Surface Forces Theory Disjoining Pressure

Returning surfactant molecules drag back underlaying layers 

Surfactant corK ntiation gradient in surface removed 

Surface film repaired by surface transport mechanism 

In addition to the Laplace capillary pressure, three additional forces can operate at surfactant concentrations below the c.m.c. Electrostatic double layer repulsion van der Waals attraction (tivdw), and steric (short-range) forces (tCst)  

In the original definition of disjoining pressure, Deryaguin [11, 12] only considered the first two terms on the right-hand side of Eq. (8.9). At low electrolyte 

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The isotherm FI(h) can be obtained experimentally or calculated on the basis of the surface forces theory. When using Eq. (10D.2) for wetting films of water or aqueous solutions, it is necessary to take into account at least three components of the disjoining pressure, i.e. the dispersion, electrostatic. If, and structural, If, contributions. 

Formation and stability studies of black foam films can be summarised as follows 1) surface forces in black foam films direct measurement of disjoining pressure isotherm DLVO- and non-DLVO-forces 2) thin foam film/black foam film transition establishing the conditions for the stability of both types of black films and CBF/NBF transition 3) formation of black foam films in relation to the state of the adsorption layers at the solution/air interface 4) stability of bilayer films (NBF) theory and experimental data. 

The CBF/NBF transition has already been considered in Section 3.4.1 with respect to the experimental n(/i) isotherms of disjoining pressure obtained with the Thin Liquid Film-Pressure Balance Technique. Theoretical concepts and comparison with the DLVO- and contemporary theories describing surface forces acting in this range of film thicknesses have also been discussed. 

The stability of suspensions containing solid particles are treated in the framework of the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory, which accounts for the electrostatic and van der Waals interactions between the particles (Verwey and Overbeek 1948, Derjaguin 1989). In the past decades it has been shown that other types of inter-particle forces may also play an important role in the stability of dispersions - hydrodynamic interactions, hydration and hydrophobic forces, steric and depletion forces, oscillatory structural forces, etc. The hydrodynamic and molecular interactions between surfaces of drops and bubbles in emulsion and foam systems (compared to that of suspensions of solid particles) are more complex due to the particles fluidity and deformability. These two features and the possible thin film formation between the colliding particles have a great impact on the hydrodynamic interactions, the magnitude of the disjoining pressure and on the dynamic and thermodynamic stability of such systems (Ivanov and Dimitrov 1988, Danov et al. 2001, Kralchevsky et al. 2002). 

The situation is still more complex in the presence of surfactants. Recently, a self-consistent electrostatic theory has been presented to predict disjoining pressure isotherms of aqueous thin-liquid films, surface tension, and potentials of air bubbles immersed in electrolyte solutions with nonionic surfactants [53], The proposed model combines specific adsorption of hydroxide ions at the interface with image charge and dispersion forces on ions in the diffuse double layer. These two additional ion interaction free energies are incorporated into the Boltzmann equation, and a simple model for the specific adsorption of the hydroxide ions is used for achieving the description of the ion distribution. Then, by combining this distribution with the Poisson equation for the electrostatic potential, an MPB nonlinear differential equation appears. 

Based on the theory given in Sections 3.5 and 3.6, the right-hand term of Equation 16.2 equals the osmotic pressure k for the liquid between the surfaces. Thus, for two approaching surfaces, the force per unit area can be regarded as an osmotic pressure. This pressure is also referred to as the disjoining pressure. 

The derivative -dAa h)/dh = is the force per unit cross-sectional area, also known as Derjaguin s disjoining pressure [4,5], Within the context of this definition, both Ao(/t) and W(fi) are positive in the case of a repulsion and negative in the case of an attraction. Molecular attraction forces prevail at long distances, while repulsive forces prevail at very short distances (the so-called Born repulsion). The principal theory that describes the interactions in a thin film is the well-known Derjaguin-Landau-Verwey-Overbeek (DLVO) theory, which focuses on the analysis of the competitive contribution of molecular (dispersion) attractive forces and electrostatic repulsion to the interaction between surfaces separated by a liquid film. 

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