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Evolution and stationarity of liquid toroidal drop in compressional Stokes flow

Published online by Cambridge University Press:  27 November 2017

B. K. Ee ,
O. M. Lavrenteva ,
I. Smagin  and
A. Nir Open the ORCID record for A. Nir [Opens in a new window]
B. K. Ee
Affiliation:
Department of Chemical Engineering, Technion-Israel Institute of Technology, Haifa 3200003, Israel
O. M. Lavrenteva
Affiliation:
Department of Chemical Engineering, Technion-Israel Institute of Technology, Haifa 3200003, Israel
I. Smagin
Affiliation:
Department of Chemical Engineering, Technion-Israel Institute of Technology, Haifa 3200003, Israel
A. Nir*
Affiliation:
Department of Chemical Engineering, Technion-Israel Institute of Technology, Haifa 3200003, Israel
*
†Email address for correspondence: avinir@tx.technion.ac.il
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Abstract

Dynamics of fluid tori in slow viscous flow is studied. Such tori are of interest as future carriers of biological and medicinal substances and are also viewed as potential building blocks towards more complex particles. In this study the immiscible ambient fluid is subject to a compressional flow (i.e., bi-extensional flow), and it comprises a generalization of our earlier report on the particular case with viscosity ratio $\unicode[STIX]{x1D706}=1$ (see Zabarankin et al., J. Fluid Mech., vol. 785, 2015, pp. 372–400), where $\unicode[STIX]{x1D706}$ is the ratio between the torus viscosity and that of the ambient fluid. It is found that, for all viscosity ratios, the torus either collapses towards the axis of symmetry or expands indefinitely, depending on the initial conditions and the capillary number, Ca. During these dynamic patterns the cross-sections exhibit various forms of deformation. The collapse and expansion dynamic modes are separated by a limited deformation into a deformed stationary state which appears to exist in a finite interval of the capillary number, $0<Ca<Ca_{cr}(\unicode[STIX]{x1D706})$ , and is unstable to axisymmetric disturbances, which eventually cause the torus either to collapse or to expand indefinitely. The characteristic dimensions and shapes of these unstable stationary tori and their dependence on the physical parameters Ca and $\unicode[STIX]{x1D706}$ are reported.

JFM classification

Low-Reynolds-number flows: Boundary integral methods Drops and Bubbles: Drops and Bubbles Low-Reynolds-number flows: Low-Reynolds-number flows

Information

Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 835 , 25 January 2018 , pp. 1 - 23
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© 2017 Cambridge University Press 

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