Confinement Effects on Effective Slip of Patterned Surfaces

Even Newtonian liquids are now known to slip past suitably engineered surfaces, such as those exhibiting super-hydrophobicity. Through friction reduction, such surfaces have potential to significantly reduce the required the motive power to drive confined flows. Studies of unconfined shear flows over such surfaces have revealed that patterned slipping surfaces are intrinsically inferior to the less realizable uniformly slipping surfaces in terms of the fluid slip velocity generated per unit pattern-averaged shear stress. In this study, a spectrally accurate semianalytical approach is used to assess the friction-reduction performance of several alternate ways of confining the flow over a patterned surface. Fluid permeates by pressure differential through a channel with plate-like walls. One of the plates forming the channel is kept fixed throughout the study to have a sinusoidal slip pattern, while the second plate can be non-slipping, uniformly slipping and patterned identically to the first surface. The gap between the plates, the degree of slip and pattern waveform parameters can be varied between limits not restricted by the model. Significantly different behaviours in permeability and the effective degree of slip of the first plate arise from the differences in patterning on the second plate.