Mathematical Sciences: Dynamics of Multi-Fluid Flow and Interfaces

点击翻译按钮获取中文摘要

9401775 Papageorgiou This research considers the interfacial stability of multi-fluid systems with particular emphasis placed on the theoretical prediction of practical operating parameter regimes in applications. The first part is concerned with a new finding on the stability of oscillatory two-phase Couette flow. It has been shown that periodic modulations in the background state can completely stabilize interfacial modes in the long wave regime. These results will be extended to all wavelengths by use of Floquet theory and numerical integration of the governing system, and with analysis where appropriate. A parallel project will address oscillatory two-phase core-annular flow both in the linear and nonlinear regime by study of dissipative partial differential systems and use of tools taken from dynamical systems theory. Nonlinear evolution equations in both two and three dimensions will be derived and solved numerically in order to model the nonlinear stability of two-fluid flows in cylindrical geometries. There are numerous technological and natural processes where instabilities in two-fluid flows are important and need to be understood. Examples include, among others, lubricated pipelining for the transport of viscous crudes, extrusion processes, enhanced oil recovery, coating processes, directional solidification in melt-grown crystal technologies, and production of photographic film. Biological applications include the collapse of pulmonary vessels in new-borne babies due to interfacial instabilities leading to rapture of the fluid covering of the tube walls. There are a number of other evolving technologies both ground-based as well as in microgravity environments which require a fundamental understanding of interfacial instabilities and rheology.