The investigation of a standing wave due to gas blowing upwards over a liquid film; its relation to flooding in wetted-wall columns

Abstract

A theory is given to predict the shape and amplitude of a standing wave formed on a liquid film running down a vertical surface, and due to an upward flow of gas over the liquid surface. The wave is maintained in position by the pressure gradients induced within the gas stream by acceleration over the windward part of the wave; over the leeward part of the wave, the gas pressure is roughly constant due to breakaway of the gas flow.The wave amplitude is found to be very sensitive to gas velocity so that the theory predicts a critical gas velocity beyond which the wave amplitude becomes very large; this critical velocity is confirmed by experiment, and the experiments confirm the predicted wave shape. The critical gas velocity also agrees reasonably well with published values of the flooding velocity in empty wetted-wall tubes; this velocity is defined as the point at which countercurrent flow of gas and liquid becomes unstable. The phenomenon of flooding, which has puzzled chemical engineers for many years, may thus be due to wave formation on the liquid film.From the theory are derived three dimensionless groups, namely, Weber number $We \equiv \rho_g U_c^2t_0|T$, liquid-film Reynolds number $Re \equiv 4\rho_l Q|\mu, and Z \equiv T(\rho_l|\mu g)^{1/3}|\mu$. Here Uc is the critical gas velocity, Q is the liquid volume flow rate per unit wetted perimeter, ρg and ρl are the gas and liquid densities, μ is the liquid viscosity and T is its surface tension; $t_0 = (3\mu Q|\rho_lg)^{1/3}$ is the liquid film thickness in the absence of gas flow. We, Re and Z are uniquely related at the flooding point, and a diagram is presented to show this relation. This diagram will enable designers to predict flooding in wetted-wall tubes, though more experimental verification is required.