Stability of liquid films on a porous vertical cylinder

The stability of liquid films flowing down a vertical porous cylinder is investigated in this paper. Fluids in the porous medium are assumed to be governed by Darcy's law. The Beaver-Joseph conditions on the liquid-porous surface are applied, and the influence of the porous medium reduces as a slip condition on the cylinder, which leads to the one-sided model. A Benney-type equation governing the interfacial shape is derived to study the nonlinear behavior of liquid films. Linear stability analysis shows that the film flow system on a porous vertical cylinder is more unstable than that on a solid impermeable vertical cylinder and that increasing the permeability of the porous medium enhances the destabilizing effect. Nonlinear studies examine our linear stability analysis. We find that, for Reynolds number Re = 0, as the permeability parameter increases, the rupture time of film decreases; for Re > 0, Rayleigh-Plateau instability is suppressed, and disturbances evolve to saturated traveling waves. By increasing the permeability parameter, the amplitude of traveling wave increases, and the wave speed increases too. Aside from that, the wave speed increases with increasing Re.