纵向非均匀多孔介质Marangoni对流不稳定性

理论研究了纵向非均匀多孔介质中流体表面张力驱动的对流不稳定性.充满液体的多孔介质层从下方加热,上方自由表面冷却,形成可引起多孔介质液层Marangoni-Benaxd对流流动的纵向温度梯度.采用线性化的Brinkman-Forchheimier方程作为控制方程组,对孔隙率分别为线性函数、正弦三角函数分布的非均匀多孔介质液层的Marangoni-Benaxd问题进行了线性稳定性分析.通过采用Chebyshev-Tau谱方法求解广义特征值问题,得到了系统临界Maxangoni数随无量纲波数变化的中性稳定性曲线,分析和比较了孔隙率的变化对液层对流稳定性和流场结构的影响,获得了纵向非均匀多孔介质液层不稳定性现象的新特征. 

Marangoni Instability in Vertically Inhomogeneous Porous Media

The surface-tension-driven instability in a vertically inhomogeneous porous media has been discussed in this paper. The system is heated from below. The upper surface is free without any deformation. Therefore, the vertical temperature gradient which can lead the Marangoni-Bernard convection is formed. The linear function and the trigonometric function are chose to describe the distribution of the porosity, and Brinkman-Forchheimier equations are for linear instability analysis. Chebyshev-tau approximation is used for general eigenvalue problem correspondingly, and the neutral instability curves, i.e. the critical Marangoni number against dimensionless wavenumber, are obtained. The influence of the distribution and its gradient of porosity on the instability of the system and streamline patterns are also analyzed. Finally, the new characteristics of the convection instability in vertically inhomogeneous porous media are discovered.