The mechanism of suppression or enhancement of three-dimensional surface waves in film flow down a vertical plane

Abstract

The energy budget in a liquid film flow down a vertical plane subject to three-dimensional disturbances is calculated. The equation relating the average time rate of change of disturbance kinetic energy to the rates of work done by the surface tension, the shear stress, the Reynolds stress, and the rate of mechanical energy dissipation is obtained. Each term in the equation is evaluated in various regions of parameter space to elucidate the physical mechanism of stabilizing an inherently unstable vertical film flow by use of plate oscillation. The Squire theorem, which states that two-dimensional disturbances are more dangerous than three-dimensional ones, is violated in certain parameter ranges. In these parameter ranges the Reynolds stress enhanced by plate oscillation may cause a falling liquid film, which is stable with respect to two-dimensional short waves, to become unstable with respect to three-dimensional disturbances.