On the Two-Phase Navier–Stokes Equations with Boussinesq–Scriven Surface Fluid
On the Two-Phase Navier–Stokes Equations with Boussinesq–Scriven Surface Fluid
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关于 Boussinesq-Scriven 表面流体的两相 Navier-Stokes 方程
DOI：
10.1007/s00021-008-0278-x
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发表时间：
2010
影响因子：
1.3
通讯作者：
J. Prüss
中科院分区：
文献类型：
--
作者：
D. Bothe;J. Prüss
本文分析了界面为Boussinesq-Scriven地面流体的两相流动的基本数学性质。这种两相流通用尖界面模型的扩展形式既包括表面张力，也包括表面粘度。对于这个具有自由界面的偏微分方程组，证明了能量是严格的拉普诺夫泛函，其中无边界接触的模型的平衡点由零速度和分散相的球体组成。形式上推导了问题的线性化，表明平衡点是线性稳定的，但非零速度可能导致线性不适定的问题。在没有表面粘度的情况下，不会出现这种现象。本文旨在对具有表面粘性的两相流进行严格的数学研究。
Abstract.Two-phase flows with interface modeled as a Boussinesq–Scriven surface fluid are analysed concerning their fundamental mathematical properties. This extended form of the common sharp-interface model for two-phase flows includes both surface tension and surface viscosity. For this system of partial differential equations with free interface it is shown that the energy serves as a strict Ljapunov functional, where the equilibria of the model without boundary contact consist of zero velocity and spheres for the dispersed phase. The linearizations of the problem are derived formally, showing that equilibria are linearly stable, but nonzero velocities may lead to problems which linearly are not well-posed. This phenomenon does not occur in absence of surface viscosity. The present paper aims at initiating a rigorous mathematical study of two-phase flows with surface viscosity.