The symmetric draining of capillary liquids from containers with interior corners

Abstract

A new lubrication model solution is found for the late-stage draining of a wetting capillary liquid from a linear interior corner. The solution exploits the symmetry of volumetric sink conditions at opposing ends of such a ‘double-drained’ interior corner flow with applications ranging from liquid recovery in microfluidic devices on Earth to liquid fuel scavenging in large fuel tanks aboard spacecraft. At long times $t$, the nominal liquid depth is $h\sim t^{-1}$, the liquid volume is $V\sim t^{-2}$ and the maximum volumetric liquid removal rate is $Q\sim t^{-3}$. The constraints under which the solution is valid are provided. To qualitatively assess the value of the solution, representative experiments are conducted at larger length scales aboard the International Space Station and at microfluidic length scales in a terrestrial laboratory. Both sets of experiments confirm the predicted power-law dependences. We show that the separation of variables solution offers a method to predict maximum drain rates from related geometries where a single drain location provides the required symmetry of the problem.