Axisymmetric boundary integral simulations of film drainage between two viscous drops

P.J.A. Janssen, P.D. Anderson, G.W.M. Peters, H.E.H. Meijer

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Abstract

Film drainage between two drops with viscosity equal to that of the matrix fluid is studiedusing a numerical method that can capture both the external problem of two touchingdrops as well as the inner problem of pressure-driven local film drainage, without assumptionsabout the dimensions of the film or the use of lubrication approximations.We use a non-singular boundary integral method that has sufficient stability and accuracyto simulate film thicknesses down to and smaller than 10−4 times the undeformeddrop radius. After validation of the method we investigate the validity of various resultsobtained from simple film-drainage models and asymptotic theories. Our results forbuoyancy-driven collisions are in agreement with a recently developed asymptotic theory.External-flow-driven collisions are different than buoyancy-driven collisions, which meansthat the internal circulation inside the drop plays a significant role in film drainage, evenfor small capillary numbers, as has been recently shown [Nemer et al, Phys. Review Letters,92, 114501, 2004]. Despite, we find excellent correspondence with simple drainagemodels when considering the drainage time only.
Original languageEnglish
Pages (from-to)65-90
JournalJournal of Fluid Mechanics
Volume567
DOIs
Publication statusPublished - 2006

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