Lateral migration of viscoelastic capsules in tube flow

Abstract

In this article, the lateral migration process of a viscoelastic capsule of spherical original shape in a tube flow is simulated. The capsule membrane follows the Skalak constitutive law for elasticity, and the membrane viscosity is modeled using the recently developed finite difference scheme. The methodology is validated carefully by simulating the tank-treading motion of an elastic capsule in shear flow. The lateral migration of viscoelastic capsules is then investigated in detail with various combinations of viscosity ratio, membrane shear viscosity, and capillary number. In general, the migration process starts with an initial transient phase, where the capsule deformation and migration velocity suddenly increase from zero to a maximum value. Following that, the deformation and migration velocity gradually reduce as the capsule moves toward the tube centerline. The capsule also performs continuous rotation during the migration, and the rotation gradually slows down with the capsule migration. The interior-exterior fluid viscosity contrast and the membrane viscosity have similar effects in reducing the capsule deformation and inclination angle to the flow direction; however, a strong membrane viscosity may introduce significant oscillations in the capsule deformation, inclination, and migration velocity. Due to the reduced capsule deformation, the migration velocity and capsule rotation become slower for capsules with higher viscosity contrast and/or membrane viscosity. Moreover, the influence of membrane viscosity on the migration dynamics intensifies at higher capillary number. Finally, empirical correlations are proposed for the migration velocity and rotation period, and the proposed relations match fairly well the simulation results, which cover wide ranges of system parameters. The discussions and analysis could be valuable for better understanding the complicated flow–capsule interaction and capsule dynamics in the migration process.