Quantitative description of foam drainage: transitions with surface mobility.

We have performed forced drainage experiments on aqueous foams of bubble diameters D varying from 0.18 to 8 mm, and made with different surfactant and protein solutions (providing different surface viscoelastic properties). Changing bubble size or surface properties allows to evolve between two drainage regimes, the respective dimensionless permeabilities also varying with these parameters. We show that the bubble size and surface properties can be incorporated into a single surface mobility parameter that controls the transition between the two drainage regimes. The permeability measurements indicate how do the hydrodynamic resistances of the foam channels and nodes depend on surface mobility. Taking advantage of the large range of experimental conditions, leading to a variation of the mobility parameter over more than 3 decades, a simple and consistent description of both the drainage regimes and the transition in between them is obtained. For the smallest bubbles (D < 0.5 mm) anomalous behaviors are observed and discussed.