A Numerical Study Of A Permeable Capsule Under Stokes Flows By The Immersed Interface Method

Abstract

Permeable and deformable capsules and their adhesion are found in many applications in biological and industrial systems such as the circulatory system. However, studies on computational modeling of those capsules are still rather lacking. In this work, the osmotic swelling and capsule-substrate adhesion of a deforming capsule immersed in a hypotonic and diluted binary solution of a non-electrolyte solute under Stokes flows is simulated using the immersed interface method (IIM). The approximate jump conditions of the solute concentration needed for the IIM are calculated numerically with the use of the Kedem-Katchalsky membrane transport relations. The thin-walled membrane of the capsule is considered to be either semi-permeable or fully permeable, and the material of the capsule membrane is assumed to be Neo-Hookean. The used properties of fluid and membrane fall 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 deformation, adhesion, and osmotic swelling of a permeable capsule. The capsule swelling (with mass transfer across the membrane) and deformation in a periodic computational domain (without adhesion) are tested for different solute concentration fields and membrane permeability properties. The numerical investigations show that the initial solute concentration field and the membrane permeability properties have much influence on the swelling and deformation behavior of a permeable capsule under Stokes flow condition. Furthermore, capsule-substrate adhesion in the presence of membrane permeability is simulated and the osmotic inflation of the initially adhered capsule is studied systematically as a function of solute concentration field and the membrane permeability properties. The results demonstrate that the contact length shrinks in dimension and deformation decreases as capsule inflates. The equilibrium contact length does not depend on the hydraulic conductivity of the membrane as also theoretically predictable. Further numerical investigations show that the inflation and partial detachment of the initially adhered capsule depend significantly on the solute diffusive permeability and the reflection coefficient of capsule membrane. Finally, the mass transfer of an adhesive capsule flowing in a vessel is simulated for various parameters. The results show that the solute mass transfer between the capsule and the vessel walls is enhanced by introducing adhesion between the capsule and the walls. Moreover, the present numerical approach is employed to simulate the adhesion of a malaria-infected red blood cell and a healthy red blood cell flowing in a capillary in the absence of mass transfer.