Inertial cell sorting of microparticle-laden flows: An innovative OpenFOAM-based arbitrary Lagrangian-Eulerian numerical approach

Abstract

The need for cell and particle sorting in human health care and biotechnology applications is undeniable. Inertial microfluidics has proven to be an effective cell and particle sorting technology in many of these applications. Still, only a limited understanding of the underlying physics of particle migration is currently available due to the complex inertial and impact forces arising from particle-particle and particle-wall interactions. Thus, even though it would likely enable significant advances in the field, very few studies have tried to simulate particle-laden flows in inertial microfluidic devices. To address this, this study proposes new codes (solved in OpenFOAM software) that capture all the salient inertial forces, including the four-way coupling between the conveying fluid and the suspended particles traveling a spiral microchannel. Additionally, these simulations are relatively (computationally) inexpensive since the arbitrary Lagrangian-Eulerian formulation allows the fluid elements to be much larger than the particles. In this study, simulations were conducted for two different spiral microchannel cross sections (e.g., rectangular and trapezoidal) for comparison against previously published experimental results. The results indicate good agreement with experiments in terms of (monodisperse) particle focusing positions, and the codes can readily be extended to simulate two different particle types. This new numerical approach is significant because it opens the door to rapid geometric and flow rate optimization in order to improve the efficiency and purity of cell and particle sorting in biotechnology applications.

FIG. 1.

Schematic of the fluid and particles in a control volume.

FIG. 2.

A schematic of the fluid-induced forces.

FIG. 3.

(a) The geometry of the spiral microchannel; (b) Rectangular cross-sectional areas of the microchannel and (c) Trapezoidal cross-sectional areas of the microchannel.

FIG. 4.

The velocity profile in the y direction at the B-B section for (a) rectangular microchannel in the middle of the width and (b) trapezoidal microchannel in one-sixth of the width near the outer wall.

FIG. 5.

Particle positions for different mesh sizes at the end of the straight entry of the spiral microchannel: (a) rectangular microchannel and (b) trapezoidal microchannel.

FIG. 6.

Particle initial distribution and equilibrium positions in the rectangular spiral microchannel (a) at $Q=3\mathrm{ml}/\min$, (b) at $Q=6\mathrm{ml}/\min$, and (c) the experimental findings of particles equilibrium positions from Rafeie et al. Reprinted with permission from Rafeie et al., Biomicrofluidics, 13, 034117 (2019). Copyright 2019 AIP Publishing LLC.

FIG. 7.

Particle distribution and equilibrium positions in a trapezoidal spiral microchannel: (a) at $Q=1.5\mathrm{ml}/\min$, (b) at $Q=6\mathrm{ml}/\min$, and (c) Experimental observations of Rafeie et al. Reprinted with permission from Rafeie et al., Biomicrofluidics, 13, 034117 (2019). Copyright 2019 AIP Publishing LLC.

FIG. 8.

(a) The distribution of the $x$-component of the vorticity of the secondary flow in the B-B section. (b) The distribution of the $x$-component of the secondary flow velocity in the B-B section at $Q=6\mathrm{ml}/\min$.

FIG. 9.

(a) Velocity profile and IPs in the middle of the B-B section at $Q=6\mathrm{ml}/\min$. (b) Inflection points for different flow rates.

FIG. 10.

Particles’ initial distribution and equilibrium positions in the rectangular spiral microchannel (a) at $Q=6\mathrm{ml}/\min$ and (b) at $Q=9\mathrm{ml}/\min$.

FIG. 11.

(a) Vorticity distribution in the B-B section. (b) Secondary flow velocity distribution in the B-B section.

FIG. 12.

(a) Main flow velocity distribution in the B-B section. (b) Velocity profile and IPs in one-sixth of the width near the outer wall of the B-B section at $Q=6\mathrm{ml}/\min$. (c) Inflection points for different flow rates.

FIG. 13.

trapezoidal microchannel at $Q=3\mathrm{ml}/\min$: (a_i) Upper view of particle positions in the first loop, (a_ii) cross section of the specified area in the first loop, (b_i) upper view of particle positions in the third loop, and (b_ii) cross section of the specified area in the third loop.

FIG. 14.

Particle distribution and equilibrium positions in a trapezoidal spiral microchannel for (a) $Q=6\mathrm{ml}/\min$ and (b) $Q=0.5\mathrm{ml}/\min$.

FIG. 15.

RBC- and CTC-like particle distribution in the trapezoidal cross section of a spiral microchannel for (a) their initial positions (e.g., the A-A section as defined in Fig. 3) and (b) their equilibrium positions (e.g., at section C-C as defined in Fig. 3).

FIG. 16.

RBC- and CTC-like particles flowing through a trapezoidal spiral microchannel for Q = 0.5 ml/min: (a) particle distribution near the entry, (b) particle distribution at the first loop, (c) particle distribution near the end, and (d) particle distribution at the end of the separation process.