# Michael Siegel : Modeling, analysis, and computations of the influence of surfactant on the breakup of bubbles and drops in a viscous fluid

We present an overview of experiments, numerical simulations, and mathematical analysis of the breakup of a low viscosity drop in a viscous fluid, and consider the role of surface contaminants, or surfactants, on the dynamics near breakup. As part of our study, we address a significant difficulty in the numerical computation of fluid interfaces with soluble surfactant that occurs in the important limit of very large values of bulk Peclet number Pe. At the high values of Pe in typical fluid-surfactant systems, there is a narrow transition layer near the drop surface or interface in which the surfactant concentration varies rapidly, and its gradient at the interface must be determined accurately to find the dropÂ?s dynamics. Accurately resolving the layer is a challenge for traditional numerical methods. We present recent work that uses the narrowness of the layer to develop fast and accurate `hybridÂ? numerical methods that incorporate a separate analytical reduction of the dynamics within the transition layer into a full numerical solution of the interfacial free boundary problem.

**Category**: Applied Math and Analysis**Duration**: 01:14:38**Date**: November 3, 2008 at 4:25 PM**Views**: 121-
**Tags:**seminar, Applied Math And Analysis Seminar

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