Flow-induced deformation of artificial capsules
Two numerical methods are presented for modeling the deformation of a microcapsule suspended in an external flow. The capsule is enclosed by a zero-thickness hyperelastic membrane obeying different non-linear constitutive laws that can be either strain-hardening or strain-softening. In the absence of fluid inertia, a boundary-integral method is used to compute the internal and external Stokes flow for the case of matched fluid viscosities. The force exerted by the capsule membrane on the fluid is obtained from a membrane equilibrium equation with negligible bending stiffness. In the first method, the local membrane equilibrium equation is solved, and the membrane geometry is reconstructed by means of projections on B-spline functions. In the second method, a variational formulation for the membrane equilibrium is developed based on a finite-element implementation. Results obtained by the two methods are compared and discussed for simple shear and planar hyperbolic flows.