Numerical study of the dynamics of a particle in a microchannel with cylindrical obstacles in inertial microfluidics

Inertial microfluidics is an emerging technology for the passive manipulation, focusing and sorting of particles. The presence of secondary flow due to flow-wise changes in the channel geometry can modify the number and location of the focusing positions. In this work, we numerically investigate the effect of secondary flow, generated by the presence of an array of cylindrical obstacles, on particle migration in a straight rectangular duct under mild inertia. We employ a combination of the lattice-Boltzmann, finite-element, and immersed-boundary methods to simulate the fully coupled system. For channels without obstacles, the particle first migrates along the shorter edge, before moving along the longer edge. However, we find the opposite behavior for the channel with larger obstacles. For medium-sized obstacles, we observe the emergence of a new stable focusing position near the centre of the channel. Moreover, as the inter-obstacle distance decreases, the particle tends to migrate to the focusing position near the channel centre for a wider range of initial positions. Our work opens the door for a better understanding of the focusing mechanisms in bespoke geometries, vital for designing and optimizing channel geometries for inertial microfluidic applications.