Meniscus draw-up and draining

Abstract

When a solid plate is removed from a pool of fluid, a film of fluid is attached to the plate. There are two possible outcomes. The edge of the fluid may be raised through a finite distance, with the edge slipping on the plate. Alternatively, a continuous film of a certain thickness may be drawn up. For plates which have a small slope, it is shown that the first alternative holds when the speed of withdrawal is sufficiently small, and that, when a critical speed is exceeded, the height of the edge above the fluid level in the pool increases with time. A related problem concerns the shape of a receding meniscus in a channel. If the static contact angle is small, lubrication theory can be applied to the film of fluid adjacent to the wall of the channel, and the results of this part of the solution can be matched to the central part of the meniscus, which is controlled by capillarity and gravity, but for which lubrication theory does not apply. As in the draw-up problem, for small speeds the shape of the meniscus is time-independent, but above a critical speed, a tail of fluid of increasing length remains in the tube.