An exact solution of visco-capillary flow in an inclined channel

An exact solution of visco capillary flow in an inclined channel is presented. Assuming that the flow is steady and unidirectional the surface shape and the velocity profile are obtained as exact solutions of the Navier-Stokes equations valid for arbitrary Reynolds numbers. The contributions of the determining parameters of the problem to the surface shape and to the velocity profile are discussed. A structural change in the velocity profile, the 'velocity overshoot', is found for cases with meniscus elevation higher than the apex height of the flow. The theoretical findings are compared to experimental results.