Numerical study of a permeable capsule under Stokes flows by the immersed interface method

A two-dimensional model to simulate the mass transfer of a permeable, deformable, and adhesive capsule flowing in a binary solution of a vessel is proposed using the immersed interface method (IIM). The fluid flow is governed by the full Navier–Stokes equations and the solute distribution is governed by the advection–diffusion equation. Mass transport across the capsule membrane is computed using the Kedem–Katchalsky equations while the adhesion between the capsule and the walls is introduced via a potential function. The model is first validated for the simple shear flow away from the substrate walls and then for capsule adhesion and deformation next to a substrate wall. It is next used to study solute transfer between the capsule and the vessel walls with and without a flow field. In the absence of a flow field, the results show that the transient of the solute transfer between the capsule and the vessel walls depends on the membrane diffusive permeability. In the presence of a Stokes flow field, behavior of the solute transfer seems to be fairly similar to that found for the stationary capsule for the same physical parameters. Moreover, the results suggest that the total solute transfer between the capsule and the vessel walls is enhanced when the capsule moves near to one wall. The increased adhesion strength between the capsule and walls would further increase the total solute transfer to the vessel walls although quite marginal.