CAPILLARY-FLOW IN AN INTERIOR CORNER

The design of fluids management processes in the low-gravity environme nt of space requires an accurate description of capillarity-controlled flow in containers. Here we consider the spontaneous redistribution o f fluid along an interior corner of a container due to capillary force s. The analytical portion of the work presents an asymptotic formulati on in the limit of a slender fluid column, slight surface curvature al ong the flow direction z, small inertia, and low gravity. The scaling introduced explicitly accounts for much of the variation of how resist ance due to geometry and so the effects of corner geometry can be dist inguished from those of surface curvature. For the special cases of a constant height boundary condition and a constant flow condition, the similarity solutions yield that the length of the fluid column increas es as t(1/2) and t(3/5), respectively. In the experimental portion of the work, measurements from a 2.2 s drop tower are reported. An extens ive data set, collected over a previously unexplored range of flow par ameters, includes estimates of repeatability and accuracy, the role of inertia and column slenderness, and the effects of corner angle, cont ainer geometry, and fluid properties. At short times, the fluid is gov erned by inertia (t less than or similar to t(Lc)) Afterwards, an inte rmediate regime (t(Lc) less than or similar to t less than or similar to t(H)) can be shown to be modelled by a constant-flow-like similarit y solution. For t greater than or equal to t(H) it is found that there exists a location z(H) at which the interface height remains constant at a value h(z(H), t) = H which can be shown to be well predicted. Co mprehensive comparison is made between the analysis and measurements u sing the constant height boundary condition. As time increases, it is found that the constant height similarity solution describes the how o ver a lengthening interval which extends from the origin to the invari ant tip solution. For t much greater than t(H), the constant height so lution describes the entire flow domain. A formulation applicable thro ughout the container (not just in corners) is presented in the limit o f long times.