Stability, Evolution, and Rupture of Foams

There is a factor that opposes the thinning of the foam film. It is called the disjoining pressure and denoted by II(/i), where h is the film thickness. The disjoining pressure manifests itself for h 10 7 m. Usually, three components are distinguished in the disjoining pressure [116]  

The molecular component of the disjoining pressure, IIm(/i), is negative (repulsive). It is caused by the London-van der Waals dispersion forces. The ion-electrostatic component, IIe(/i), is positive (attractive). It arises from overlapping of double layers at the surface of charge-dipole interaction. At last, the structural component, IIs(/i), is also positive (attractive). It arises from the short-range elastic interaction of closed adsorption layers. 

The disjoining pressure II(/i), defined by Eq. (7.4.13) as the sum of the three components, is a nonmonotone function of the film thickness h for h 10-6 m. In this range of h, there is one or two intervals (depending on the type and concentration of the surfactant and electrolyte in the dispersive liquid) where 

This inequality is the most severe condition of the hydrodynamic stability of the liquid film [241]. Therefore, an instability and rupture of the film are considered to occur when the film thickness attains a critical value /icr, as the liquid flows out of the film. The critical thickness is determined by the condition 

Mechanism of rupture. Black films. The mechanism of hydrodynamic instability of thin foam films was analyzed in [278, 279, 411], The stability of ultrathin films is governed by a competition between capillary forces and the molecular component of the disjoining pressure. An instability can arise when dU/dh 0 and the capillary pressure is not too large. This is possible if 

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