A Generalized View of Foam Drainage:  Experiment and Theory

A new experimental method is presented using fluorescein dye to determine the spatial and temporal variations of the liquid volume fraction in aqueous foams. This method is used for quantitative studies of liquid redistribution (drainage) in three types of experiments: forced, free, and pulsed drainage. Characteristic quantities, such as the drainage velocity, show power-law dependences on experimental parameters that are inconsistent with traditional foam drainage models based on Poiseuille-type flow in the liquid-carrying channels (Plateau borders) of the foam. To obtain a theoretical description, the foam drainage equation is generalized using an energy argument which accounts for viscous dissipation in both the channels and the nodes (or vertices, which are the junctions of four channels) of the liquid network. Good agreement with results for all three types of drainage experiments is found when using this new model in the limit where the dissipation is dominated by the nodes.