Dynamics of nonspherical compound capsules in simple shear flow

Abstract

The dynamics of an initially ellipsoidal compound capsule in a simple shear flow is investigated numerically using a three-dimensional front-tracking finite-difference model. Membrane bending resistance is included based on Helfrich’s energy function besides the resistances against shear deformation and area dilatation governed by the constitutive law of Skalak et al. In this paper, we focus specifically on how the presence of a spherical inner capsule and its size affects the characteristics and transition of various dynamical states of nonspherical compound capsules (i.e., the outer capsule). Significant differences in the dynamical characteristics are observed between compound capsules and homogeneous capsules in both qualitative and quantitative terms. We find the transition from swinging to tumbling can occur at vanishing viscosity mismatch through increasing the inner capsule size alone to a critical value regardless of the initial shape of the nonspherical compound capsule (i.e., prolate or oblate). Besides, for compound capsules with viscosity mismatch, the critical viscosity ratio for the swinging-to-tumbling transition remarkably decreases by increasing the inner capsule size. It is thus concluded that the inner capsule size is a key governing parameter of compound capsule dynamics apart from the capillary number, aspect ratio, and viscosity ratio that have been long identified for homogeneous capsules. Further, we discuss the mechanisms underlying the effects of the inner capsule on the compound capsule dynamics from the viewpoint of the effective viscosity of internal fluid and find that the effects of the inner capsule on compound capsule dynamics are qualitatively similar to that of increasing the internal viscosity on homogeneous capsule dynamics. However, in quantitative terms, the compound capsule cannot be viewed as a homogeneous capsule with higher viscosity as obvious inhomogeneity in fluid stress distribution is induced by the inner membrane.