Analysis of capillary drainage from a flat solid strip

A long and narrow solid strip coated with a thin liquid layer is used as a model of a generic fluid mass probe in a spacecraft propellant tank just after a small thruster firing. The drainage dynamics of the initial coating layer into the settled bulk fluid affects the interpretation of probe measurements as the sensors' signal depends strongly on whether a sensor is in contact with vapor or with liquid. We analyze the drainage under various conditions of zero-gravity (i.e., capillary drainage) and with gravity aligned with the strip length, corresponding to the thruster acceleration. Long-time analytical solutions are found for zero and non-zero gravity. In the case with gravity, an approximate solution is found using matched asymptotics. Estimates show that a thrust of 10⁻³g₀ significantly reduces drainage times.