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Dynamic and stationary shapes of rotating toroidal drops in viscous linear flows

Published online by Cambridge University Press:  21 July 2021

Sumit Malik Open the ORCID record for Sumit Malik [Opens in a new window] ,
O.M. Lavrenteva Open the ORCID record for O.M. Lavrenteva [Opens in a new window]  and
A. Nir Open the ORCID record for A. Nir [Opens in a new window]
Sumit Malik
Affiliation:
Department of Chemical Engineering, Technion-Israel Institute of Technology, Haifa3200003, Israel
O.M. Lavrenteva
Affiliation:
Department of Chemical Engineering, Technion-Israel Institute of Technology, Haifa3200003, Israel
A. Nir*
Affiliation:
Department of Chemical Engineering, Technion-Israel Institute of Technology, Haifa3200003, Israel
*
†Email address for correspondence: [email protected]
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Abstract

Dynamic and stationary axisymmetric deformation of viscous toroidal drops submerged in slow viscous flow are studied numerically. The immiscible ambient fluid is subject to a combination of rotation and extensional/compressional (biextensional) flow. The creeping flow approximation is assumed. The numerical simulations are performed with the help of the boundary integral method. The process under consideration is governed by three dimensionless parameters: the capillary number that characterizes the ratio of viscous and surface tension forces; the Bond number, that characterizes the ratio of centrifugal and surface tension forces; and the ratio of viscosity of the two fluids. Our simulations for the equal viscosity case demonstrated that, depending on the governing parameters, the toroidal drop either collapses, extends indefinitely or it attains a stationary toroidal shape. The latter may be stable or unstable with respect to axisymmetric disturbances. Conditions for the realization of each of the dynamic regimes and stationary states in terms of governing parameters are presented. In particular, stable toroidal shapes result under the combined action of rotation and extensional flow, and were not found under the action of rotation and compressional flow.

JFM classification

Drops and Bubbles: Drops Mathematical Foundations: Computational methods
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 923 , 25 September 2021 , A3
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

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