Linear stability analysis of liquid films flowing down a porous wall

The paper conducted a linear stability analysis on the Newtonian liquid films flowing down a porous wall, especially concerning about the case of moderate Reynolds number. It was considered that the flow at the porous wall satisfied the Beavers-Joseph slip boundary condition. And the momentum integral method was used to obtain the dispersion relation and the neutral stability condition. The results show that the permeability of porous wall promotes the instability of liquid film flow and accelerates the movement of liquid film surface fluctuation. With the increase of the Reynolds number, the maximum growth rate increases first and then decreases in the range of moderate Reynolds number. The extremum values and cutoff wave number of growth rate were related to the wall permeability. The mechanism of porous media permeability affecting the stability has been discussed by energy analysis. It is considered that the existence of porous wall slip velocity increases the average flow velocity and decreases the velocity gradient, which leads to the decrease of viscous dissipation and the reinforcement of flow instability.