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Drag, deformation, and drift volume associated with a drop rising in a density stratified fluid

Vaseem A. Shaik and Arezoo M. Ardekani*

  • School of Mechanical Engineering, Purdue University, West Lafayette, Indiana 47907, USA

  • *ardekani@purdue.edu
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Phys. Rev. Fluids 5, 013604 – Published 29 January, 2020

DOI: https://doi.org/10.1103/PhysRevFluids.5.013604

Abstract

We consider a drop of constant density and uniform interfacial tension rising in a linearly density stratified fluid. In the limits of weak inertia and stratification effects, we calculate the drag acting on the drop, the flow fields inside and outside the drop, the drop deformation, and the drift volume induced by the drop using the method of matched asymptotic expansions. Stratification or inertia increase the drag, and this enhanced drag acting on a drop is equal to 3λ+23λ+12 times the enhanced drag acting on a rigid sphere, where λ is the viscosity ratio. This relation between the enhanced drags of a drop and a rigid sphere holds even in the presence of both of these effects (stratification and inertia). On the other hand, stratification does not result in any deformation of the drop up to the first order of approximation. At zero inertia and small advective transport rate of density, the drift volume induced by the drop rising in a stratified fluid is finite (but large compared to the drop's volume), unlike the drift volume in a homogeneous fluid, which is infinite.

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Outline

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Phys. Rev. Fluids 5, 013604– Published 29 January, 2020
  • Received 7 March 2019
Article part of CHORUS
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