Deformation of spherical compound capsules in simple shear flow

The deformation of a compound capsule (an elastic capsule with a smaller capsule inside) in simple shear flow is studied by using three-dimensional numerical simulations based on a front tracking method. The inner and outer capsules are concentric and initially spherical. Skalak et al.'s constitutive law is employed for the mechanics of both the inner and outer membranes. Our results concerning the deformation of homogeneous capsules (i.e. capsules without the inner capsules) are quantitatively in agreement with the predictions of previous numerical simulations and perturbation theories. Compared to homogeneous capsules, compound capsules exhibit smaller deformation. The deformations of both the inner and outer capsules are significantly affected by the capillary numbers of the inner and outer membranes and the volume ratio of the inner to the outer capsule. When the inner capsule is small, it presents smaller deformation than the outer capsule. However, when the inner capsule is sufficiently large, it can present larger deformation than the outer capsule, even if the inner membrane has much lower capillary number than the outer membrane. The underlying mechanisms are discussed: (i) the inner capsule is deformed by rotational flow with lower rate of strain rather than by simple shear flow that deforms the outer capsule, and thus the inner capsule exhibits smaller deformation; and (ii) when the inner and outer membranes are sufficiently close (i.e. the inner capsule is sufficiently large), the hydrodynamic interaction between the two membranes becomes significant, which is found to inhibit the deformation of the outer capsule but to promote the deformation of the inner capsule.