含不溶性表面活性剂两相薄膜模型的建模与分析
Modeling and Analysis of a Two-Phase Thin Film Model with Insoluble Surfactant
摘要：
在本文中，我们考虑一个两相薄膜组成的两个不混溶的粘性流体的表面上赋予一层不溶性的表面活性剂的上层流体。两个膜的高度和表面活性剂浓度的控制方程推导出使用润滑近似。考虑重力但忽略毛细效应，所得到的发展方程系统是抛物型的，强耦合的，二阶的和退化的两个膜高度的方程。相反，考虑毛细力并忽略重力的影响，发展方程系统是抛物形的、退化的、对于膜高度为四阶的，与表面活性剂浓度的二阶传输方程强耦合。两个系统的局部适定性和渐近稳定性。
英文摘要：
In this paper we consider a two-phase thin film consisting of two immiscible viscous fluids endowed with a layer of insoluble surfactant on the surface of the upper fluid. The governing equations for the two film heights and the surfactant concentration are derived using a lubrication approximation. Taking gravitational forces into account but neglecting capillary effects, the resulting system of evolution equations is parabolic, strongly coupled, of second order and degenerated in the equations for the two film heights. Incorporating on the contrary capillary forces and neglecting the effects of gravitation, the system of evolution equations is parabolic, degenerated and of fourth order for the film heights, strongly coupled to a second order transport equation for the surfactant concentration. Local well-posedness and asymptotic stability are shown for both systems.
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