Capillary channels in a gravitational field∗

The liquid shape between two vertical parallel plates in a gravity field due to capillary forces is studied. When the physical system achieves its mechanical equilibrium, the capillary surface has mean curvature proportional to its height above a horizontal reference plane and it meets the vertical walls in a prescribed angle. We examine the shapes of these interfaces and their qualitative properties depending on the sign of the capillary constant. We focus to obtain estimates of the size of the meniscus, as for example, its height and volume.