Mathematical Sciences: Dynamics of Multi-Fluid Flow and Interfaces

数学科学：多流体流动和界面动力学

• 批准号: 9401775
• 负责人: Demetrios Papageorgiou
• 金额: $ 3.75万
• 依托单位: New Jersey Institute of Technology
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-07-01 至 1997-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9401775&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Dynamics; Multi; Fluid

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.

小行星9401775 本研究考虑了多流体系统的界面稳定性，特别强调应用中实际操作参数制度的理论预测。 第一部分是关于振荡两相Couette流的稳定性的新发现。 结果表明，在长波区，背景态的周期性调制可以完全稳定界面模。 这些结果将通过Floquet理论和控制系统的数值积分以及适当的分析扩展到所有波长。 一个平行的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核-环形流。 在二维和三维的非线性演化方程将推导和数值求解，以模拟圆柱形几何形状的双流体流动的非线性稳定性。 在许多技术和自然过程中，双流体流动的不稳定性是重要的，需要理解。 例子包括，除其他外，润滑管道运输粘性原油，挤压工艺，提高石油回收率，涂层工艺，定向凝固的熔体生长晶体技术，和生产照相胶片。 生物学应用包括新生儿肺血管的塌陷，由于界面不稳定导致管壁流体覆盖层破裂。 还有许多其他不断发展的技术，包括地基技术和微重力环境技术，这些技术需要对界面不稳定性和流变学有基本的了解。