A 27 cm long straight square microchannel in viscoelastic fluid for submicron- sized particle and bacteria focusing

doi:10.21203/rs.3.rs-5056917/v1

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A 27 cm long straight square microchannel in viscoelastic fluid for submicron- sized particle and bacteria focusing

https://doi.org/10.21203/rs.3.rs-5056917/v1

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published 12 Nov, 2024

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Particle focusing within a flow cell is an essential step in performing flow cytometry and fluorescence-activated cell sorting (FACS). Viscoelastic particle focusing, in which particles suspended in a synthetic polymer solution migrate laterally against the main flow direction, has attracted considerable attention because it enables particle focusing without any external force. In this work, we demonstrate a viscoelastic flow focusing device that enables simple and robust focusing of submicron-sized particles in the channel center by optimizing operating conditions such as channel length, flow rate and PEO (poly(ethylene oxide)) concentration. The device was fabricated using a common soft lithography technique for the polydimethylsiloxane (PDMS) channel, which has a width of 50 µm and a height of 50 µm with a channel length of 27 cm. The focusing performance was first demonstrated using submicron-sized polystyrene (PS) beads ranging from 870 nm to 50 nm and then using biological particles such as E. coli bacteria to demonstrate the biological feasibility of the device. The PS beads, which ranged in diameter from 870 nm to 100 nm, were focused to the center of the channel, achieving over 90% of the focusing efficiency for down to 510 nm beads, and 62% of focusing efficiency even in 100nm sized bead.

The device also was able to align a bacterial suspension in the center of the channel at flow rates up to 30 µL/min, demonstrating its biological relevance. The developed viscoelastic flow focusing device was able to align submicron particles within a narrow flow stream in a highly robust manner, validating its use as a flow focusing platform for high throughput and accurate flow cytometry of submicron objects.

Submicron-sized particles

viscoelastic particle focusing

PEO (poly(ethylene oxide))

Particle focusing within a flow-cell is an essential step for performing flow cytometry and fluorescence-activated cell sorting (FACS). Moreover, focusing on submicrometer- and nanometer-scale targets is highly important for various applications in biology, chemistry, engineering, and medicine. Advancements in microfluidics have provided significant opportunities for submicron-sized particle manipulation via robust and low-cost lab-on-a-chip platforms. Various microfluidic techniques for focusing submicrometer particles and cells have been developed, which are classified into two main methods: active and passive focusing [1]. Active techniques use external forces whereas passive techniques rely solely on the intrinsic properties of fluids within channels without any physical force. Various external force such as DEP (dielectrophoresis) [2], acoustophoresis [3], thermophoresis [4] and optical tweezers [5] are widely used as active methods. In contrast, Methods such as inertial microfluidics [6], DLD (deterministic lateral displacement) [7], viscoelastic microfluidics [8], and hydrophoresis [9] are used for particle focusing as passive methods.

Viscoelastic microfluidics, which offers precise manipulation and centerline focusing of micro/nanoparticles suspended in polymer solutions without any external force, has attracted much attention since it enables the focusing and separation of submicron-sized particles. Currently, simple and label-free particle manipulation methods in viscoelastic fluid have been explored to promote the focusing of biological particles such as bacteria and exosomes by size-dependent elastic lift forces [1][10]. Owing to the device’s simple configuration, small size, and no power consumption, many related studies have been conducted. Yang et al. demonstrated 3D particle focusing along a 50 µm wide straight square microchannel by using inertial and viscoelastic forces in a viscoelastic fluid, which is known as elasto-inertial particle focusing [11]. Seo et al. used a holographic microscopy technique to show single-line focusing in a microchannel under viscoelastic fluid flow [12].

Recently, several studies have focused on and aligned microparticles within a simple rectangular channel by optimizing the channel length [13] or modifying the channel cross-sectional shape [14][15][16]. Nam et al. proposed a microfluidic device for highly efficient, sheathless particle separation via an elasticity-dominant non-Newtonian fluid, which was based on viscoelasticity-induced particle lateral migration [13]. Particle focusing and enrichment were achieved under viscoelastic fluid flow via straight channels with gradually contracted cross-sections and high aspect ratios [14]. In our previous work, microchannels with various cross-sectional shapes (e.g., rhombus, pentagon, hexagon, and parallelogram) were fabricated via basic MEMS processes [15][16], which were utilized for particle focusing under Newtonian and non-Newtonian fluid flows.

In this work, we demonstrate a viscoelastic flow-focusing device that allows simple and robust centerline focusing of submicron-sized particles by optimizing operational conditions such as the channel length, flow rate and concentration of PEO (poly(ethylene oxide)). Owing to the presence of PEO, the elastic lift force continuously acts on suspended submicron-sized particles, enabling field-free focusing of up to 100 nm-sized particles. The device was simply fabricated via a standard soft-lithography technique with a 27 cm long polydimethylsiloxane (PDMS) channel, and the focusing performance was evaluated for submicron-sized polystyrene (PS) beads ranging from 870 nm to 100 nm and biological particles such as E. coli bacteria. The developed flow-focusing device could align submicron-sized particles within a narrow flow stream in a highly robust manner, validating its use as a flow-through focusing platform to perform high-throughput and accurate flow cytometry of submicron -sized objects. This platform is expected to be valuable for many applications, such as point-of-care diagnostics, bioassays, and rare sample processing.

Device fabrication and sample preparation

Figure 1 presents a schematic of the fabricated microfluidic device, with a channel width and height of 50 µm × 50 µm, respectively. The PDMS-glass microfluidic device was fabricated via a standard soft-lithographic technique. Briefly, the device was fabricated via photolithography using SU-8 2050 photoresist, PDMS molding, and plasma bonding processes.

A PEO solution was used as the viscoelastic fluid, with concentrations ranging from 0.1 to 0.5 wt%. The PEO solution was prepared by dissolving PEO (Mw = ~ 600 kDa, Sigma‒Aldrich, Burlington, MA, USA) in DI water. Fluorescent polystyrene (PS) particles (Thermo Scientific Inc., Waltham, MA, USA) of 870, 510, 250, 180, and 100 nm (1×10⁵ particles/ml) were added to the PEO solution with concentrations of 0.1 to 0.5 wt%. Tween 20 (Sigma‒Aldrich, Burlington, MA, USA) was added to the suspensions at 0.1 wt% as a surfactant to prevent particle aggregation during the particle focusing and separation experiments. The sample fluid was injected into the microfluidic device via syringe pumps (LEGATO 111, KD Scientific Inc., Holliston, MA, USA).

The focusing positions of the particles were recorded and captured approximately 27 cm downstream from the inlet via a CMOS camera (Suzhou ZWO Co., Ltd., Jiangsu Province, China) mounted on an optical microscope (BX-60, Olympus, Tokyo, Japan). The fluorescence images were captured from the top and side of the microchannel with long exposure times of 600 to 800 ms to analyze the particle focusing positions. All the processing and analysis of the captured images were performed via open-source ImageJ software, and the fluorescence intensity profiles across the microfluidic channel were obtained and fitted with a Gaussian distribution.

Elasto-inertial focusing

Figure 1 illustrates the particle migration in a viscoelastic fluid along the cross-section of the channel. The particles in a viscoelastic fluid are subject to both elastic forces and inertial forces (including the shear gradient lift force and the wall effect lift force) [11], which result in randomly dispersed particles reaching a state of equilibrium as they flow through a straight microchannel.

As evidenced by prior research [17, 18], particles within viscoelastic fluids are subject to two distinct forces. The inertial lift force (F_L) and the elastic lift force (F_E) which depends on the diameter (d) of the particle, are the two forces at play [19][20]. The inertial lift force (F_L) is comprised of two distinct forces: the shear gradient lift force and the wall lift force. The shear gradient lift force acts to propel particles situated in proximity to the channel center towards the wall, whereas the wall lift force exerts a force upon particles in close proximity to the wall, directing them towards the channel center. Conversely, the elastic force (F_E) arises from an imbalance in the distribution of the first normal stress (N₁), which contributes to lateral particle migration. It can thus be concluded that particle migration in viscoelastic fluids is the result of a combination of inertial and viscoelastic effects. The particle trajectories and equilibrium positions under fluid flow are determined by the competition between these forces [20].

The inertial lift force (F_L) and elastic force (F_E) can be expressed as [21][22]:

$$\:{F}_{L}\:=\:\frac{{\rho\:}_{f}{{U}_{max}}^{2}{d}^{4}}{{{D}_{h}}^{2}}{f}_{L}\left(Re,{x}_{c}\right)$$

$$\:{F}_{E}\:=\:{f}_{E}{d}^{3}\nabla\:{N}_{1}=\:-2{f}_{E}{d}^{3}{\eta\:}_{p}\lambda\:\nabla\:{\dot{\gamma\:}}^{2}\:\:\:\:\:\:\:\:$$

where ρ_f is the fluid density, U_max is the maximum velocity of the channel flow, f_L (Re, x_c) is the inertial lift coefficient, d is the diameter of the particle, D_h is the hydraulic diameter, Re is the Reynolds number, f_E is the elastic lift coefficient, η_p is the polymeric contribution to the solution viscosity, λ is the relaxation time of the viscoelastic fluid, and $\:\gamma\:\:̇$ is the characteristic shear rate.

When a particle moves through a fluid or when the fluid flows past the particle, a viscous drag force (F_D) is generated. This force arises from the velocity difference between the particle and the fluid and can significantly affect particle migration. In a uniform Stokes flow, this can be expressed as the following equation [23]:

$$\:{F}_{D}\:=\:3\pi\:{\mu\:}_{f}d({v}_{f}-\:{v}_{p})$$

where µ_f is the dynamic viscosity of the fluid and where v_f and v_p represent the velocities of the fluid and particles, respectively.

In the case of particles focused in viscoelastic fluids, the relative importance of the elastic effect to the inertial effect leads to different particle focusing phenomena. That is, the number of particle focusing points can be determined by the Reynolds number (Re) and Weissenberg number (Wi) [24][25]. The fluid elasticity (El) is defined as the ratio of the Weissenberg number to the Reynolds number and is a significant factor that governs the focusing behavior. A comparison of these two dimensionless numbers makes it possible to identify the major force responsible for the particle focusing phenomena: viscoelasticity-dominant focusing and elasto-inertial focusing [20]. These parameters can be defined as follows [22]:

Re = ρ_f U_maxD_h/µ_f (4)

Wi = 𝜆 𝛾̇ = 2𝜆U_max/D_h (5)

El = Wi/Re = 2𝜆 µ_f/(𝜌D_h²) (6)

Viscoelastic flow-focusing allows simple and robust focusing of submicron-sized particles by combination of both elastic and inertial forces (including the shear gradient lift force and the wall effect lift force), which result in randomly dispersed particles reaching a state of equilibrium as they flow through a straight microchannel. Here, we explore the focusing efficiency of submicron-sized particles, which is defined as the fraction of particles in the central region within 10 µm for a channel width of 50 µm (1/5 of the channel width). The focusing efficiency of sub-micron particles were investigated by varying flow rate, particle size, PEO concentration, and channel length.

Initially, the particles were randomly distributed at the inlets of the microchannel. Under the combined influence of the driving forces (elastic lift force, wall effect lift force, etc.), the particles laterally migrated toward the center of the channel after passing through the long, straight, square microchannel. To investigate the effect of channel length on particle focusing, 0.1 wt% PEO solution including 870 nm PS particles was injected into the inlets of 15 cm and 27 cm long PDMS microchannels. Figure 2(a) shows the distributions of the particles in both channels as the flow rate increased from 0.5 µL/min to 20 µL/min. The dotted lines indicate the ends of the microchannel walls, which were obtained from bright-field images under the same experimental conditions. Focusing efficiency and normalized fluorescence intensity profiles of both channels were plotted in Fig. 2(b) and Fig. 2(c), respectively. Compared with the focusing efficiency of 15 cm long channel, that of 27 cm long channel was 10 ~ 20% higher at all flow rates except when it was very low. In Fig. 2(b), the 27 cm long channel showed a focusing efficiency of 90% at a flow rate of 20 µl/min, indicating that particles were focused into a narrower width due to the continuous effect of the elasto-inertial force on the particles along the channel length. Also, the normalized fluorescent intensity of 27 cm long channel was sharper and higher than that of 15 cm channel (Fig. 2(c)).

Subsequently, experiments were conducted to elucidate the effect of particle size and flow rate. The experiments utilized PS particles with sizes of 510, 250, 180, and 100 nm, respectively, and a 27 cm long PDMS microchannel with 0.1 wt% PEO solution. The flow rate was increased from 0.5 to 20 µL/min, and the results demonstrated that particle size and flow rate exert significant influence on the phenomenon under study. Figure 3(a) shows the distribution of the particles in 27 cm long channel, whose focusing efficiency according to flow rates was plotted in the Fig. 3(b) and the normalized fluorescent intensity profiles for various sized particles were plotted as in the Fig. 3(c).

Figure 3(a) depicted that particle focusing due to elastic force occurred from 10µL/min for 510 nm particles, 15 µL/min for 250 nm particles, and 20 µL/min for 180 nm particles. In Fig. 3(b), the focusing efficiency of each particle were displayed as flow rate. While the flow rate increased, particles shows better single focused flow stream which refers focusing efficiency was improved by higher flow rate. Comparing the focusing efficiency of 500nm particle at flow rate of 0.5 µl/min and that of 20µl/min, the focusing efficiency improves 33% ,and it becomes 29%, 25% and 13% as the particle size was 250nm, 180nm and 100nm, respectively. Focusing efficiency for 100 nm particles is only 30% even at high flow rate of 20 µL/min as shown in Fig. 3(b). That is 100 nm particles were not focused well and displayed only a faint band in the center under 0.1 wt% PEO concentration because the elastic force applied to particles got dramatically smaller (F_E ∝ d³) as particles became smaller. We further investigated the focusing efficiency of flow rate over 20µl/min (Fig. S1), which it is maintained up to flow rate of 50µl/min in each particle. However, the focusing efficiency started to decrease from 50µ/min to 60µl/min. We believe it is caused by the inertial force being more dominant than the elastic force.

Wi presenting elastic force relative to viscous force was only 3.4×10^− 1 at a flow rate of 0.5 µL/min and less than 10 at a flow rate of 10 µL/min. Wi became more than 10 at a flow rate of 20 µL/min for 0.1 wt% PEO concentration, 10 µL/min for 0.3 wt% PEO concentration and 5 µL/min for 0.5 wt% PEO concentration. As PEO concentration increased, higher elastic effects occurs at same flow rate so particles could be focused even at lower flow rates.

The dependence of particle focusing on PEO concentration and particle size was investigated for PEO concentrations of 0.1, 0.3, and 0.5 wt% at a flow rate of 20 µL/min. Figure 4(a) shows fluorescence images of 510, 250, 180, and 100 nm particles at different PEO concentrations. As the PEO concentration increased from 0.1 wt% to 0.5 wt%, the focusing efficiency of the 510, 250, and 180 nm particles improved because of the enhanced elastic effect. Focusing efficiency for 510 nm particles increased from 66–78% and 91% as the PEO concentration increased from 0.1 wt% to 0.3 wt% and 0.5 wt%. For 0.5 wt% PEO solution, the focusing efficiencies for 250 and 180 nm particles were 84% and 80%, respectively, which showed the focusing efficiency less than 60% for 0.1 wt% PEO solution. Even for 100 nm particles, which were not focused in the 0.1 wt% PEO solution, particle focusing began for 0.3 wt% PEO and became clear at the channel center, forming a band for 0.5 wt% PEO solution (focusing efficiency of 62%).

El presenting elastic force relative to inertial force was only 5.2 for 0.1 wt% PEO concentration, and increased to 17.8 and 64.7 for 0.3 and 0.5 wt% PEO concentration, respectively. It was because viscosity (µ_f) and relaxation time (𝜆) increased as PEO concentration increased (Eq. (3), El ∝ 𝜆, µ_f). Therefore, smaller particles could be better focused by the elastic force rather than inertial force as PEO concentration increased (Eqs. (1) and (2), F_L ∝ 1/µ_f and F_E ∝ 𝜆) [25][26]. We executed experiments from a low flow rate of 0.5 µL/min and shear thinning did not occur because the shear rate under a flow rate of 0.05 µL/min did not fall within the range where viscosity decreased [27].

We further extended our investigation to focus on nanoparticles with dimensions less than 100 nm. For the optimal flow rate of 20 µL/min and a channel length of 27 cm, we investigated the dependence of various fluid concentrations, ranging from 0.1 wt% to 0.5 wt%, on the focus of 50 nm particles. However, the 50 nm particles showed little focus for the 0.5 wt% PEO solution (Fig. S3), whose focusing efficiency was only 35%. It is significantly more challenging to focus the particles less than 100 nm due to the weak elastic forces (Eq. (2), F_E ∝ d³).

Focusing on Escherichia coli

To verify the usefulness of the device for biological submicron-sized samples, we performed elasto-inertial focusing of bacteria (Escherichia coli) with an average diameter of 900 nm. The bacterial samples including 1.8×10⁶ cells/ml, which was sufficient to visualize the stream of bacterial flows by bright field observation (without fluorescent dye), were vortexed prior to injection to prevent aggregation. 0.1 wt% PEO in PBS solution, was injected into the channel inlet for the bacteria focusing, whose flow rates were from 0.5 µL/min to 20 µL/min. Figure 5(a) shows the optical microscopy images of bacterial cells focused by elasto-inertial force for different flow rates. The images were obtained using a high-speed camera set to a frame rate and exposure time of 3000 fps and 30 µs, respectively. The lateral distribution of each bacteria was measured from the images.

Figure 5(b) depicts the focusing width of bacteria as the flow rate increases. In each flow condition, we measured the migration for at least 150 bacteria cells in flowing channel using the ImageJ software. The focusing width of bacteria within 2-sigma were only 42.3 µm (not focused) at a low flow rate of 1 µL/min and decreased about 9.7 µm at a flow rate of 10 µL/min and totally focused to channel center showing 4.1 µm focusing width at a flow rate of 20 µL/min.

This study demonstrated the effective elasto-inertial focusing of submicron-sized particles and biological samples via a microfluidic device with varying PEO concentrations and flow rates. Our developed device focused submicron/nanosized particles ranging in diameter from 100 ~ 1000 nm via viscoelastic flow focusing featuring a 50 µm width and 50 µm height with a 27 cm channel length. Under flow-through conditions, a focusing width of less than 10 µm was achieved at a flow rate of 5 µL/min for 870 nm beads, 10 µL/min for 510 nm beads, 15 µL/min for 510 nm beads and 20 µL/min for 180, 100 nm beads. Furthermore, the device was applied to the focusing of biological samples, and bacterial cells were perfectly focused at a flow rate of 20 µL/min. The developed viscoelastic flow focusing device could align submicron-sized particles within a narrow flow stream in a highly robust manner, validating its use as a flow-through focusing platform for high-throughput and accurate flow cytometry of submicron-sized objects.

Competing interests The authors declare no competing interests.

Data availability No datasets were generated or analyzed during the current study.

Acknowledgments

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korean government (No. RS-2023-00240465). This work was partially supported by the Ministry of Trade, Industry, and Energy (No. 20009860).

Author Contribution

Y.S.C conducted experiment , analysis of data and data acquisition. S.W.L and Y.H.C proposed the idea and experimental step. M.H.L proposed and advised the experimental methods. Y.S.C, S.W.L and Y.H.C wrote the paper. Y.H.C managed whole process.

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No competing interests reported.

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A 27 cm long straight square microchannel in viscoelastic fluid for submicron- sized particle and bacteria focusing

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Introduction

Materials and methods

Device fabrication and sample preparation

Elasto-inertial focusing

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Conclusion

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