Drainage of a mobile, symmetric, plane-parallel thin liquid film between two gas bubbles (foam film) is studied. An analytical solution for the rate of thinning of such a liquid film with an insoluble surfactant and having both film elasticity and surface viscosity is presented for the first time. Analysis is extended to the more general case of a soluble surfactant and compared with previous analyses. Surfactant material parameters affecting the rate of thinning are identified and grouped into a single dimensionless parameter, the surfactant number which describes the transition from a mobile to an immobile film. Significant deviation from the Reynolds velocity is found when this dimensionless parameter is small.
Since draining foam or emulsion films are generally of nonuniform thickness with a thick region or 'dimple' as the central part and separated from the Plateau border by a thinner 'barrier ring', an analytical solution is not possible. Hence a numerical model was developed. This model simulates the hydrodynamics associated with the drainage of an axisymmetric, dimpled, mobile foam film with an insoluble surfactant. This extends the work of Joye (1994) which was limited to immobile films. Results of the parametric study indicate that the rate of drainage of these films is dependent on surfactant properties viz. elasticity, surface dilatational viscosity, surface shear viscosity and surface diffusivity. These properties are grouped into a single dimensionless parameter which is the same as obtained by our analytical solution for a plane parallel film and which correlates with the rate of drainage of the foam film. This parameter describes the transition from a mobile film to an immobile film. The simulations indicate considerable motion of the interface for draining mobile foam films.
Foam texture in a porous medium is governed by the hydrodynamics of individual foam films (lamellae) flowing through pores of varying size. The stability of foam in a particular application depends upon the stability of a lamella in the porous medium, especially as the lamella expands in translating from a small pore (pore throat) to a larger pore (pore body). The numerical simulator developed above is extended to translating foam films to model the effect of various parameters on foam stability. The model predicts that the travelling lamella is unstable only for certain ranges of surfactant properties, porous media geometry and flow conditions, for e.g. gas flow rate and capillary pressure. Simulations show that mobile foam films stretch in going from a pore throat to a pore body and may thin down to the critical thickness and break, under certain conditions. In contrast immobile foam films are very stable due to an entrainment effect which occurs as the film expands in going from a pore throat to a pore body. The critical capillary pressure at which a moving lamella will break is determined as a function of film and porous medium properties. Further the concept of asymmetric drainage of foam films in porous media has been explored.