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The coalescence of liquid drops in a viscous fluid: interface formation model

Published online by Cambridge University Press:  24 June 2014

James E. Sprittles*
Affiliation:
Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK School of Mathematics, University of Birmingham, Birmingham B15 2TT, UK
Yulii D. Shikhmurzaev
Affiliation:
Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK School of Mathematics, University of Birmingham, Birmingham B15 2TT, UK
*
Email address for correspondence: J.E.Sprittles@warwick.ac.uk

Abstract

The interface formation model is applied to describe the initial stages of the coalescence of two liquid drops in the presence of a viscous ambient fluid whose dynamics is fully accounted for. Our focus is on understanding (a) how this model’s predictions differ from those of the conventionally used one, (b) what influence the ambient fluid has on the evolution of the shape of the coalescing drops and (c) the coupling of the intrinsic dynamics of coalescence and that of the ambient fluid. The key feature of the interface formation model in its application to the coalescence phenomenon is that it removes the singularity inherent in the conventional model at the onset of coalescence and describes the part of the free surface ‘trapped’ between the coalescing volumes as they are pressed against each other as a rapidly disappearing ‘internal interface’. Considering the simplest possible formulation of this model, we find experimentally verifiable differences with the predictions of the conventional model showing, in particular, the effect of drop size on the coalescence process. According to the new model, for small drops a non-monotonic time dependence of the bridge expansion speed is a feature that could be looked for in further experimental studies. Finally, the results of both models are compared to recently available experimental data on the evolution of the liquid bridge connecting coalescing drops, and the interface formation model is seen to give a better agreement with the data.

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Papers
Copyright
© 2014 Cambridge University Press 

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