Drainage of the continuous phase liquid from a foam plays a pivotal role in determining its stability to collapse. A theoretical model for the drainage of the liquid during generation of a foam by bubbling and its subsequent collapse is presented. The model accounts for drainage in the films as well as in the plateau border channels. Drainage of the films is modeled using Reynold's equation for the flow between parallel flat circular disks under the influence of van der Waals, electrical double-layer, and plateau border suction forces with film rupture occurring when the film thickness attains a certain critical value. Since this model accounts for collapse at the foam/gas interface during generation, it is able to predict the steady state height attained by pneumatic foams. The model is also able to predict the establishment of a drainage equilibrium when the opposing forces of gravity and plateau border suction gradient balance each other. The effect of various parameters such as superficial gas velocity, electrolyte concentration, and bubble size on the steady state height and collapse half-life (time required for the foam to collapse to half the steady state height) is examined. It is shown that, for a given system, there is an upper limit on the superficial gas velocity beyond which a steady state height will not be attained. With increasing salt concentration, the stability of a foam first increases, attains a maximum, and then decreases. The steady state height and the collapse half-life decrease with a decrease in bubble size due to an increase in the capillary pressure. It is shown that, for a given system, there is an upper limit to the salt concentration and a lower limit to the bubble size beyond which no drainage equilibrium is possible and complete collapse will occur. It is also shown that plots of dimensionless foam height versus dimensionless time practically coincide for most of the period of collapse, a feature which is consistent with some experimental results.
