N. Pelekasis

Spherical capsules in three-dimensional unbounded Stokes flows: effect of the membrane constitutive law and onset of buckling

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

Nonlinear radial oscillations of encapsulated microbubbles subject to ultrasound: The effect of membrane constitutive law

\varepsilon

Transient response of a capsule subjected to varying flow conditions: Effect of internal fluid viscosity and membrane elasticity

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

Equilibrium shapes and stability of charged and conducting drops

\varepsilon

A hybrid finite-boundary element method for inviscid flows with free surface

is identified within which stable equilibrium shapes are obtained. For smaller values of

Acoustic detection of microbubble resonance

\varepsilon

Effect of membrane viscosity on the dynamic response of an axisymmetric capsule

, 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

Parametric stability and dynamic buckling of an encapsulated microbubble subject to acoustic disturbances

\varepsilon

Nonlinear oscillations of liquid shells in zero gravity

, 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.

Nonlinear oscillations and collapse of elongated bubbles subject to weak viscous effects

The nonlinear radial oscillations of bubbles that are encapsulated in an elastic shell are investigated numerically subject to three different constitutive laws describing the viscoelastic properties of the shell: the Mooney-Rivlin (MR), the Skalak (SK), and the Kelvin-Voigt (KV) models are used in order to describe strain-softening, strain-hardening and small displacement (Hookean) behavior of the shell material, respectively. Due to the isotropic nature of the acoustic disturbances, the area dilatation modulus is the important parameter. When the membrane is strain softening (MR) the resonance frequency decreases with increasing sound amplitude, whereas the opposite happens when the membrane is strain hardening (SK). As the amplitude of the acoustic disturbance increases the total scattering cross section of a microbubble with a SK membrane tends to decrease, whereas that of a KV or a MR membrane tends to increase. The importance of strain-softening behavior in the abrupt onset of volume pulsations, that is often observed with small insonated microbubbles at moderately large sound amplitudes, is discussed.