Three-dimensional dynamics of oblate and prolate capsules in shear flow.

We study computationally the dynamics of oblate and prolate spheroidal capsules in simple shear flow with small inertia for a range of dimensionless shear rates. The capsule is modelled as a liquid droplet enclosed by a hyperelastic membrane, and its equatorial plane is initially tilted out of the plane of shear. We find, at low shear rates, the well-accepted tumbling motion is not always stable for both oblate and prolate capsules. For an oblate capsule, the dominant stable modes for increasing dimensionless shear rate are as follows: rolling with the equatorial plane staying in the plane of shear, precessing following Jeffery's orbit [Proc. R. Soc. London A 102, 161 (1922)], and tumbling. Interestingly, the order of modes is reversed for a prolate capsule: tumbling, precessing, and rolling with increasing dimensionless shear rate. At transitional regimes, we find the stable motion of a capsule can depend on its initial titled angle, even at the same shear rate. At high dimensionless shear rates, a spheroidal capsule undergoes a complicated oscillating-swinging motion: Its major axis oscillates about the plane of shear in addition to the swinging about a mean angle with flow direction found previously, and the amplitudes of both oscillations decrease when increasing the dimensionless shear rate towards a steady tank treading motion asymptotically. We summarize the results in phase diagrams and discuss the reorientation of both oblate and prolate capsules in a wide range of dimensionless shear rates.

Collapse of a bubble in an electric field.

A low-Mach-number analysis is presented of the collapse of a bubble in an electric field, which is assumed to be homogeneous, but may be unsteady. Ellipsoidal shape deformations are accounted for in the analysis, but are assumed to be small. It is shown that the presence of an electric field leads to additional terms in a modified Rayleigh-Plesset equation. This differential equation for the bubble radius and a corresponding equation for ellipsoidal shape deformations have been integrated numerically. The results indicate that a bubble can be made to collapse by instantaneously switching on an electric field. Also, nonharmonic volumetric oscillations are observed for time-dependent electric fields of sufficiently large amplitude. It is shown that the rate of a collapse driven by external pressure variations due, for instance, to acoustic forcing can be accelerated.

Collisions of liquid coated solid spherical particles in a viscous fluid.

An analytical description is presented for the head-on collision of two spherical rigid particles that are coated with a thin layer of one liquid and immersed in another. Lubrication theory is used to resolve the spatio-temporal evolution of the coating surfaces, in conjunction with the fluid flow in the gap region between the particles. The analysis is carried out up to the point where the gap region has almost completely been drained; intermolecular forces are neglected. The effects of particle inertia, the ratio of particle radii, surface tension, and the viscosity ratio of the coating and carrier fluids are studied; these are parameterised by St, beta, Ca and m, respectively. The results of the present work elucidate the effect of the above-mentioned factors on the conditions under which particles rebound (assumed to occur if the distance between the particles becomes very short while the relative velocity does not vanish) or stick. In particular, summarizing flowmaps show that the likelihood of particles rebounding increases with increasing St and decreasing beta, Ca and m. On the other hand, it is shown that the force on approaching particles depends on all of these parameters in a non-monotonic manner.