Diffuse interface models for transport processes at fluidic interfaces

流体界面传输过程的扩散界面模型

• 批准号: 166899348
• 负责人: Professor Dr. Harald Garcke
• 金额: --
• 依托单位: Lehrstuhl für Mathematik
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 财政年份: 2010
• 资助国家: 德国
• 起止时间: 2009-12-31 至 2016-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/166899348?language=en
• 关键词: Diffuse; interface; models; transport; processes

Topological transitions like droplet coalescence or droplet break-up are fundamental features of two-phase flows. In recent years, diffuse interface models turned out to be a promising approach to describe such phenomena. Species transport across fluidic interfaces and the effects exerted by soluble and insoluble surfactants are additional issues of still increasing technological importance. For those phenomena, novel thermodynamically consistent diffuse interface models shall be developed taking in particular general densities into account. Based on rigorous mathematical analysis, existence and qualitative behaviour of solutions will be investigated, this way enhancing the understanding of the fundamental model properties. Starting from energy and entropy inequalities, stable and convergent numerical schemes shall be formulated and implemented in two and three spatial dimensions. By numerical simulations, the models shall be validated and further improved.

液滴合并或液滴破碎等拓扑转变是两相流的基本特征。近年来，扩散界面模型被证明是描述此类现象的一种有前途的方法。物质跨流体界面的传输以及可溶性和不溶性表面活性剂所产生的影响是技术重要性仍在不断增加的其他问题。对于这些现象，应开发新的热力学一致的扩散界面模型，特别考虑一般密度。基于严格的数学分析，将研究解的存在性和定性行为，从而增强对基本模型属性的理解。从能量和熵不等式出发，在两个和三个空间维度上制定和实施稳定且收敛的数值格式。通过数值模拟，对模型进行验证并进一步完善。