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# Ellen R. Peterson : A Droplet Spreading on a Thin Liquid Film: a Gradient Flow Formulation

We consider a droplet spreading on a thin liquid film where both fluids are Newtonian, incompressible, and immiscible. Rather than following the typical asymptotic derivation for a thin film, we formulate the model through a gradient flow approach. The sign of the spreading parameter indicates the spreading behavior (complete or partial spreading) and is a relation between the three interfacial tensions: fluid/air, fluid/drop, and drop/air. We are particularly interested in the case where the spreading parameter is negative. In this case, the drop is expected to spread to a static lens and we find the corresponding equilibrium solution. Finally, we make a comparison between the theoretical model and experimental results.

**Category**: Applied Math and Analysis**Duration**: 01:34:54**Date**: November 7, 2011 at 4:25 PM**Views**: 110-
**Tags:**seminar, Applied Math And Analysis Seminar

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