Recirculation model for liquid flow in foam channels

Although extensively studied in the past, drainage of aqueous foams still offers major unaddressed issues. Among them, the behaviour of foam films during drainage has great significance as the thickness of the films is known to control the Ostwald ripening in foams, which in turn impacts liquid drainage. We propose a model relating the films' behavior to the liquid flow in foam channels. It is assumed that Marangoni-driven recirculation counterflows take place in the transitional region between the foam channel and the adjoining films, and the Gibbs elasticity is therefore introduced as a relevant parameter. The velocity of these counterflows is found to be proportional to the liquid velocity in the channel. The resulting channel permeability is determined and it is shown that Marangoni stresses do not contribute to rigidify the channel's surfaces, in strong contrast with the drainage of horizontal thin liquid films. New experimental data are provided and support the proposed model.