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Dissolution and growth of a multicomponent drop in an immiscible liquid

Published online by Cambridge University Press:  10 June 2016

Shigan Chu  and
Andrea Prosperetti Open the ORCID record for Andrea Prosperetti [Opens in a new window]
Shigan Chu
Affiliation:
Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD 21218, USA
Andrea Prosperetti*
Affiliation:
Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD 21218, USA Department of Science & Technology and J. M. Burgers Center for Fluid Dynamics, University of Twente, 7500AE Enschede, The Netherlands
*
†Email address for correspondence: [email protected]
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Abstract

The mass flux at the surface of a drop in an immiscible host liquid is dictated by the composition of the drop surface. In a binary system, this composition is essentially constant in time and equals the solubility of the drop constituent in the host liquid. This situation has been treated in a classic study by Epstein and Plesset (J. Chem. Phys., vol. 18, 1950, pp. 1505–1509). The situation is very different for ternary and higher-order systems in which, due to the mutual interaction of the drop constituents, their concentration at the drop surface markedly differs from the respective solubilities and depends on time. This paper presents a thermodynamically consistent analysis of this situation, for both growing and dissolving drops, with and without an initial concentration of the drop constituents in the host liquid. In some cases the results, which have important implications e.g. for solvent extraction processes in the chemical and environmental remediation industries, show major deviations from the predictions of approximations in current use, including simple extensions of the Epstein–Plesset theory.

JFM classification

Drops and Bubbles: Drops Complex Fluids: Emulsions
Type
Papers
Information
Journal of Fluid Mechanics , Volume 798 , 10 July 2016 , pp. 787 - 811
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Copyright
© 2016 Cambridge University Press 

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