Flow of Capsules Through Expansion and Contraction Geometries

We numerically simulate the flow of a membrane bound capsule as it moves through a straight cylindrical channel with a sudden expansion or constriction. A three-dimensional axisymmetric volume of fluid method with a front tracking scheme is used to simulate the flow. The capsule flow dynamics are characterized by calculating the deformation parameter as the capsule flows through the expansion / contraction and the excess pressure drop required to maintain a constant flow rate. We study the capsule dynamics at a low but finite Reynolds number for a variety of drop sizes, elastic capillary numbers, and channel expansion ratios. The dynamic deformation of the capsule is determined for different constitutive equations for the membrane tension such as Hooke’s law, Mooney-Rivlin law and Evans and Skalak's law for biological membranes. For small deformations, the non-linear constitutive equations reduce to the linear Hooke’s law. Geometries and elastic capillary numbers are chosen to ensure large deformations to highlight the effect of membrane tension laws on capsule behavior. In addition, the effect of membrane viscosity is also included in some of the dynamic studies. The viscosity of the encapsulated fluid also has a strong effect on the overall flow behavior of the capsule. At large capsule fluid viscosities, the motion and deformation of the capsule is damped and the effect of the different membrane constitutive laws on capsule dynamics diminishes.