The dynamic response of an initially spherical capsule subject to different externally imposed flows is examined. The neo-Hookean and Skalak et al. (Biophys. J., vol. 13 (1973), pp. 245-264) constitutive laws are used for the description of the membrane mechanics, assuming negligible bending resistance. The viscosity ratio between the interior and exterior fluids of the capsule is taken to be unity and creeping-flow conditions are assumed to prevail. The capillary number ε is the basic dimensionless number of the problem, which measures the relative importance of viscous and elastic forces. The boundary-element method is used with bi-cubic B-splines as basis functions in order to discretize the capsule surface by a structured mesh. This guarantees continuity of second derivatives with respect to the position of the Lagrangian particles used for tracking the location of the interface at each time step and improves the accuracy of the method. For simple shear flow and hyperbolic flow, an interval in ε is identified within which stable equilibrium shapes are obtained. For smaller values of ε, steady shapes are briefly captured, but they soon become unstable owing to the development of compressive tensions in the membrane near the equator that cause the capsule to buckle. The post-buckling state of the capsule is conjectured to exhibit small folds around the equator similar to those reported by Walter et al. Colloid Polymer Sci. Vol. 278 (2001), pp. 123-132 for polysiloxane microcapsules. For large values of ε, beyond the interval of stability, the membrane has two tips along the direction of elongation where the deformation is most severe, and no equilibrium shapes could be identified. For both regions outside the interval of stability, the membrane model is not appropriate and bending resistance is essential to obtain realistic capsule shapes. This pattern persists for the two constitutive laws that were used, with the Skalak et al. law producing a wider stability interval than the neo-Hookean law owing to its strain hardening nature.

We consider a neutrally buoyant and initially uncharged drop in a second liquid subjected to a uniform electric field. Both liquids are taken to be leaky dielectrics. The jump in electrical properties creates an electric stress balanced by hydrodynamic and capillary stresses. Assuming creeping flow conditions and axisymmetry of the problem, the electric and flow fields are solved numerically withboundary integral techniques. The system is characterized by the physical property ratios R (resistivities), Q (permitivities) and λ (dynamic viscosities). Depending on these parameters, the drop deforms into a prolate or an oblate spheroid. The relative importance of the electric stress and of the drop/medium interfacial tension is measured by the dimensionless electric capillary number, Cae. For λ = 1, we present a survey of the various behaviours obtained for a wide range of R and Q. We delineate regions in the (R,Q)-plane in which the drop either attains a steady shape under any field strength or reaches a fold-point instability past a critical Cae. We identify the latter with linear instability of the steady shape to axisymmetric disturbances. Various break-up modes are identified, as well as more complex behaviours such as bifurcations and transition from unstable to stable solution branches. We also show how the viscosity contrast can stabilize the drop or advance break-up in the different situations encountered for λ = 1.

We present a numerical model of the hydrodynamic interactions between two capsules freely suspended in a simple shear flow. The capsules are identical and each consists of a liquid droplet enclosed by a thin hyperelastic membrane, devoid of bending resistance and obeying a neo-Hookean constitutive law. The two capsules are slightly prestressed with a given inflation ratio in order to avoid the small deformation instability due to compression observed for a single capsule in simple shear flow. The viscosity ratio between the interior and exterior fluids of the capsule is taken to be unity and creeping flow conditions are assumed to prevail. The boundary-element method is used with bi-cubic B-splines as basis functions on a structured mesh in order to discretize the capsule surface. A new method using two grids with initially orthogonal pole axes is developed to eliminate polar singularities in the load calculation and to allow for long computation times. Two capsules suspended in simple shear flow usually have different velocities and thus eventually pass each other. We study this crossing process as a function of flow strength and initial particle separation. We find that hydrodynamic interactions during crossing lead to large shape alterations, elevated elastic tensions in the membrane and result in an irreversible trajectory shift of the capsules. Furthermore, a tendency towards buckling is observed, particularly during the separation phase where large pressure differences occur. Our results are in qualitative agreement with those obtained for a pair of interacting liquid droplets but show the specific role played by the membrane of capsules.