Effective slip for flow through a channel bounded by lubricant-impregnated grooved surfaces

This study aims to investigate effective slip arising from pressure-driven flow through a slit channel bounded by lubricant-impregnated grooved surfaces. The problem for flow over longitudinal grooves is solved analytically using the methods of domain decomposition and eigenfunction expansion, while that for flow over transverse grooves is solved numerically using the front tracking method. It is found that the effective slip length and the lubricant flow rate can depend strongly on the geometry of the microstructure, the direction of flow, and the lubricant viscosity. In particular, the effective slip can be effectively enhanced by increasing the thickness of a lubricating film atop the ribs. Under the same conditions, a flow that is parallel to the lubricant-impregnated grooves will have a larger effective slip, but also a larger lubricant flow rate, when compared with the case of flow normal to the grooves. It is also shown that, in the case of transverse grooves, because of the downward displacement of the interface between the working/lubricating fluids, the effective slip length and lubricant flow rate may vary non-monotonically with the groove depth.