Phase diagrams of nonionic foam films: construction by means of disjoining pressure versus thickness curves

The thickness h of foam films can be measured as a function of the disjoining pressure Pi using a thin film pressure balance. Experimental Pi-h curves of foam films stabilized with nonionic surfactants measured at various concentrations resemble the p-V-m isotherms of real gases measured at various temperatures (p is the pressure and V-m is the molar volume of the gas). This observation led us to adopt the van der Waals approach for describing real gases to thin foam films, where the thickness h takes the role of V-m and the disjoining pressure Pi replaces the ordinary pressure P. Our analysis results in a phase diagram for a thin foam film with spinodal, binodal as well as a critical point. The thicker common black film corresponds to the gas phase and the compact Newton black film for which the two surfaces are in direct contact corresponds to the dense liquid. We show that the tuning parameter for the phase behavior of the film is the surface charge density, which means that Pi-h curves should not be referred to as isotherms. In addition to the equilibrium properties the driving force for the phase transition from a common black film to a Newton black film or vice versa is calculated. We discuss how this transition can be controlled experimentally. (C) 2004 Elsevier Inc. All rights reserved.