Modeling of liquid-gas meniscus for textured surfaces: effects of curvature and local slip length

Surface texturing at the micro/nanolevel allows air to be trapped in sufficiently small cavities, thereby reducing the flow resistance over the surface in the laminar regime. The nature of the liquid-gas meniscus plays an important role in defining the boundary condition and it depends on the flow conditions and geometrical properties of textures. In the present work, we employ the unsteady volume of fluid model to investigate the behavior of the liquid-gas meniscus for ridges arranged normal to the flow direction to substantiate the frictional resistance of flow in a microchannel. It is found that the assumption of 'zero shear stress' at the liquid-gas interface grossly overpredicts the effective slip length with meniscus curvature and local partial slip length playing the dominant role. Numerical simulations performed in the laminar regime (20 < Re < 120) over single layered ridges normal to the flow direction revealed the effect of texture geometry on the reduction in pressure drop. In single layered structures, lotus-like geometries exhibited a greater reduction in drag (more than 30%) when compared to all other texture geometries. It is recognized that the flow experiences expansion and contraction cycles as it flows over the transverse ridges increasing the frictional resistance. Our findings will help to modify the boundary condition at the liquid-gas meniscus for accurate modeling in the laminar regime and to optimize the texture geometry to improve drag reduction.