A microchannel with topographical texture on one or more of its walls is often employed to achieve objectives such as mixing, pumping and bio-molecular detection in microfluidics. Flow through a microchannel with sinusoidal ridges on one of its walls, when the ridges are oriented in the direction of flow, is studied. The classical infinitely-slow-variation or lubrication analysis is extended through a systematic scaling and perturbation procedure for applicability to moderately slow variations. Finite element simulations are used to assess the relative strengths and weaknesses of moderately and infinitely slow-variation theories as well as a small-amplitude theory from the literature based on the domain perturbation technique. Depending on the wavelength of patterning, the hydraulic permeability can either decrease or increase with pattern amplitude with a transitional behavior from an initial decrease to subsequent increase is observed at certain wavelengths.

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