Gibbs film elasticity

In concentrated emulsions and foams the thin liquid films that separate the droplets or bubbles from each other are very important in determining the overall stability of the dispersion. In order to be able to withstand deformations without rupturing, a thin liquid film must be somewhat elastic. The surface chemical explanation for thin film elasticity comes from Marangoni and Gibbs (see Ref. [199]). When a surfactant-stabilized film undergoes sudden expansion, then immediately the expanded... 

For maximum mechanical stability, the interfacial film resulting from the adsorbed surfactants should be condensed, with strong lateral intermolecular forces, and should exhibit high film elasticity. The liquid film between two colliding droplets in an emulsion is similar to the liquid lamella between two adjacent air sacs in a foam (Chapter 7) and shows film elasticity for the same reasons (Gibbs and Marangoni effects). 

The effective film elasticity is especially important in emulsions in which the interfacial tension is small and can not ensure the stability of surfaces against the deformation due to random causes. The Gibbs effect is a thermodynamicfactorof colloid stability (this emphasizes only the nature of the effect, and one need not assume that this factor can ensure high stability of disperse systems). 

Film Elasticity The differential change in surface tension of a surface film with relative change in area. Also termed surface elasticity, dilata-tional elasticity, areal elasticity, compressional modulus, surface dilata-tional modulus, or modulus of surface elasticity. For fluid films, the surface tension of one surface is used. The Gibbs film (surface) elasticity is the equilibrium value. If the surface tension is dynamic (time-dependent) in character, then for nonequilibrium values, the term Marangoni film... 

Nordli et al. (146) later found larger relaxation time for the films with the higher-molecular-weight surface-active species derived from North Sea crude. For crude W/0 emulsions, Neumann and Paczynska-Lahme (120) con-ciured that the emulsions are stabilized by thick films with Gibbs elasticity, and the more the interfacial activities of... 

In the case where E is used to describe purely the elasticity, then E can be termed the film elasticity of compression modulus . In the general case where the surface behaviour has both an elastic and viscous component, then E can be termed the surface dilational modulus . Basically, E is the measure of the ability of a film to adjust its surface tension in an instant of stress and should be relatively large for the film to remain stable. By combining equation (2.2) with the Gibbs adsorption isotherm equation, it can be shown that E is proportional to (dy/dc), where c is the concentration of the surfactant in the thin film. 

A notable characteristic of stable films is their resistance to mechanical disturbance. Gibbs [178] considered the important property to be the elasticity of the film E ... 

The stabihty of a single foam film can be explained by the Gibbs elasticity E which results from the reduction ia equiUbrium surface concentration of adsorbed surfactant molecules when the film is extended (15). This produces an iacrease ia equiUbrium surface tension that acts as a restoring force. The Gibbs elasticity is given by equation 1 where O is surface tension and is surface area of the film. 

Surfactants form semiflexible elastic films at interfaces. In general, the Gibbs free energy of a surfactant film depends on its curvature. Here we are not talking about the indirect effect of the Laplace pressure but a real mechanical effect. In fact, the interfacial tension of most microemulsions is very small so that the Laplace pressure is low. Since the curvature plays such an important role, it is useful to introduce two parameters, the principal curvatures... 

It is also important that the emulsifier films have sufficient elasticity to enable recovery from local disturbances (see Gibbs-Marangoni effect page 274). 

The subscript G specifies elasticity determined from isothermal equilibrium measurements, such as for the spreading pressure-area method, which is a thermodynamic property and is termed the Gibbs surface elasticity, EG. EG occurs in very thin films where the number of molecules is so low that the surfactant cannot restore the equilibrium surface concentration after deformation. 

Surfactants also reduce the coalescence of emulsion droplets. The latter process occurs as a result of thinning and disruption of the liquid film between the droplets on their close approach. The latter causes surface fluctuations, which may increase in amplitude and the film may collapse at the thinnest part. This process is prevented by the presence of surfactants at the O/W interface, which reduce the fluctuations as a result of the Gibbs elasticity and/or interfacial viscosity. In addition, the strong repulsion between the surfactant layers (which could be electrostatic and/or steric) prevents close approach of the droplets, and this reduces any film fluctuations. In addition, surfactants may form multilayers at the O/W interface (lamellar liquid crystalline structures), and this prevents coalescence of the droplets. 

The elasticity depends on the rate of film expansion. Under quasistatic equilibrium conditions its values are very low and in such a case it is called Gibbs elasticity. When there is no equilibrium it is called Maiangoni elasticity. The largest value of the elasticity modulus, acquired when the adsorption layer behaves as insoluble one, is called Marangoni dilatation modulus Em). 

Bianko and Marmur [99] have developed a new technique for the measurement of Gibbs elasticity of foam films. In order to exclude the effect of the mass transfer of the surfactant, the stretching of an isolated soap bubble is used. The surface tension needed for the calculation of the elasticity modulus is determined by the pressure in the bubble and the radius of curvature. The modulus obtained are considerably lower than those derived by the technique of Prins et al. [95]. 

Another indirect method for the estimation of Gibbs elasticity modulus is based on the determination of the surface dilatation modulus E in experiments in which the surfaces of the surfactant solutions undergo small amplitude deformations of oscillatory nature [100-102], It is shown [100, see also Chapter 7] that the concentration dependence of a Gibbs elasticity modulus at constant film thickness should be nearly the same as the concentration dependence of (twice) the surface elastic modulus E when film thickness and frequency are related by... 

The contemporary level of knowledge in foam science enables the solution of many problems related to the kinetics of various processes in a foam (such as film thinning and rupture, foam drainage, diffusion, development of film deformation accounting for the Gibbs and dynamic elasticity, etc.) and to establish the equilibrium conditions of the individual foam elements (films and borders). Thus, it allows the qualitative, and sometime semi-quantitative, interpretation of foam stability. 

Two types of elasticity could be distinguished equilibrium (Gibbs elasticity) and dynamic (Marangoni elasticity). According to Gibbs the modulus of elasticity of the film is... 

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