Three-dimensional numerical simulations using front-tracking method are presented on the hydrodynamic interaction between two deformable particles suspended in simple shear flow. Particles are modeled as liquid capsules, that is, liquid drops surrounded by elastic membranes. Small and finite inertia are considered. Two sets of simulations are presented. In the first set, interaction between two identical capsules are considered. In the limit of zero inertia, it has been known from past research that the hydrodynamic interaction between two deformable particles results in an irreversible shift in the trajectories of the particles as one particle rolls over the other. We show that the presence of inertia can significantly alter the capsule trajectories, and the capsules engage in a symmetric spiraling motions. In the second set of simulations, we consider the interaction between two non-identical capsules which differ from each other in terms of capillary number. The interaction between them results in greater lateral separation as compared to that of an identical pair. This result suggests that the shear-induced diffusion mechanism may play an even greater role in mixing in suspension of bidisperse particles. The long-time trajectory of the non-identical capsules at finite Re shows that they move in spirals with different radii while translating along the streamwise direction. The more deformable capsule moves with smaller radius, and vice versa.

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