A numerical lift force analysis on the inertial migration of a deformable droplet in steady and oscillatory microchannel flows at different Capillary numbers and oscillation frequencies

Inertial migration of deformable particles has become appealing in recent years due to its numerous applications in microfluidics and biomedicine. The physics underlying the motion of such particles is contingent upon the presence of lift forces in microchannels. This importance initiated several works to analyze and quantify such forces acting on particles. However, since most of such attempts have focused on solid and non-deformable particles, we extend the lift force analysis for the case of deformable droplets and study the effects of Capillary numbers on their dynamics in this paper. Furthermore, utilizing oscillatory flows as an alternative for steady currents within the microchannels has been proved to be beneficial by introducing new equilibrium positions for the particles. Therefore, the present analysis includes the oscillatory regimes and identifies the effects of oscillation frequencies on lift forces as well. We then propose an expression that mimics the lift force behavior in oscillatory flows accurately. Finally, we introduce a procedure to derive and predict a simple expression for the steady and averaged oscillatory lift for any given combination of Capillary number and oscillation frequency within a continuous range.