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.