Problems in non-Newtonian and free surface flows

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The study of flow problems in polymeric liquids poses numerous challenges for mathematical analysis. The topics addressed in this project include asymptotic analysis of the breakup of liquid jets, analysis of stability and control of viscoelastic flows, and numerical simulation of drop breakup under shear, a fundamental process in the formation of emulsions. Applications of viscoelastic flows arise in manufacturing of plastics, foods, and other products, as well as in biological problems such as blood flow. The effect of polymer additives in suppressing breakup of drops is exploited both in nature (in spider webs) and in technology (to control sizes of drops in the spraying of liquids). Instabilities in the flow of complex fluids often pose limits for polymer processing techniques. The research carried on under this project will clarify fundamental mathematical issues underlying such phenomena to enable a better understanding of these flows and the development of methods for their simulation.