Drainage and stability of 2D foams: Foam behaviour in vertical Hele-Shaw cells

Abstract

An integrated numerical model was developed to predict the spatial and temporal evolution of the bubble size distribution within foams. In order to validate the modelling, experiments in a vertical pseudo-2D Hele-Shaw cell were carried out since the bubble size distribution in this system can be readily measured. The model combines a population balance sub-model for predicting the bubble size with a liquid drainage sub-model. The liquid drainage model is a version of the standard foam drainage equation that has been modified to account for a pseudo-2D geometry. It has also been modified to account for the confined shape of the bubble and the size of the gap between the vessel walls, as well as the different Plateau border shapes and orientations found in this system. The population balance model is used to predict the change of bubble size as films fail and bubbles coalesce. The population balance and liquid drainage models are fully coupled, with the bubble size distribution influencing the drainage and the capillary pressure exerted by the Plateau borders influencing coalescence. In order to validate this integrated numerical model, the size of bubbles in a rising pseudo-2D foam was measured with image analysis. The numerical model reasonably predicted the evolution of the mean bubble size and was in strong agreement with the bubble size distribution over the depth of the pseudo-2D foam. The predictions are very close to the measured experimental data.