Unsynchronized motion of inner and outer membranes of compound capsules in shear flow

Despite its significance in understanding behaviors of biological cells with nucleus or designing functions of complex artificial capsules in applications, the dynamics of elastic capsules enclosing complicated internal structures in flow is still largely unexplored. In this study, by using our own three-dimensional front-tracking finite-difference model, we present a numerical investigation into the dynamics of a compound capsule in a simple shear flow whose inner and outer membranes have the same prolate ellipsoidal shape at the rest state. Particular interest is focused on the unsynchronized motion of the inner and outer membranes. Regarding the dynamical regime, both the inner and outer capsules can undergo either synchronized or unsynchronized dynamical regimes (i.e., swinging or tumbling), which strongly depends on the inner-to-outer capillary number ratio Cain/Caout, the inner-to-outer volume ratio φ, and the prolate aspect ratio a/b. Particularly, via establishing a phase diagram based on a/b and φ at Cain/Caout = 1, we find that the inner and outer membranes can exist simultaneously in different dynamical regimes, even if they have the same deformability and the same shape. More importantly, if the detailed oscillation behavior is also concerned besides the capsule's dynamical regime, such as the transient shape and the oscillating period, unsynchronization is always obvious between the inner and outer capsules. Specifically, the inner capsule exhibits a slower oscillation than the outer capsule no matter if they lie in the swinging or tumbling regime.