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Effects of non-uniform interfacial tension in small Reynolds number flow past a spherical liquid drop

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Abstract

A singular perturbation solution is given for small Reynolds number flow past a spherical liquid drop. The interfacial tension required to maintain the drop in a spherical shape is calculated. When the interfacial tension gradient exceeds a critical value, a region of reversed flow occurs on the interface at the rear and the interior flow splits into two parts with reversed circulation at the rear. The magnitude of the interior fluid velocity is small, of order the Reynolds number. A thin transition layer attached to the drop at the rear occurs in the exterior flow. The effects could model the stagnant cap which forms as surfactant is added but the results apply however the variability in the interfacial tension might have been induced.

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Authors and Affiliations

  1. Centre for Differential Equations, Continuum Mechanics and Applications, School of Computational and Applied Mathematics, University of the Witwatersrand, Johannesburg, Private Bag 3, Wits 2050, South Africa

    D P MASON

  2. Department of Mathematical Sciences, University of South Africa, P.O. Box 392, Pretoria, 0003, South Africa

    G M MOREMEDI

Authors
  1. D P MASON
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  2. G M MOREMEDI
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Correspondence to D P MASON.

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MASON, D.P., MOREMEDI, G.M. Effects of non-uniform interfacial tension in small Reynolds number flow past a spherical liquid drop. Pramana - J Phys 77, 493–507 (2011). https://doi.org/10.1007/s12043-011-0170-8

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  • DOI: https://doi.org/10.1007/s12043-011-0170-8

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