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Applied Math Colloquium

Friday, November 22nd, 2013, 11:30 AM
Cullimore Lecture Hall, Lecture Hall II
New Jersey Institute of Technology

Particles at Interfaces: Capillary Attraction, Elasticity, and Coating Flows

G. M. "Bud" Homsy

University of British Columbia, Canada

Abstract

Experiments on dip coating of liquids with small particles adsorbed at the interface show very significant deviations from the classical result of Landau & Levich, exhibiting both a large increase in the coating thickness and a non-classical dependence of this thickness on the speed U of the moving substrate. Plausible physical explanations lead us to consider the capillary attraction between particles as well as a bending stiffness associated with a particulate "jammed state". Capillary attraction alone produces a surfactant-like response that is computed asymptotically for small particles and weak gravity. While this leads to film thickening, the theory is insufficient to explain the data. We then consider the problem when the interface has an elastic bending stiffness and a constant surface tension. We assume the elasticity number El - the ratio of surface elasticity to viscous forces - is small and develop the solution for the free boundary as a matched asymptotic expansion in the small parameter El^(1/7). A remarkable aspect of the problem is the occurrence of multiple solutions, and five of these are found numerically. In any event, the film thickness varies as U^(4/7), in agreement with experiments. It is possible to connect the problems of pure elasticity and elasto-capillarity, but connecting one of the five elasto-capillary branches to the classical result remains an elusive goal.