Effect of membrane permeability on capsule substrate adhesion: Computation using immersed interface method

A two-dimensional thin-walled capsule of a flexible permeable membrane is adhered onto a rigid planar substrate under adhesive forces (derived from a potential function). The capsule and the surrounding environment are filled with a diluted binary solution of different solute concentrations. The Stokes flow problem is solved by the immersed interface method (IIM) with equal viscosities for enclosed and surrounding fluid of the capsule. The numerical results obtained are verified against two simplified theoretical solutions with reasonable concurrence. The osmotic inflation of the adhered capsule is studied systematically as a function of solute concentration field and the membrane permeability properties. Our findings indicate that contact length shrinks in dimension and deformation decreases as capsule inflates. Also the equilibrium contact length does not depend on the hydraulic conductivity of the membrane as theoretically expected. Further numerical investigations show that the inflation and detachment of the initially adhered capsule depend significantly on the solute diffusive permeability and the reflection coefficient of capsule membrane.