Permeability and effective slip in confined flows transverse to wall slippage patterns

The pressure-driven Stokes flow through a plane channel with arbitrary wall separation having a continuous pattern of sinusoidally varying slippage of arbitrary wavelength and amplitude on one/both walls is modelled semi-analytically. The patterning direction is transverse to the flow. In the special situations of thin and thick channels, respectively, the predictions of the model are found to be consistent with lubrication theory and results from the literature pertaining to free shear flow. For the same pattern-averaged slip length, the hydraulic permeability relative to a channel with no-slip walls increases as the pattern wave-number, amplitude, and channel size are decreased. Unlike discontinuous wall patterns of stick-slip zones studied elsewhere in the literature, the effective slip length of a sinusoidally patterned wall in a confined flow continues to scale with both channel size and the pattern-averaged slip length even in the limit of thin channel size to pattern wavelength ratio. As a conseque...