Modeling the interactions between deformable capsules rolling on a compliant surface.

By integrating mesoscale models for hydrodynamics and micromechanics, we examine the fluid-driven motion of pairs of capsules on a compliant, adhesive substrate. The capsules, modeled as fluid filled elastic shells, represent cells or polymeric microcapsules. We show that both the relative and the average velocities of two closely spaced, rolling capsules depends on the elasticity of the capsules, the adhesive interaction between the capsules and the substrate, and the compliance of the substrate. We first focused on a stiff surface and found that pairs of rigid capsules always separate from each other, while for deformable capsules, the dynamic behavior depends critically on the strength of the adhesive interaction. For strong adhesion to the substrate, the capsules again roll away from each other, while for a relatively weak adhesion, the capsules actually approach each other. In the case of soft substrates, any significant deformations of the surface that are caused by the capsules give rise to a force that propels the particles to move rapidly apart. Thus, in the case of strong adhesion between the capsules and the soft substrates, both rigid and flexible capsules are driven to separate. On the other hand, for weak adhesion, the elastic particles approach each other, similar to the behavior on stiff surfaces. These findings reveal that the interactions between the capsules are mediated by the nature of the underlying layer. We can harness this information to design surfaces that actively control the relative separation between the capsules. This could be utilized to regulate the motion of biological cells, as well as polymeric microcapsules, and thus, could prove to be useful in various biological assays or tissue engineering studies.