Review of Spontaneous Capillary Driven Flow along Interior Corners

This paper briefly reviews the recent development in understanding the spontaneous capillary driven flow along interior corners from both static and dynamic point of views. Interior corners are a common geometric element for effective liquid transport in micro-scale in terrestrial condition or in large length scale in micro-gravity onboard spacecraft system. Spontaneous capillary driven flows take place along the interior corners when certain geometric conditions are satisfied and when capillary forces dominate body forces such as gravitational forces. From the static point of view, the spontaneous capillary driven flow discussed herein is related to the non-existence of equilibrium capillary surfaces in containers possessing the interior corners when certain boundary conditions undergo sudden changes such as gravity vanishing abruptly. The non-existence of the equilibrium surface in a cylindrical container of uniform cross section can be identified using Concus-Finn method. In a generic cylindrical container with an interior corner of 2α, the method can be applied to show that the equilibrium surface fails to exist in zero gravity when contact angle is less than π/2-α. In general the spontaneous capillary flow along the interior corners is in the regime of laminar flows. The dynamics of such flow has been analyzed successfully using scaling and perturbation method yielding closed form analytic solutions which are useful for design purpose. A typical result is that in the viscous regime the movement of the meniscus tip is proportional to t^1/2.