Well-posedness of a Two-phase Flow with Soluble Surfactant
Well-posedness of a Two-phase Flow with Soluble Surfactant
复制标题
可溶性表面活性剂两相流的适定性
DOI：
10.1007/3-7643-7385-7_3
复制
发表时间：
2005
期刊：
影响因子：
--
通讯作者：
G. Simonett
中科院分区：
文献类型：
--
作者：
D. Bothe;J. Prüss;G. Simonett
在大多数流体/液体界面处普遍存在的表面活性剂的存在对表面张力具有显著影响，因此对相边界处的应力平衡具有显著影响：毛细力的局部变化引起动量沿着界面的传输-所谓的马兰戈尼效应。这种系统的动力学的数学模型进行了研究的情况下，其中的表面活性剂是可溶于相邻的体相之一。这导致了质量和动量的两相平衡，并由界面和相关体相的物种方程补充。在该模型中，表面活性剂和相邻的体相流体的运动耦合的界面动量源项，代表Marangoni应力的装置。利用Lp-极大正则性，我们得到了该模型在一定初始构型下的适定性.证明是基于最近的L p -理论的两相流没有表面活性剂。
The presence of surfactants, ubiquitous at most fluid/liquid interfaces, has a pronounced effect on the surface tension, hence on the stress balance at the phase boundary: local variations of the capillary forces induce transport of momentum along the interface — so-called Marangoni effects. The mathematical model governing the dynamics of such systems is studied for the case in which the surfactant is soluble in one of the adjacent bulk phases. This leads to the two-phase balances of mass and momentum, complemented by a species equation for both the interface and the relevant bulk phase. Within the model, the motions of the surfactant and of the adjacent bulk fluids are coupled by means of an interfacial momentum source term that represents Marangoni stresses. Employing L p -maximal regularity we obtain well-posedness of this model for a certain initial configuration. The proof is based on recent L p -theory for two-phase flows without surfactant.