Study of the motion of a spheroidal drop in a linear shear flow

The motion of a spheroidal deformable drop in a simple shear flow is simulated using a finite-difference/front-tracking method. The effect of surface tension coefficient, viscosity ratio and inertia on lateral migration and deformation of the drop is investigated. It is revealed that the deformation of a spheroidal drop is directly related to the capillary and Reynolds numbers. In the limit of finite Reynolds numbers, the equilibrium position of prolate drops depends strongly on the viscosity ratio; the final position of more viscous drops is closer to the wall in contrast with the spherical ones. As the deformability of drops increases and the inertial force decreases, the rate of migration of the prolate drops increases. Although the steady-state position does not depend on the capillary and Reynolds numbers, the migration rate depends considerably on these dimensionless parameters. In addition, the rate of migration is a decreasing function of the aspect ratio due to different direction of the lift force acting on the drop.