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Inertial effects on the dynamics, streamline topology and interfacial stresses due to a drop in shear

Published online by Cambridge University Press:  19 August 2011

Rajesh Kumar Singh  and
Kausik Sarkar
Rajesh Kumar Singh
Affiliation:
Department of Mechanical Engineering, University of Delaware, Newark, DE-19716, USA
Kausik Sarkar*
Affiliation:
Department of Mechanical Engineering, University of Delaware, Newark, DE-19716, USA
*
†Email address for correspondence: [email protected]
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Abstract

Deformation of a viscous drop in shear at finite inertia and the streamlines around it are numerically investigated. Inertia destroys the closed streamlines found in Stokes flow. It creates reversed streamlines and streamlines spiralling around the vorticity axis. Spiralling streamlines spiral either towards the central shear plane or away from it depending on the viscosity ratio and the inertia. The zones of open or reversed streamlines as well as streamlines spiralling towards or away from the central shear plane are delineated for varying viscosity ratio and Reynolds number. In contrast to the infinite extent of the closed Stokes streamlines around a rigid sphere in shear, the region of the spiralling streamlines in the vorticity direction both for a rigid sphere and a drop shrinks with inertia. Inertia increases deformation, and introduces oscillations in drop shape. An approximate analysis explains the scaling of oscillation frequency and damping with Reynolds and capillary numbers. The steady-state drop inclination angle with the flow axis increases with increasing Reynolds number for small Reynolds number. But it decreases at higher Reynolds number, especially for larger capillary numbers. For smaller capillary numbers, drop inclination reaches higher than (the direction of maximum extension), critically affecting the interfacial stresses due to the drop. It changes the sign of first and second normal interfacial stress differences (and thereby these components of the effective stresses of an emulsion of such drops). Increasing viscosity ratio orients the drop towards the flow axis, which increases the critical Reynolds number above which the drop inclination reaches more than .

JFM classification

Drops and Bubbles: Drops Complex Fluids: Emulsions Non-Newtonian Flows: Rheology
Type
Papers
Information
Journal of Fluid Mechanics , Volume 683 , 25 September 2011 , pp. 149 - 171
Copyright
Copyright © Cambridge University Press 2011

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