Deformation and osmotic swelling of an elastic membrane capsule in Stokes flows by the immersed interface method

Although permeable and deformable capsules are found in many applications in biological and industrial systems, studies on computational modeling of these capsules are still rather lacking. In this work, the osmotic swelling of a deforming capsule immersed in a diluted binary solution of a non-electrolyte solute under Stokes flows is simulated using the immersed interface method (IIM). The approximate jump conditions for solute concentration are calculated with the use of the Kedem–Katchalsky relations. The capsule membrane is considered to be either semi-permeable or fully permeable, and the material of capsule membrane is assumed to be Neo-Hookean. The employed properties of fluid and membrane lie in the range of a typical biological system. The numerical validation tests indicate that the present calculation procedure has achieved good accuracy in modeling the swelling and deformation of permeable capsules. The capsule swelling (with mass transfer across the membrane) and deformation are tested for different solute concentration fields and membrane permeability properties. Our numerical investigations show that the initial solute concentration field and the membrane permeability properties have much influence on the swelling/deformation of a permeable capsule under Stokes flows.