Microscale roughness on an otherwise smooth hydrophobic surface can significantly reduce the resistance to an external liquid flow. We study static drag reduction over a lubricant- infused surface by looking at an array of two-dimensional transverse grooves partially filled with a second immiscible fluid. Numerical simulations at separate length scales are used to probe the static drag reduction property and the dynamic wetting behavior. Nano-scale phase field simulations are used to extract the characteristic contact line velocities. Micron-scale two-phase simulations using the level set method are used to model the interface deformation and the flow in and above the cavities. We study the dependence of the effective slip by varying viscosity ratios, capillary numbers, the static contact angle and the filling rate of the cavity (meaning the amount of lubricant fluid). We observe an increase of the effective slip with the cavity filling and identify a potentially new failure mode.
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