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: when inertia is small but finite, the capsules do undergo an irreversible displacement, but the lateral separation between them first decreases before they roll over each other, unlike in case of zero-inertia. For moderate to high inertia,the capsules reverse their directions of motion before coming close to each other. The reversal of motion occurs progressively earlier in time (that is, the capsules come less closer to each other) with increasing inertia. Thus, the shear-induced diffusion can be absent in presence of inertia. The long-time behavior of the capsule-capsule interaction at finite inertia

showed that the capsules engage in spiraling motions.

Based on our simulations, four different regimes of capsule-capsule interaction at finite inertia are identified: (i) a self-diffusive type interaction,

(ii) an outwardly spiraling motion, (iii) a fixed-orbit spiraling motion, and (iv) an inwardly spiraling motion in which the capsules settle with zero relative velocity. The reversal of motion, and the spiraling trajectories at finite inertia have no analogy in the limit of zero inertia. Such motions are explained by analyzing the flow

field around a deformed capsule which shows reverse flow regions and off-surface stagnation points, similar to those

previously reported in case of rigid spheres and cylinders under torque-free condition. In the second set of simulations, we consider the interaction between two non-identical capsules which differ from each other in terms of their size, capillary number and viscosity ratio. WHen inertia is small, one particle rolls over the other, but their displacements in the velocity-gradient direction are not the same. Our results show that the final lateral displacement of the rigid particle is higher than that for the deformable particle. At moderate inertia, dissimilar particles also engage in spiralling motion, but our results show that the spiralling trajectories are now asymmetrical. Further, the time-averaged lateral position of the particles is no longer zero. As a result, the particle-pair slowly drift with the flow. These results have implications for sheared suspension of mono- and bi-disperse deformable particles at finite inertia.