The Mechanism of Flow Patterns and Rivulet Instability in Gravity-Driven Film Flow on a Porous Wall with Uniform Heating

Properties of porous mediums have significant impacts on the spreading pattern of falling-film along a vertical heated wall. In this paper, we investigate the combined effect of porosity and uniform heating on the flow instability of a falling liquid film. Based on the film thickness equation derived by the long wave theory, linear stability analysis and numerical simulations are given to verify the influences of various dimensionless parameters, and the physical mechanism for the flow instability is explained. With the uniform heating, it is shown that the increasing Marangoni number and Biot number both enhance the rivulet instability because the Marangoni force becomes larger with bigger values of the two numbers. For porous properties, the existence of Darcy number causes the contact line to move faster and results in a destabilizing effect, while a bigger Beavers-Joseph coefficient causes the contact line to move slower and plays a stabilizing role. Increment of porous thickness and the thermal conductivity ratio slightly enhances or impedes the flow instability, respectively, and neither of the two parameters influences the moving speed of the contact lines.