Mathematical Sciences: Dynamics of Multi-Fluid Flow and Interfaces

[401775] Papageorgiou本研究考虑了多流体系统的界面稳定性，特别强调了应用中实际操作参数体系的理论预测。第一部分是关于振荡两相库埃特流稳定性的新发现。研究表明，背景态的周期调制可以完全稳定长波状态下的界面模式。这些结果将通过使用Floquet理论和控制系统的数值积分扩展到所有波长，并在适当的地方进行分析。一个并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解决线性和非线性状态下的振荡两相岩心环流。在二维和三维的非线性演化方程将被导出和数值求解，以模拟在圆柱几何两流体流动的非线性稳定性。在许多技术和自然过程中，双流体流动的不稳定性是重要的，需要了解。例如，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、熔体生长晶体技术中的定向凝固以及照相胶片的生产。生物学方面的应用包括新生儿肺血管的塌陷，这是由于界面不稳定导致覆盖在管壁上的液体破裂。还有许多其他不断发展的技术，无论是地面还是微重力环境，都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.