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Coalescence of drops with mobile interfaces in a quiescent fluid

Published online by Cambridge University Press:  11 July 2013

M. B. Nemer ,
P. Santoro ,
X. Chen ,
J. Bławzdziewicz  and
M. Loewenberg
M. B. Nemer*
Affiliation:
Thermal & Fluid Experimental Science, Sandia National Laboratories, Albuquerque, NM 87185, USA
P. Santoro
Affiliation:
Jefferies International Limited, 68 Upper Thames Street, London EC4V 3BJ, UK
X. Chen
Affiliation:
Exotic Credit Derivative Trading, Citigroup, New York City, NY 10013, USA
J. Bławzdziewicz
Affiliation:
Department of Mechanical Engineering, Texas Tech University, Lubbock, TX 79409-1021, USA
M. Loewenberg
Affiliation:
Department of Chemical and Environmental Engineering, Yale University, New Haven, CT 06520-8286, USA
*
†Email address for correspondence: mbnemer@sandia.gov
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Abstract

A study on the axisymmetric near-contact motion of drops with tangentially mobile interfaces under the action of a body force in a quiescent fluid is described. A long-time asymptotic analysis is presented for small-deformation conditions. Under these conditions the drops are nearly spherical, except in the near-contact region, where a flattened thin film forms. According to our analysis, a hydrostatic dome does not form in the near-contact region at long times, in contrast to the assumption underlying all previous analyses of this problem. Instead, the shape of the film in the near-contact region results from the absence of tangential stresses acting on it. As a result, the long-time behaviour of the system is qualitatively different than previously predicted. According to the theory presented herein, the minimum film thickness (rim region) decays with time as ${h}_{m} \sim {t}^{- 4/ 5} $, and the thickness at the centre of the film decays as ${h}_{0} \sim {t}^{- 3/ 5} $, which is a faster decay than predicted by prior analyses based on a hydrostatic dome. Numerical thin-film simulations quantitatively confirm the predictions of our small-deformation theory. Boundary-integral simulations of the full two-drop problem suggest that the theory also describes qualitatively the long-time evolution under finite-deformation conditions.

JFM classification

Drops and Bubbles: Breakup/coalescence Drops and Bubbles: Drops Complex Fluids: Emulsions
Type
Papers
Information
Journal of Fluid Mechanics , Volume 728 , 10 August 2013 , pp. 471 - 500
Copyright
©2013 Cambridge University Press 

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