Toroidal drops in viscous flow

Toroidal drops are known since the experiments by Plateau (1854) in rotating fluids. Such shapes and other non-spherical configurations have become of interest in various technological areas, and recently also as potential carriers of drugs (Champion et al., 2007) or building blocks for more complex assemblies (Velev et al., 2000). Such geometry is obtained, for example, when a drop, falling free in a viscous fluid, experiences a finite surface deformation which develops into a toroidal form (Kojima et al., 1984; Baumann et al., 1992; Sostarecz & Belmonte 2003). In this presentation we shall revisit the stable compression of spherical drops in bi-axial viscous extension, within a finite range of the capillary number, Ca, and show that loss of stability can lead to formation of toroidal shapes. We demonstrate numerically that there is a limited range of Ca in which toroidal stationary solutions exist, and that such drops in this flow are inherently unstable (Zabarankin et al., 2013). However, there is a potential of shape stabilization if the drops are comprised of a mild yield stress material. References BAUMANN, N., JOSEPH, D. D., MOHR, P. & RENARDY, Y. 1992 Vortex rings of one fluid in another in free fall. Phys. Fluids A 4 (3), 567–580. CHAMPION, J. A., KATARE, Y. K. & MITRAGOTRI, S. 2007 Particle shape: A new design parameter for micro- and nanoscale drug delivery carriers. J. Contr. Release 121 (1–2), 3–9. KOJIMA, M., HINCH, E. J. & ACRIVOS, A. 1984 The formation and expansion of a toroidal drop moving in a viscous fluid. Phys. Fluids 27 (1), 19–32. PLATEAU, J. 1857 I. Experimental and theoretical researches on the figures of equilibrium of a liquid mass withdrawn from the action of gravity.–Third series. Philosophical Magazine Series 4 14 (90), 1–22. SOSTARECZ, M. C. & BELMONTE, A. 2003 Motion and shape of a viscoelastic drop falling through a viscous fluid. J. Fluid Mech. 497, 235–252. VELEV, O. D., LENHOFF, A. M. & KALER, E. W. 2000 A class of microstructured particles through colloidal crystallization. Science 287 (5461), 2240–2243. ZABARANKIN, M., SMAGIN, I., LAVRENTEVA, O. M. & NIR, A. 2013 Viscous drop in compressional Stokes flow. J. Fluid Mech. 720, 169–191

Boundary Integral simulations of motion and deformation of visco-plastic drops in a non-isothermal viscous fluid

Non UBCUnreviewedAuthor affiliation: TechnionFacult

Shear-induced particle migration in a poly-dispersed concentrated suspension of particles in viscoplastic fluid

Non UBCUnreviewedAuthor affiliation: TechnionFacult

Tensile Strength of the Chromaffin Granule Membrane

Catecholamine release from chromaffin granules, suspended in sucrose solutions of various osmotic strengths, was determined at different temperatures between 2° and 44°C. Dynamic measurements showed that steady state is achieved within 15 min of incubation at all temperatures. The effect of temperature on the release was established in terms of the median granular fragility (MGF) defined as the concentration of sucrose solution causing 50% lysis. The MGF was determined as the inflection point of the Gaussian distribution of granular fragility. The MGF was found to decrease with fall in temperature implying a corresponding increase of the tensile strength of the vesicle membrane. Critical resultant forces at lysis were calculated and found to vary from 8.2 dyn/cm at 2°C to 4.2 dyn/cm at 44°C. These compare well with tensions at lysis found earlier for erythrocytes

The weakly inertial settling of particles in a viscous fluid

In this paper we investigate the influence of fluid inertia on the settling of a finite assemblage of solid spherical particles in a constant gravity field at small Reynolds number, Re. We show that the first effect of fluid inertia on particle velocities scales as Re, for times much larger than the viscous–relaxation time. In this case the Eulerian acceleration terms associated with the unsteadiness of the stresslet in the far velocity field and the entire local fluid inertia (acceleration and advective terms) contribute at O(Re). As a particular example, Oseen velocities are calculated of two spheres falling along the line of their centres. The inertia–induced relative motion between the particles is in excellent agreement with previous experimental results