Flow-induced differential lateral migration of deformable particles by inner/outer viscosity ratio

We investigate the practicality of flow-driven separation of deformable particles (DP) such as cells, droplets, and capsules in microfluidic flow. We use lattice Boltzmann-immersed boundary method to model the hydrodynamic coupling between DP and the fluid. We find that whether a DP migrates towards the wall or to the center at steady state depends strongly on particle Reynolds number \textit{Re}, capillary numbers \textit{Ca}, and viscosity ratio $\lambda $. The lateral steady state position $d$* and velocity is determined by the competition between the inertia- and deformation-driven forces. In the deformation-dominated regime (\textit{Ca} \textgreater \textgreater \textit{Re}), DP migrates towards the channel centerline and flow faster for sufficiently small $\lambda $. In the inertia-dominated regime (\textit{Ca} \textless \textless \textit{Re}), $d$* is between the channel center and the wall and flow slower for small $\lambda $. For sufficiently large $\lambda $, DP migrates towards the wall as the inertia-driven lift effects increase and the particle velocity decreases. In the intermediate regime (\textit{Ca} \textasciitilde \textit{Re}), we find that $d$* has non-monotonic dependence on $\lambda $, leading to complicated dependence of particle velocity. We find that the non-monotonic trend is a consequence of inertia-deformation coupling, and only occurs if the inertia- and deformation-driven lift effects are comparable. This result could provide be further utilized for separating soft particles with different internal fluid property.