL min⁻¹. At different experimental flow rates, the fluorescence results of the 10 μm particles are shown in Video S1.†

The fluorescence distribution image of the 10 μm particles at the micro-channel inlet (Q = 0.25 mL min⁻¹), where particles enter the two channels, is shown at the far left end of Fig. 2A. The other fluorescence images in Fig. 2A illustrate the separation process of the 10 μm particles in the outlet region at different inlet flow rates. At low flow rates (Q = 0.25–1 mL min⁻¹), the particles near the trailing edge of the filtering lobe in the side channel are directed back into the main channel at the outlet position. This particular particle movement increases the particle count in the main channel, contributing to increase the filtration efficiency. At the flow rates of 0.25 and 0.5 mL min⁻¹, the particles are primarily directed towards the main channel in the region between the second and third filtering lobes at the exit. At higher inlet flow rates, such as 0.75 and 1 mL min⁻¹, the particles are redirected from the region between the third and fourth filtering lobes back into the main channel. At a flow rate of 1 mL min⁻¹, the fluorescence intensity of the particles flowing into the main channel through the filtering lobes diminishes. More particles tend to stay in the side channel, leading to a decrease in the particle filtration efficiency and it still remains above 50% (Fig. 2C). At a flow rate of 2 mL min⁻¹, the particles in the side channel do not return to the main channel near the outlets. The fluorescence bands of both channels become increasingly concentrated, the filtration efficiency is decreased to its lowest value at 45.90% (Fig. 2C).

When Q = 3 mL min⁻¹, the fluorescence bands in the side channel become fainter. Particles once again start to move along the filtering lobes into the main channel. In the main channel, particles begin to migrate towards the midpoint of the long side of the rectangular channel cross-section, and the aggregation effect is enhanced. This phenomenon is consistent with the results reported by Ciftlik et al.⁵³ As the flow rate increased (Q = 4–6 mL min⁻¹), particles in the side channel migrate towards the main channel, forming a backflow region between the filtering lobes near the side channel, without forming fluorescence bands (as indicated by the green arrow in Fig. 2A for a flow rate of 4–6 mL min⁻¹). The fluorescence bands of the particles in the main channel continuously migrate towards the outer wall surface as the flow rate increases within the specified range. Thus, as the Reynolds number continues to increase, the particles move closer to the outer wall surface, thereby reducing the particle entry into the side channel. This configuration establishes a self-cleaning mechanism, which will be analysed in detail in the following part.

At 6 mL min⁻¹, more particles in the side channel migrate towards the main channel, leading to a further increase in the filtration efficiency to attain its maximum value of 96.08% (Fig. 2C and D). As the flow rate increases from 7 to 8 mL min⁻¹, the particles in the side channel stop returning to the main channel along the filtering lobes. At this point, the fluorescence bands of the particles in the side channel are stronger than when they are at 6 mL min⁻¹. The filtration efficiencies of 91.25% and 83.90%, at 7 and 8 mL min⁻¹ respectively, are still higher than their values at the lower flow rates (Q = 0.25–4 mL min⁻¹). As shown at the bottom of Fig. 2C, the filtration efficiency rapidly increases and attains its maximum value as the flow rate exceeds 2 mL min⁻¹. However, when the flow rate exceeds 6 mL min⁻¹, the filtration efficiency once again decreases slowly. Therefore, the filtration efficiency varies with increasing flow rate in a complex manner.

To clearly illustrate the inertia migration and filtration mechanisms of particles in the biomimetic channel, the analysis is conducted on the fluorescence intensity of particle distribution at two outlets (indicated by the yellow horizontal line in the second image of Fig. 2A), as depicted in Fig. 2B. At low flow rate, the particles are distributed over a wide range in the channel. As the flow rate increases, particle focusing improves, consistent with the classical Segre–Silberberg effect.⁵⁴ Another analysis is conducted on the variation of the peak fluorescence intensity with the flow rate. The positions of the peak fluorescence intensity in the main and side channels are defined as the equilibrium positions of particle focusing, as depicted at the top of Fig. 2C. In the main channel, the changes of the equilibrium positions are not pronounced at lower flow rates. After the flow rate exceeds 1 mL min⁻¹, the particle equilibrium positions initially move towards the outer wall and then stabilises. Thus, the particles will less entry into biomimetic structures, reduce the possibility of blockage. In the side channel, the particle equilibrium positions gradually move towards the inner wall, and once the flow rate exceeds 2 mL min⁻¹, the enhancement of the Dean vortex causes small particles move towards the outer side wall. Thus, the particles quickly approach the trailing edges of the filtering lobes, leading to an increase in the filtration efficiency. At high flow rates, the particle equilibrium positions slowly move towards the outer wall, which will be subsequently analysed in detail.

To further analyse the fluid mechanisms of the designed micro-chip, we numerically study the fluid velocity distribution in the biomimetic channel. Several typical positions in Fig. 1C are defined to study the velocity contours along four typical cross-sections 1–4 at various inlet flow rates, which is clearly shown in Fig. 3A and B. The left sides of the velocity contours represent the side channel with large radius of curvature and the right side of the velocity contours are the main channel.

Fig. 3 Simulated velocity contour along the cross-sections (A) 1 and (B) 4. The white lines represent streamlines. All left side figures represent the side channel. The colour level represents the magnitude of the flow velocity. Dimensionless velocity profiles at the positions (C) d4 and (D) m4. The dimensionless velocity at each position is normalised using its maximum velocity under the given conditions. Dashed lines indicate the boundaries where the velocity undergoes a rapid change (w = 177 μm).

From Fig. 3A and S2A and B,† it can be observed that during the fluid flow through the cross-sections 1–3, the fluid in the side channel go through three stages. At low flow rate (Q = 0.25 mL min⁻¹), no apparent Dean flow is present. As the flow rate increases (Q = 3 mL min⁻¹), two counter-rotating Dean vortices perpendicular to the main flow direction are generated. The curvature of the side channel is greater than that of the main channel, thus the Dean flow in the side channel is stronger than in the main channel. When Q = 8 mL min⁻¹, the generated Dean vortices in the cross-sections of the main and side channels will become obvious. Simultaneously, the positions of the high-flow regions in the side channel (main channel) gradually approach the trailing edge of the filtering lobes (outer wall surface), a phenomenon that is prominent at cross-section 4 (Fig. 3B and S2C†). To analyse the velocity distribution of the fluid along the flow direction (Z = 0), six positions are selected along the outlet section of the biomimetic channel, as shown in Fig. 1C. These positions are labelled as d2, d3, d4, m2, m3 and m4. The velocity profiles and contours at the outlet section of the main and side channels are shown in Fig. S2A and B and S4.† Owing to the combined effect of the filtering lobes and Dean flow, significant variations are observed in the velocity profiles in both the side and main channels at different flow rates.

In the side channel, as shown in Fig. 3C, the velocity profile in the side channel no longer represents a standard parabolic Poiseuille flow; instead, the fluid velocity near the trailing edges of the filtering lobes rapidly increases. When the flow rate exceeds 2 mL min⁻¹, the fluid velocity near the trailing edge of the side channel increases, and the velocity profile begins to exhibit a prominent velocity peak. This phenomenon is more obvious with increasing flow rate (Fig. S3A and S4A–D†), a significant amount of fluid in the side channel will flow back into the main channel in the region between the filtering lobes. Thus, the maximum fluid velocity in the side channel (main channel) at position m4 (d4) is noticeably smaller (larger) than the respective velocities at d2 and d3 (m2 and m3). Consequently, the particles are more likely to migrate towards the main channel when Q ≥ 2 mL min⁻¹, and the filtered solution are retained in the side channel, enhancing the efficiency of particle filtration at high flow rates.

In the main channel, when Q ≤ 2 mL min⁻¹, the velocity profile within the main channel in Fig. 3D also does not represent a standard parabolic Poiseuille flow; the velocity near the leading edge of the filtering lobes is greater than that near the outer wall side. At a flow rate of 2 mL min⁻¹, symmetric velocity profiles begin to appear in the main channel (Fig. S3B†), and this flow rate is referred to as the critical flow rate. When Q ≥ 2 mL min⁻¹, the velocity profiles in the main channel exhibit a trend opposite to that at low flow rates, the position of the maximum velocity further shifts towards the outer wall. Consequently, the equilibrium positions of the particles in the main channel also move towards the outer wall, and the efficiency of particle filtration at high flow rates is increased.

The velocity curves in Fig. 3C and D show that the critical flow rate is 2 mL min⁻¹, which aligns with the experimental conclusion in Fig. 2C, where the particle filtration efficiency is at its lowest when Q = 2 mL min⁻¹. This confirms that by utilising numerical velocity profiles and critical flow rate to analyse the fluid mechanisms in the experiments is feasible. Once the critical flow rate has been identified, the quick prediction of the flow rate range for efficient particle filtration becomes possible.

Based on the above fluid velocity simulation, we attempt to draw on existing theoretical force models for particle migration in simple microchannel to deepen the understanding of the particle filtration process. Three novel filtration processes are summarized in Fig. 4, each filtration process can be described in detail as follows:

Fig. 4 Schematic of the developed three novel filtration processes. F_D, F_LS, F_LW and F_R are the Dean drag force, shear-induced inertial lift force, wall-induced inertial lift force and the resultant force acting on the particles, respectively. In this schematic diagram, only particles near the filtering lobe structure are subjected to force analysis.

(1) First filtration process (green circle): the particles moving in the side channel owing to the combined effects of F_L and F_D, experience a resultant force (F_R) direct towards the right. As these particles reach the trailing edge of the filtering lobe, they collide with the filtering lobe, and bounce into the region between the filtering lobes. Then, they move with the fluid into the main channel and ultimately exit the filter through the main channel (outlet 1), completing the particle separation process.

(2) Second filtration process (blue circle): because of the incoming flow from the side channel, the flow rate at the outlet section of main channel is enhanced (Fig. S3A and S4A–D†), a backflow zone is formed in the region between the filtering lobes, as shown in Fig. S5 and S6.† In the side channel, a clockwise vortex develops in the region between the filtering lobes. When particles in the side channel approach the vicinity of the vortex, the particles move along the filtering lobe towards the main channel. Thus, the particles exiting the filter from main channel, enhance the particle filtration efficiency.

(3) Third filtration process (yellow circle): at low flow rates, the particles near the filtering lobe in the main channel experience an F_L and F_D, resulting in a F_R directed to the left, guiding the particles towards the filtering lobe. However, influenced by the inflow from the side channel and the collision with the leading edge of the filtering lobe, the particles near the outlet section of main channel follow a spiral “ricochet” trajectory along the leading edge of the filtering lobe, preventing them from entering the side channel. With increasing the flow rate, as depicted in the cross-sectional view shown in Fig. 3C and D and 4, the effects of the Dean flow and the inflow from the side channel along the filtering lobe are strengthen. The velocity profile in the main channel shifts towards the outer wall, causing more particles accumulate near the outer wall, reducing the likelihood of upstream particles migrating to the side channel. This phenomenon not only enhances the particle filtration efficiency, but also provides a self-cleaning mechanism, ensuring the prolonged and efficient operation of the filter.

4.2. Effect of the particle diameter

To further illustrate the effect of particle diameters on the performance of biomimetic filter, three sets of polystyrene particles with different diameters (5, 15 and 20 μm) are individually injected into the biomimetic filter (w = 200 μm, α = 13°) at inlet flow rates ranging from 0.25 to 8 mL min⁻¹. The analysis focus on the filtration efficiency and the mechanisms of the biomimetic micro-channel for particles of varying diameters. In Fig. 5A–C, the fluorescence images depicting the motion of the particles with different diameters at various inlet flow rates are shown, clearly illustrating the migration process. The fluorescence trajectories indicate that the particle filtration efficiency is influenced by the flow rate and particle diameter.

Fig. 5 Fluorescent stream images illustrating the trajectories of (A) 5, (B) 15 and (C) 20 μm particles in the outlet region at different flow rates. The pseudo-coloured 5, 15 and 20 μm particles are represented with red, blue and green, respectively. The white dotted lines in the images mark the channel walls. The scale bar is 100 μm. The green arrows indicate the locations of the backflow regions between the filtering lobes. The red arrows indicate the locations where the “ricochet” motion occurs. For all flow rates, the fluorescence results of the particles with different diameters are shown in Video S2.†

For the 5 μm particles at low flow rates (Q ≤ 2 mL min⁻¹), those particles (a_p/D_h = 0.05) do not meet the requirements of particle focusing (a_p/D_h ≥ 0.07). As a result, the particles are dispersed in both the main and side channels, leading to a broad distribution of particle fluorescence and insignificant changes in the particle equilibrium positions. Due the small diameter, these particles are influenced by the fluid flow from the side channel to the main channel, forcing them to migrate along the filter lobes towards the main channel. At this point, the filtration efficiency for the 5 μm particles is similar to that of other particles with different diameters, reaching ∼60% at Q ≤ 2 mL min⁻¹. As the flow rate exceeds 2 mL min⁻¹, the aggregation of 5 μm particles is improved. At higher flow rates (Q = 4–8 mL min⁻¹), despite the decrease in particle focusing, the enhanced effect of the Dean vortices and the backflow zone (indicated by the green arrow in Fig. 5A) causes the particles in the main channel to shift towards the outer wall, stabilising their equilibrium positions (Fig. 6B). Meanwhile, more particles from the side channel enter the main channel along the filtering lobes, resulting in an increment in the filtration efficiency shown in Fig. 6A, reaching a maximum value close to 70%.

Fig. 6 (A) Filtration efficiency for particles ranging from 5 to 20 μm in diameter. (B) Dimensionless main and side channel equilibrium positions as a function of the inlet flow rate. (C) Flow rate ratio at outlet 1 for particles ranging from 5 to 20 μm in diameter. (D) Microscopic images of the 15 μm particles sampled at the inlet and the two outlets at Q = 6 mL min⁻¹.

For the 15 μm particles (a_p/D_h = 0.16 > 0.07), at low flow rates (Q ≤ 0.5 mL min⁻¹), the fluorescence focusing of particles is better than that of 5 and 10 μm particles. Similar to the experimental phenomenon of the 10 μm particles shown in Fig. 2A, the particles in the side channel can migrate towards the main channel along the filter lobes. When Q = 2–4 mL min⁻¹, the fluorescence stripes of the particles in the side channel gradually darken with increasing the flow rate, more particles start to migrate towards the main channel. The equilibrium positions of particles in the main channel are close to the outer wall, reduce the possibility of particles entering the side channel to achieve self-cleaning purpose, thereby rapidly increasing the filtration efficiency. At Q = 6 mL min⁻¹, a single-line fluorescence focus appears in the side channel, closely following the trailing edge of the filter lobe and migrates back to the main channel along the filter lobe near the outlet section, achieving the maximum particle filtration efficiency of 97.14% (Fig. 6A and D). As the flow rate further increases, the fluorescence stripes reappear in the side channel. Although the filtration efficiency slightly decreases, it remains above 80%.

For the 20 μm particles, the focusing effect is improved with increasing the particle diameter and the flow rate. At low flow rate (Q = 0.5 mL min⁻¹ in Fig. 5C), the particles aggregate in the middle sections of the main and side channels. As the flow rate increases, the particles in the side channel (main channel) gradually approach the inner wall (the leading edge of the filter lobes). The fluorescence stripes of the particles in the side channel (main channel) darken (brighten) with increasing flow rate, leading to a gradual increase in the filtration efficiency. At 6 mL min⁻¹, the optimal filtration efficiency with 87.82% is achieved. However, when Q > 6 mL min⁻¹, the particles in the side channel again exhibit well-focused fluorescence stripes, resulting in a reduction in the particle filtration efficiency. When particles in the main channel approach the leading edge of the filter lobes (Q = 2–8 mL min⁻¹), a noticeable “ricochet” motion occurs (indicated by the red arrow in Fig. 5C).

Next, fluorescence intensity distributions are measured at the same outlet section (Fig. S7A–C†). By comparing the changes in the equilibrium positions of particle focusing in the main and side channels (as shown in Fig. 6B), we attempt to explain the mechanism behind the impact of fluid flow rate and particle diameter on the filtration efficiency. At low flow rate, the fluorescence bands in the side channel are wide, the equilibrium positions can be compared only qualitatively. When the flow rate is low (Q < 1 mL min⁻¹), the equilibrium positions of particles with different diameters in both the main and side channels do not show significant changes. Eqn (1) and (3) indicate that the magnitudes of the F_L and F_D depend on U_f and a_p (F_L ∝ U_f²a_p⁴, F_D ∝ U_f²a_p). At low flow rates, the F_L dominates, the Dean effect is almost negligible.^27,55 Large particles are subjected strong F_L, and they quickly migrate to the equilibrium position (midpoint of the long wall of rectangular channel) even at low flow rates. This movement results in the decrease in f_L, and a convergence of F_D with F_L. When large particles reach the equilibrium position, the Dean force on the large particles is also enhanced, 20 μm particles migrate closer to the inner wall than 15 μm particles. As the flow rate further increases, as shown in Fig. 3A, the Dean vortices will be formed more obvious. The small particles are attracted by the Dean vortices, and the equilibrium position of the particles in the main and side channels are gradually shifted towards the outer walls. Thus, the number of small particles entering the main channel along the filter lobes are increased, thereby enhancing the filtration efficiency. Interestingly, with an increase in particle diameter, the flow rate at which the particle equilibrium positions begin to move towards the outer walls in both channels also increases. The large particles experience strong F_D, they can overcome the effect of Dean vortices and continuously move towards the inner walls of the main and side channels. The closer they are to the inner walls, the greater the F_L they are received. Finally, under the combined effect of F_L and the Dean vortices, they slowly migrate towards the outer walls of two channels. Therefore, the equilibrium positions of the 5 μm particles shift towards the outer wall at 1 mL min⁻¹, while the 20 μm particles begin to move towards the outer wall at 6 mL min⁻¹. The particles with diameters of 10 and 15 μm are more prone to outward migration, increasing the likelihood for the particles to enter the main channel along the filter lobe, resulting in a higher filtration efficiency compared with the 20 μm particles.

For each experiment, the flow rate ratio of outlet 1 (φ) is shown in Fig. 6C. As the inlet flow rate increases, the flow rate ratio initially stabilises and then starts to exhibit a decreasing trend. The flow rate in the main channel decreases, whereas the flow rate in the side channel increases, indicating an increased filtrate flow rate in the side channel, which is conducive to enhancing the yield of clean water. As the inlet flow rate increases, more fluid is pressed into the side channel at the inlet section, leading to a reduction in the flow rate ratio. This further confirms that under high flow rate conditions, the biomimetic filter exhibits high efficient filtration. Additionally, we observe that for the same inlet flow rate, the flow rate ratio increases with the particle diameter. This behaviour is related to the entry of particles from the main channel to the side channel in the inlet section. When the particle diameter is small, the particles in the main channel near the outer wall are likely to pass through the gap of two filter lobes (Fig. 1C, minimum distance of 43 μm), and migrate towards the side channel. Larger particles tend to be closer to the leading edge of the filter lobes, hindering the fluid from entering the side channel along the gap of two filter lobes, resulting in an increased flow rate ratio.

A comparison of the filtration efficiencies of the particles with different diameters (Fig. 6A) reveal that once the flow rate exceeds 2 mL min⁻¹, the filtration efficiency of the particles rapidly increases, reaching its maximum value at 6 mL min⁻¹. Simultaneously, we correlate the filtration efficiency and the particle diameter for different inlet flow rates to obtain the optimal operational zone, represented by the green region in Fig. 7. Through a comprehensive comparison of Fig. 3C, 6A and 7, we find that the critical flow rates obtained from numerical simulations align well with the experiments. Besides, the locations of the velocity peaks appearing at the leading edges of filter lobes in Fig. 3C, which are almost near the 177 μm position in the side channel (indicated by the grey dashed line in Fig. 3C). When the particle diameter is less than 23 μm, the particles in side channel are more likely to migrate towards the main channel, thereby enhancing the filtration efficiency. Through the integration of experiments and numerical simulations, the critical flow rate for the designed filter is determined to be 2 mL min⁻¹, and this critical flow rate is applicable to particles smaller than the critical diameter (23 μm).

Fig. 7 Comparison the experiments and numerical simulations on the filtration efficiencies based on the particle size (a_p) and inlet flow rate. For ease of comparison, experimental particle filtration efficiencies are binned into low (40–60%), moderate (60–80%) and high (80–100%) efficiencies, which are depicted by a red box, black dash and green circle, respectively.

4.3. Effect of biomimetic structure

In this section, the impact of the biomimetic structures (filter lobe angles and channel widths) on the particle filtration efficiency is systematically investigated. The minimum distance between the two filter lobes is kept the same as 43 μm. The filtration efficiency of the filter and the flow rate ratio of outlet 1 are compared in detail.

When the filter lobe angle is α = 13°, 17°, and 21°, the filtration efficiencies for the particles with diameters in the range of 10–20 μm are compared in Fig. 6A, 8A and S8A,† respectively. At a filter lobe angle of 21° (Fig. 8A), a small increment in the filtration efficiency is observed for the 15 μm particles at low flow rates, indicating the minor effect of filter lobe angle on the filtration efficiency. Additionally, when the filter lobe angles are 17° (Fig. S8B†) and 21° (Fig. 8D), the influence of the particle size on the outlet flow rate ratio is minimal. Therefore, this section will focus on the 20 μm particles as an example to compare the changes in the filtration efficiency and outlet flow rate ratio with variations in the filter lobe angle and channel width. As the filter lobe angle increases, the filtration efficiency is decreased lightly (Fig. 8B), but the impact is small. Furthermore, as shown in Fig. 8E, the influence of the filter lobe angles on the outlet flow rate ratio can be neglected when Q < 2 mL min⁻¹. When the inlet flow rates exceed the critical value, the flow rate ratio is decreased with increasing the filter lobe angle. In other words, as the filter lobe angle is increased, the filtrated flow rate in the side channel is also increased. Thus, even the Dean number in Tables S1–S3† is increased slightly with the increase in the curvature radius, i.e., the filter lobe angle α. The filtration efficiencies of particles are mainly effected by the inlet flow rate.

Fig. 8 (A) Filtration efficiency for particles ranging from 10 to 20 μm in diameter when the filter lobe angle is 21°. (B) Comparative chart of the filtration efficiency for the 20 μm particles for filter lobe angles of 13°, 17° and 21°. (C) Comparative chart of the filtration efficiency for the 20 μm particles in the channel with width of 200 and 300 μm, respectively. (D) Flow rate ratio for particles ranging from 10 to 20 μm in diameter at a filter lobe angle of 21°. (E) Comparative chart of the flow rate ratio for the 20 μm particles when the filter lobe angles are 13°, 17° and 21°. (F) Comparative chart of the flow rate ratio for the 20 μm particles in the channel with width of 200 and 300 μm, respectively.

According to Fig. 8C, changing the channel width (while keeping α constant at 13°) has a pronounced impact on the filtration of particles by the filter. The typical fluorescent stream images for the 10 μm particles in channel with w = 200 μm (first row of Fig. 9A–C) and w = 300 μm (first row of Fig. 9D and E) are compared with the numerical flow field velocity and streamline distributions on the Z = 0 cross-section (second row of Fig. 9A–E) under the corresponding conditions. The fluid streamlines and the formed vortex between the filtering lobes in simulations are consistent well with the fluorescent stream in experiments. As shown in Tables S1 and S4,† the Dean number is decreased with increasing the width of the rectangular channel. Thus, the filtration efficiency of the particles in the channel with w = 300 μm is lower than the results relating to the 200 μm channel. The critical flow rate is increased from 2 (w = 200 μm, Re_c = 255) to 3 mL min⁻¹ (w = 300 μm, Re_c = 276). The Reynolds numbers for both cases are close to each other, indicating that the critical flow rate can still be determined for channels of different sizes. The flow rate ratios for both channel widths are increased initially, then they are gradually decreased when the inlet flow rates exceed the critical value (Fig. 8F). The flow rate ratio for the 300 μm channel is lower than that of the 200 μm channel. Therefore, for wider channel, achieving a larger filtrate flow in the side channel can be accomplished by increasing the inlet flow rate, further enhancing the filtration efficiency.

Fig. 9 (A–C) Fluorescent stream images (w = 200 μm) illustrating the particle trajectories of 10 μm particles at inlet flow rates of 0.5, 4 and 6 mL min⁻¹. (D and E) Fluorescent stream images (w = 300 μm) illustrating the particle trajectories of 10 μm particles at inlet flow rates of 7 and 8 mL min⁻¹. The white dotted lines in these images mark the channel walls. The green arrows indicate the locations of the vortex between the filtering lobes. The first row shows the experimental fluorescent stream images. The second row shows the numerical flow field velocity and streamline distributions on the Z = 0 cross-section under the corresponding conditions.

A broad velocity profile is formed within the channel when w = 300 μm (Fig. 9D and E, S2D, S4E and F†). The fluid velocity profile also tilts towards one side of the filter lobes when the flow rate increases to 3 mL min⁻¹, but the tilt is not as pronounced as when w = 200 μm. The ability of the particles to enter the main channel from the side channel is weakened, leading to a decrease in the filtration efficiency. Thus, the experimentally predicted critical flow rate in Fig. 8C matches the numerical simulation results in Fig. S4E.† For the same inlet flow rate, the increased in the channel width leads to a decrease in the flow rate ratio. As a result, the particles in the outlet do not return to the main channel along the filter lobes, and the critical flow rate for the 300 μm channel is higher than that for the 200 μm channel.

As the flow rate increases to its maximum value of 8 mL min⁻¹, as shown in Fig. S6,† two independent vortices form between the filter lobes, and the counter-clockwise vortex moves in the direction opposite to the other vortex. This movement hinders the particles from returning to the main channel along the filter lobes. Consequently, with further increases in the flow rate, the particle filtration efficiency tends to decrease as shown in Fig. 2C, 6A, 8A–C, and S8A.†

4.4. Purification of bi-disperse suspensions

In practical applications, the filtration devices typically need to deal with complex samples that are often widely dispersed. Therefore, the filtration performance of biomimetic filters is assessed using a mixture of polystyrene beads. The bi-disperse suspensions are divided into two groups, experiment 1 (10 and 15 μm particles) and experiment 2 (10 and 20 μm particles). Two suspensions are injected into the biomimetic filter (w = 200 μm, α = 13°) at inlet flow rates of 0.25–8 mL min⁻¹, respectively. Typical filtration efficiencies of monodisperse and bi-disperse suspensions are quantitatively compared in first row of Fig. 10.

Fig. 10 (A) Comparison of filtration efficiency in monodisperse and bi-disperse experiments. (B) Fluorescent stream image at the outlet region of experiment 1 (10 and 15 μm particles) at 6 mL min⁻¹. The image is composed by overlaying pictures of red fluorescence at 10 μm and blue fluorescence at 15 μm. The white dotted lines in the images mark the channel walls. The scale bar is 100 μm. (C) Microscopic images of experiment 1 (10 and 15 μm particles) sampled at the two outlets at 6 mL min⁻¹. (D) The filtration efficiency comparison of yeast cells with the monodisperse suspensions (5 and 10 μm particles). (E) The bright-field image of yeast cells at the outlet region at 6 mL min⁻¹. The red arrows indicate the streamline of yeast cells. The scale bar is 100 μm. (F) Microscopic images of yeast cells sampled at the two outlets at 6 mL min⁻¹.

As shown in Fig. 10A, the filtration efficiency of the bi-dispersed solution is close to the results of the monodisperse suspensions, only small differences are observed. When Q = 2 mL min⁻¹, the filtration efficiency of bi-disperse suspension in experiment 1 (10 and 15 μm) is 2.94% higher than that of 10 μm particles, but 4.79% lower than that of 15 μm particles. The efficiency of experiment 2 (10 and 20 μm) is close to that of 20 μm particles, at 54.41%. At the optimum operating condition of 6 mL min⁻¹, the 10 and 15 μm particles move closely following the trailing edge of the filter lobe and migrate back to the main channel along the filter lobe at the outlet section, the filtration efficiency of experiment 1 (10 and 15 μm) reaches its maximum (96.20%, Fig. 10B and C, and S9A†). Meanwhile, as there are still small amounts of 20 μm particles remaining in the side channel (white arrows in Fig. S9B and C†), the efficiency of experiment 2 (10 and 20 μm) is 89.54%, 1.71% higher than the monodisperse suspensions with 20 μm particles. As the flow rate further increases (Q = 8 mL min⁻¹), the filtration efficiencies of both experiments 1 and 2 decrease, but remain above 80%.

Thus, the biomimetic filter possesses the capability to handle complex samples with high filtration efficiency. Additionally, it is believed that the purification performance of the filter can be estimated based on the particle size distribution of complex samples, which typically aligns closely with the filtration performance when dealing with large particle sizes.

4.5. Separation of yeast cells

Yeast cells are known as a type of single-celled eukaryotic microorganism, being renowned for their predominant role in industrial-scale fermentation production of bread, beer, and wine.^56,57 In the field of biology, yeast cells are often used as a model organism for investigating fundamental scientific questions in cell biology, genetics, molecular biology, and so on.^58,59 Its simple cell structure and ease of cultivation allow researchers to study the fundamental mechanisms of life processes. Therefore, the efficient separation of yeast cells for scientific research purposes is particularly important. In this section, yeast cells are pumped into a biomimetic filter (w = 200 μm, α = 13°) at inlet flow rates ranging from 0.25 to 8 mL min⁻¹ to obtain highly concentrated yeast cell suspensions.

As the diameter of yeast cells typically falls within the range of 3–11 μm,⁶⁰ we compare their filtration efficiency with the monodisperse suspensions (5 and 10 μm particles) in Fig. 10D. When the flow rate is low (Q ≤ 2 mL min⁻¹), the filtration efficiency of yeast cells is similar to that of 5 μm particles, fluctuating around 60%. As the inlet flow rate increases, the filtration efficiency of yeast cells, similar to 5 and 10 μm particles, begins to show an upward trend. When Q = 6 mL min⁻¹, yeast cells exhibit a phenomenon similar to that of 10 μm particles: most yeast cells in the side channel are focused, moving closely following the trailing edge of the filter lobe, and migrating back to the main channel along the filtering lobes at the outlet section, resulting in the maximum filtration efficiency (77.95%, Fig. 10E). Additionally, observations of sample images captured from samples taken from both outlet solutions reveal that yeast cells at 6 mL min⁻¹ remain intact and undistorted (Fig. 10F). With further increases in the flow rate, the filtration efficiency gradually decreases but remains above 70%.

All in all, the high filtration efficiencies of particle suspensions and yeast cells further demonstrate the biomimetic filter is a high-throughput filtration tool to process large quantities of biological samples in a short time.

5. Conclusions

Compared to previous devices that utilised the inertial focusing principle, the biomimetic filter can achieve high-throughput (Re_max = 1021) and high-efficiency filtration of particles (with maximum filtration efficiencies of 96.08% and 97.14% for 10 and 15 μm particles respectively at the optimum operating condition of 6 mL min⁻¹). The decreasing trend in the flow rate ratio is observed with increasing flow rate, and a larger particle size leads to a larger flow rate ratio at the same flow condition. Subsequently, a combination of experiments and numerical simulations is employed to reveal the intricate fluid velocity distribution of micro-fluidic flow within the main and side channels. In addition, a threshold for flow rate is identified, which can be used to quickly predict the flow rate range for efficient particle filtration. Three novel filtration processes are established: collision, low-pressure induction and “ricochet” motion filtration models. In addition, changes in the angle of the filter lobes have a minor effect on filtration efficiency but a significant effect on the flow rate ratio, and the flow rate ratio decreases with an increase in the angle of the filter lobes. The critical flow rate is increased from 2 mL min⁻¹ (w = 200 μm, Re_c = 255) to 3 mL min⁻¹ (w = 300 μm, Re_c = 276) with the widening of the channel width, which will result in a higher filtrate flow rate in the side channel and further improve the filtration efficiency. Finally, the proposed filter is employed to process bi-disperse suspensions and yeast cells with high efficiency. The highest filtration efficiencies (when the flow rate is 6 mL min⁻¹) for the bi-disperse suspensions with 10 and 15 μm particles, 10 and 20 μm particles, and yeast cells being 96.20%, 89.54%, and 77.95%, respectively.

In summary, this biomimetic filter chip offers several advantages, including high processing throughput, excellent filtration efficiency, self-cleaning capability and the ability to filter small particles. Consequently, this novel filter may also be expanded for label-free high-throughput filtration of various small particles from large volumes of fluids.

Author contributions

Xiao Hu: conceptualization, software, formal analysis, writing – original draft. Longfei Yu: experiment, formal analysis, writing – original draft. Zuchao Zhu: resources, supervision. Fubing Bao: methodology, resources, supervision. Jianzhong Lin: methodology, resources, supervision. Chengxu Tu: methodology, resources, supervision. Peifeng Lin: resources.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This work was supported by the National Natural Science Foundation of China with Grant No. 12202392, Major Program of the National Natural Science Foundation of China with Grant No. 12132015, the Joint Funds of the National Natural Science Foundation of China with Grant No. U2006221, Natural Science Foundation of Zhejiang Province with Grant No. LD24E050002.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d4lc00039k

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