Hydrodynamic interactions between pairs of capsules and drops in a simple shear: Effects of viscosity ratio and heterogeneous collision

Abstract

Hydrodynamic interactions between a pair of capsules in simple shear are numerically investigated using a front-tracking finite difference method. The membrane of the capsule is modeled using different hyperelastic constitutive relations. We also compare the pair interactions between drops to those between capsules. An increased viscosity ratio leads to a reduced net cross-stream separation between capsules as well as drops after collision. At low viscosity ratios, for the same capillary number drop-pairs show higher cross-stream separation than those for capsule-pairs, while substantially large viscosity ratios result in almost the same value for both cases. We investigate pair-collisions between two heterogeneous capsules ${\mathrm{C}}_1$ and ${\mathrm{C}}_2$ with two different capillary numbers. The maximum deformation of ${\mathrm{C}}_1$ was seen to increase with increasing stiffness (decreasing capillary number) of ${\mathrm{C}}_2$, even though the stiffness of ${\mathrm{C}}_1$ was kept fixed. The findings are similar for a drop-pair, however, with a smaller maximum deformation for the same combinations of capillary numbers. The final cross-stream drift of the trajectory of ${\mathrm{C}}_1$ decreases with the increasing stiffness of ${\mathrm{C}}_2$, but the relative trajectory between the capsules remains unchanged. The maximum deformation and the cross-stream drift of the trajectory of ${\mathrm{C}}_1$ are shown to approximately vary with power-law functions of the ratio of the capillary numbers of ${\mathrm{C}}_1$ and ${\mathrm{C}}_2$. An analytical explanation of the dependence on the two capillary numbers is offered. Different membrane constitutive laws result in similar deformation and drift in trajectory.