Quasi Steady Capillary Corner Flow

It is possible to drain slender containers filled with wetting liquids via capillary flows along the interior corners of the container. Usually the well established equations governing such flows demand numerical techniques. In the case of container draining unique boundary conditions resulting from local section geometry allow for a quasi-steady assumption and in turn permit analytical solutions. The quasi-steady assumption may also be employed for certain problems in which the corner flows cause passive capillary migration of the fluid within the container. The analytic solutions are useful because of the ease in which geometric effects may be observed. Container draining and capillary migration by means of corner flows are studied in a variety of container geometries. It is shown that careful selection of cross sectional shape can be used to maximize drain rates and minimize capillary migration times. Three-dimensional effects for these flows are investigated in tapering containers. Some simple micro-scale experiments are reported that provide confidence in the assumptions and application of the important boundary conditions that enable the solutions.