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Lubrication theory is broadly applicable to the flow characterization of thinfluid films and the motion of particles near surfaces. We offer an extension tolubrication theory by starting with Stokes equations and consideringhigher-order terms in a systematic perturbation expansion to describe the fluidflow in a channel with features of a modest aspect ratio. Experimental resultsqualitatively confirm the higher-order analytical solutions while numericalresults are in very good agreement with the higher-order analytical results. Weshow that the extended lubrication theory is a robust tool for an accurateestimate of pressure drop in channels with shape changes on the order of thechannel height, accounting for both smooth and sharp changes in geometry.

Extended Lubrication Theory: Improved Estimates of Flow in Channels with Variable Geometry