Coupling boundary integral and shell finite element methods to study the fluid structure interactions of a microcapsule in a simple shear flow

We simulate the motion of an initially spherical capsule in a simple shear flow in order to determine the influence of the bending resistance on the formation of wrinkles on the membrane. The fluid structure interactions are obtained numerically coupling a boundary integral method to solve for the Stokes equation with a nonlinear finite element method for the capsule wall mechanics. The capsule wall is discretized with MITC linear triangular shell finite elements. We find that, at low flow strength, buckling occurs in the central region of the capsule. The number of wrinkles on the membrane decreases with the bending stiffness and, above a critical value, wrinkles no longer form. For thickness to radius ratios below 5%, the bending stiffness does not have any significant effect on the overall capsule motion and deformation. The mean capsule shape is identical whether the wall is modeled as a shell or a two-dimensional membrane, which shows that the dynamics of thin capsules is mainly governed by shear elasticity and membrane effects.