Mathematical Sciences: Dynamics of Multi-Fluid Flow and Interfaces

9401775这项研究考虑了多流体体系的界面稳定性，特别强调了实际操作参数在应用中的理论预测。第一部分是关于振荡两相Couette流稳定性的一个新发现。结果表明，背景态的周期调制可以完全稳定长波区的界面模。这些结果将通过使用弗洛奎特理论和调节系统的数值积分，并在适当的情况下进行分析，扩展到所有波长。一个平行项目将通过研究耗散偏微分系统和使用动力系统理论中的工具来研究线性和非线性区域的两相芯-环状振荡流动。推导和数值求解二维和三维的非线性演化方程，以模拟柱状几何结构中双流体流动的非线性稳定性。在许多技术和自然过程中，双流体流动中的不稳定性很重要，需要了解。除其他外，例子包括用于输送粘性原油的润滑管道、挤压工艺、提高石油采收率、涂层工艺、熔融生长晶体技术中的定向凝固以及摄影胶片的生产。生物学应用包括新生婴儿由于界面不稳定导致管壁液体覆盖层破裂而导致肺血管崩溃。在地面和微重力环境中还有许多其他不断发展的技术，这些技术需要对界面不稳定性和流变学有基本的了解。

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.