Mathematical Sciences: Stability and Bifurcation in Two-Layer Shearing Flows

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This research will examine flows which involve two immiscible fluids. For such flows, there are a number of theoretical possibilities for the shape of the boundary which separates the two fluids. However, experimental results indicate that some boundary shapes are preferred over others. This work will investigate the selection mechanisms for boundary shapes. Physical modeling, analytical, and computational techniques will be used to study the stability of various stable arrangements and the appearance of new arrangements from unstable configurations. This work could lead to a better understanding of practical applications including the formation of bicomponent fibers, transport of oil in pipelines, ink-jet printing, and lubrication with two fluids.