  We present theoretical and numerical results that demonstrate the sensitivity
of the shape of a static meniscus in a rectangular channel to localised
geometric perturbations in the form of narrow ridges and grooves imposed on the
channel walls. The Young--Laplace equation is solved for a gas/liquid interface
with fixed contact angle using computations, analytical arguments and
semi-analytical solutions of a linearised model for small-amplitude
perturbations. We find that the local deformation of the meniscus's contact
line near a ridge or groove is strongly dependent on the shape of the
perturbation. In particular, small-amplitude perturbations that change the
channel volume induce a change in the pressure difference across the meniscus,
resulting in long-range curvature of its contact line. We derive an explicit
expression for this induced pressure difference directly in terms of the
boundary data. We show how contact lines can be engineered to assume prescribed
patterns using suitable combinations of ridges and grooves.

Fluid Dynamics