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