A moving-frame boundary-integral method for particle transport in microchannels of complex shape

Abstract

A new, three-dimensional algorithm is developed to accurately simulate low-Reynolds number, flow-driven motion of a neutrally buoyant spherical particle in plane-parallel microchannels of complex shape. The channel profile may consist of an arbitrary number of straight line segments with sharp corners in an arbitrary configuration. This geometry provides a suitable model for particle transport in many microfluidic devices with multiple branch bifurcations. The particle may be comparable with the narrowest channel dimensions, but is typically much smaller than the overall channel domain, which creates difficulties with a standard boundary-integral approach. To make simulations feasible, the 3D problem is solved locally in a computational cell that is smaller than the full domain and is dynamically constructed around the particle as it moves through the channel; the outer boundary conditions are provided by the 2D flow that would exist in the channel in the absence of the particle. Difficulties with particle-corner close interactions are alleviated using special iterative techniques, (near-) singularity subtractions and corner-fitted, gap-adaptive discretizations of the cell boundary. The algorithm is applied to simulate “pinched-flow fractionation” and predict how particle interactions with a narrow pinch region and sharp corners result in particle focusing and separation in the outlet according to their size. As another application, the particle motion through a T-bifurcation with sharp corners is simulated, with calculation of the particle flux partition ratio for a broad range of parameters. It is demonstrated how the particle-corner interactions can make the side branch inaccessible to particles, even for relatively strong fluid suction through this branch.