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Effect of interfacial slip on the thin film drainage time for two equal-sized, surfactant-free drops undergoing a head-on collision: A scaling analysis

A. Ramachandran1 and L. G. Leal2

  • 1Department of Chemical Engineering & Applied Chemistry, University of Toronto, Toronto, Ontario, Canada M5S 3ES
  • 2Department of Chemical Engineering, University of California, Santa Barbara, Santa Barbara, California 93106, USA

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Phys. Rev. Fluids 1, 064204 – Published 21 October, 2016

DOI: https://doi.org/10.1103/PhysRevFluids.1.064204

Abstract

Using a scaling analysis, we assess the impact of interfacial slip on the time required for the thin liquid film between two drops undergoing a head-on collision to drain to the critical thickness for rupture by van der Waals forces. Interfacial slip is included in our continuum development using a Navier slip boundary condition, with the slip coefficient modeled using previous theories [Helfand and Tagami, J. Chem. Phys. 57, 1812 (1972); Goveas and Fredrickson, Eur. Phys. J. B 2, 79 (1998)]. Slip decreases hydrodynamic resistance and speeds up film drainage. It renders the dependence of the drainage time on capillary number stronger in the spherical-film regime, but, interestingly, this dependence is altered only weakly in the dimpled-film regime. A subtle effect of slip is that it increases the range of capillary numbers in which the film remains predominantly spherical in shape during drainage (as opposed to being dimpled), leading to significantly faster drainage for these capillary numbers. Slip also leads to an increase in the critical capillary number beyond which coalescence is not possible in a head-collision.

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Phys. Rev. Fluids 1, 064204– Published 21 October, 2016
  • Received 21 January 2016

©2016 American Physical Society

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