Numerical study of microfluidic effects and red blood cell dynamics in 'deterministic lateral displacement' geometries

Abstract

The last two decades have seen microfluidics gaining increasing interest from the fields of medical diagnostics and bio-chemical processes, due to its immense potential for point-of-care diagnostic applications. Since blood plays a crucial role in many physiological and diagnostic processes, red blood cells (RBCs) have been the focus of a large volume of microfluidics research. The isolation of red blood cells and other blood components, based on the manifest morphological characteristics, is required in many applications, e. g. flow cytometry. The deterministic lateral displacement (DLD) is one such popular microfluidic technique that has shown great promise toward cellular separations. The DLD technique separates particles based on their hydrodynamic size. It has been demonstrated for size-based separations down to unprecedented size resolutions of ~ 10 nm. The DLD consists of a large number of obstacle pillars placed in a microfluidic channel. The layout of these obstacles is such that the obstacle array presents a fixed angle to the average fluid flow through the microfluidic channel. Size-based separation comes about due to steric interaction of particles with the pillars. Particles larger than a ‘critical’ size are forced to move along the obstacle array incline. The larger particles, following the array incline, are displaced perpendicular to the average flow direction, and are said to be on the displacement mode. Particles smaller than this critical size flow along the average fluid flow direction, zigzagging around the obstacles. The trajectories followed by these smaller particles are classified as zigzag mode. Micro-particles therefore follow different trajectory modes based on their size, eventually leading to their spatial separation. The particles are separated passively, i. e. other than the pressure drop needed to drive the fluid flow through the DLD micro-channel, there is no need for any external forces for particle sorting. Numerous studies since the advent of the DLD have focussed on widening the scope of applications covered by the technique. In this thesis, I take a more physical approach, focussing on understanding the microhydrodynamics and RBC dynamics within the DLD geometries. For these investigations, I have used an in-house numerical solver that incorporates ingredients for fluid flow solution, RBC membrane deformation, and an explicit coupling algorithm between the two. The lattice Boltzmann method is used for obtaining a fluid flow solution at low Reynolds numbers, and the finite element method is used for computing the membrane energetics. The immersed boundary method explicitly couples these two solutions with non-matching boundaries, at each time step. Firstly, I investigate subtle flow hydrodynamic effects through DLD obstacle arrays. Here, fluid-only simulations uncover and map anisotropic flow permeability of the obstacle arrays. The research reveals that if the unit cell of the obstacle array geometrically forms a parallelogram, the array induces an anisotropic pressure gradient normal to the average flow direction. Contrarily, if the obstacle arrangement reflects a rotated square in its unit cell, anisotropy is entirely absent. Such anisotropic pressure conditions in the DLD cause local flow deviations and can lead to unintended particle motion arising from locally varying critical separation size. I find that elevated levels of such anisotropy are also brought about by pillar shape design and asymmetric array gaps. Furthermore, strategies to minimise anisotropic flow effects are proposed. The research on deformable RBC flow through the DLD tackles both single and collective cell dynamics in these arrays. Single cell dynamics is studied for special, non-cylindrical obstacle pillar shapes. In addition to the particle-obstacle steric contact, dynamic RBC motion leads to effects that influence cell trajectories in the DLD. Such effects are strongly tied to the interplay between RBC deformability, dynamic motion (such as tumbling and tank-treading) and the flow-field generated by the pillar shape. In certain cases, wall-induced hydrodynamic cell migration becomes significant enough such that the deformed tank-treading RBC undergoes displacement mode without steric contact with the pillars. Here, migration velocity experienced by the cells interacting with special pillar shapes causes a reversal of the phase-bifurcation trend. The uncovering of this mechanism, opens the door for research on novel DLD pillar designs that exploit wall-induced soft particle migration. Lastly, the research turns to collective RBC dynamics at high volume fractions, in standard DLD arrays with cylindrical pillars. Here, I research the effect of increasing cell volume fraction on the displacement and zigzag modes, with the help of appropriate statistical measures. I find that the displacement mode suffers a breakdown at higher volume fractions, while the zigzag mode remains robust. This has important implications for cell separation applications in the DLD, where smaller particles (e. g. platelets) need to be separated from a dense background of RBCs and vice versa. The investigations undertaken in this thesis identify subtle hydrodynamic and particle effects in DLD arrays that explain previously unresolved particle behaviour. This research should help improve the design and fabrication of DLD devices, especially those targeted at improved separation and manipulation of deformable RBCs.