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The design of fluids management processes in the low-gravity environment of space requires an accurate description of capillarity-controlled flow in containers. Here we consider the spontaneous redistribution of fluid along an interior corner of a container due to capillary forces. The analytical portion of the work presents an asymptotic formulation in the limit of a slender fluid column, slight surface curvature along the flow direction z, small inertia, and low gravity. The scaling introduced explicitly accounts for much of the variation of flow resistance due to geometry and so the effects of corner geometry can be distinguished 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 increases as t1/2 and t3/5, respectively. In the experimental portion of the work, measurements from a 2.2 s drop tower are reported. An extensive data set, collected over a previously unexplored range of flow parameters, includes estimates of repeatability and accuracy, the role of inertia and column slenderness, and the effects of corner angle, container geometry, and fluid properties. At short times, the fluid is governed by inertia (t[lsim ]tLc). Afterwards, an intermediate regime (tLc[lsim ]t[lsim ] tH) can be shown to be modelled by a constant-flow-like similarity solution. For t[ges ]tH it is found that there exists a location zH at which the interface height remains constant at a value h(zH, t)=H which can be shown to be well predicted. Comprehensive comparison is made between the analysis and measurements using the constant height boundary condition. As time increases, it is found that the constant height similarity solution describes the flow over a lengthening interval which extends from the origin to the invariant tip solution. For t[Gt ]tH, the constant height solution describes the entire flow domain. A formulation applicable throughout the container (not just in corners) is presented in the limit of long times.