Capillary flow in interior corners: The infinite column

Abstract

Capillary flow of a sinusoidally perturbed liquid column in an interior corner of infinite extent is solved using lubrication theory. Due primarily to the length scales selected to nondimensionalize the momentum equation, an analytic time scale governing the settling of the perturbation is determined. The time scale, which is shown to be independent of a steady base state flow, proves useful in rapidly predicting transients for surface settling in certain liquid-bearing tanks of spacecraft employing interior corners for fluids management purposes. The asymptotic analysis is extended to address flows along interior corners whose faces are slightly nonplanar. The generalized formulation is presented for the case of a perfectly wetting fluid in a second-order polynomial corner. A leading-order analytic solution for small corner angles is provided. It is shown that a “convex corner” decreases the response time of the liquid and increases the capillary flow rate along the corner by increasing both the driving force and cross-sectional area of the flow. Gravity acting normal to the corner axis along the bisector of the corner angle is also considered and is found to accelerate, decelerate, or destabilize such flows depending on its sign and magnitude.