Long-Wave Models for a Countercurrent Flow of Liquid Film and Turbulent Gas Flow

Abstract

The paper considers the countercurrent flow of a vertically falling liquid film and a turbulent gas. In the case of small Reynolds numbers and when certain conditions for the characteristics of such a flow are met, the problem is reduced to one model equation for the film thickness. For long-wave weakly nonlinear disturbances, various nonlinear integrodifferential equations are obtained from this equation for the deviation of film thickness from the undisturbed level. Their specific type depends on the values of the magnitude of one parameter. This parameter is the ratio of the friction force from the side of the gas acting on the unperturbed film flow to the force of gravity. It is shown that, in addition to the countercurrent flow, such models also appear in a number of other gas-film flows. Both their radical differences and some common features are discussed. Several universal solutions of these model equations are presented.