  This paper presents new analytical formulae for flow in a channel with one or
both walls patterned with a longitudinal array of ridges and arbitrarily
protruding menisci. Derived from a matched asymptotic expansion, they extend
results by Crowdy (J. Fluid Mech., vol. 791, 2016, R7) for shear flow, and thus
make no restriction on the protrusion into or out of the liquid. The slip
length formula is compared against full numerical solutions and, despite the
assumption of small ridge period in its derivation, is found to have a very
large range of validity; relative errors are small even for periods large
enough for the protruding menisci to degrade the flow and touch the opposing
wall.
