Toroidal drops in viscous flow
April 3-7, 2016
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.
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PLATEAU, J. 1857 I. Experimental and theoretical researches on the figures of equilibrium of a liquid mass withdrawn from the action of gravity.–Third series.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.
Avinoam Nir, Olga M. Lavrenteva, Irina Smagin, and Michael Zabarankin, "Toroidal drops in viscous flow" in "Design and Manufacture of Functional Microcapsules and Engineered Products", Chair: Simon Biggs, University of Queensland (Aus) Co-Chairs: Olivier Cayre, University of Leeds, UK Orlin D. Velev, North Carolina State University, USA Eds, ECI Symposium Series, (2016). http://dc.engconfintl.org/microcapsules/12