Research Projects

In the present proposal, theoretical and numerical investigations will be made to understand the impact of hydrophobic/superhydrophobic surfaces on the instability and transition behaviour of the pressure-driven parallel flow in a fluid-porous superimposed channel. The top surface of the channel is hydrophobic/superhydrophobic. Most of the existing studies are based on no-slip conditions, and the impact of slip conditions due to hydrophobic surfaces is limited to isotropic slip, which is also under linear theory only.  Therefore, in this proposal, a rigorous linear stability analysis will be made to understand the effect of isotropic and anisotropic slip conditions on such parallel flow in homogeneous porous-fluid systems. The linear analysis will be extended by developing a weakly nonlinear theory via Landau equations.  The analysis will be continued to highlight the impact of inhomogeneous and anisotropic porous layer. The nonlinear transition theory for purely fluid channel can be obtained as a particular case of the fluid-porous superimposed system. Finally, the role of slip condition due to hydrophobic surface on a relatively high permeable porous medium will be investigated.