Stability of Equilibria for Two-Phase Flows with Soluble Surfactant
Stability of Equilibria for Two-Phase Flows with Soluble Surfactant
复制标题
可溶性表面活性剂两相流平衡稳定性
DOI：
10.1093/qjmam/hbq003
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发表时间：
2010
影响因子：
0.9
通讯作者：
J. Prüss
中科院分区：
文献类型：
--
作者：
D. Bothe;J. Prüss
表面活性剂的存在，普遍存在于大多数流体-液体界面，对表面张力有显着的影响，因此在相边界的应力平衡：毛细力的局部变化引起的动量传输沿着界面-所谓的马兰戈尼效应。作者在最近的一篇论文中讨论了表面活性剂可溶于相邻体相之一的情况下控制此类系统动力学的数学模型。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。在本文中，我们开发了一个严格的李雅普诺夫泛函的问题，并确定和研究系统的平衡。我们表明，他们是线性稳定的，这将使我们能够证明，他们也是稳定的非线性问题。
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 for the case in which the surfactant is soluble in one of the adjacent bulk phases has been discussed in a recent paper of the authors. 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. In this paper, we develop a strict Lyapunov functional for the problem and identify and study the equilibria of the system. We show that they are linearly stable, which will allow us to prove that they are also stable for the nonlinear problem.
具有表面张力的两相纳维斯托克斯方程解的定性行为
影响因子：
1.4
作者：
M. Köhne;J. Prüss;M. Wilke
通讯作者：
M. Wilke