Effect of the substrate on the stability of super-hydrophobic and liquid infused surfaces in a shear driven flow*

Experimental studies have shown failure of super-hydrophobic surfaces (SHS) and liquid-infused surfaces (LIS) under turbulent flows, loosing their drag reducing properties. Shear driven drainage of the infused liquid is observed in LIS and pressure fluctuations inducing wetting of the substrate in SHS. Here it is investigated the stability of SHS and LIS in a shear driven flow configuration through numerical simulations where the substrate is composed of longitudinal square bars. The dynamics of the interface is solved using the level set method fully coupled to the Navier Stokes equations. The substrate is modeled using the immersed boundary method. The initial perturbation is taken from the linear stability analysis of two superposed fluids. It is analyzed the deformation of the interface in time as the perturbation grows. The preferential mode of interface deformation and instability mechanism will be discussed as function of Reynolds number, Weber number, and viscosity ratio. A simulation with two fluids without the substrate is performed as reference case to assess how the geometrical properties of the substrate stabilize the flow.