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

这项研究将考察涉及两种不相容流体的流动。对于这种流动，对于分隔两种流体的边界形状有许多理论上的可能性。然而，实验结果表明，某些边界形状比其他形状更受欢迎。这项工作将研究边界形状的选择机制。物理模型、分析和计算技术将被用来研究各种稳定排列的稳定性和不稳定构型中新排列的出现。这项工作可以更好地理解实际应用，包括双组分纤维的形成、石油在管道中的传输、喷墨打印以及两种流体的润滑。

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.