A two-phase flow model for a soft poroelastic drop suspended in a Stokes flow

In this work a two-phase flow model is constructed to study the combined effects of interfacial slip, permeability and elasticity of the porous skeleton inside a viscous drop under simple linear flows. This two-phase flow model describes a viscous fluid filling a deformable elastic skeleton inside a drop whose interface deforms according to the balance of traction on the interface. When the viscous dissipation of the interior porous flow is negligible (compared to the friction between the fluid and the skeleton), the two-phase flow is reduced to a poroelastic Darcy fluid. At the interface between such an interior poroelastic fluid and an exterior Stokesian fluid, both slip and permeability are taken into account. The permeating flow induces dissipation that depends on the elastic stress of the interior solid. By exploring the interfacial slip, permeability and interior elasticity various flow patterns are found at equilibrium of these slightly deformed poroelastic drops. These results shed light on the rheology of a suspension of poroelastic spherical particles, and give insight to possible flow patterns of a system of self-propelling swimmers with porous flow (such as intracellular cytosol) inside.