The Kabalnov-Wennerstrom Theory

Consider a flat-parallel O/W/0 emulsion film with a hole in it. By contrast with the previous section, the film is assumed to be covered with a surfactant monolayer, being in thermodynamic equilibrium with the micellar solution in the 

The second difference of this model from de Vries s theory is that both the hole radius and the film thickness are allowed to vary. At an arbitrary hole radius a, the film adjusts its thickness to a value at which the hole free energy has a minimum. At this stage, the disjoining pressure penalty which might be involved in this adjustment is disregarded. This may be a reasonable approximation, because, as will be shown later, the optimal thickness may be of the order of hundreds of A, a distance at which the interactions are weak. 

The free energy of the hole F can be represented as the sum of four terms. The first term is equal to the increment of the smface area for the planar part of the film multiplied by the interfacial tension of the planar monolayer  

The first two terms are identical to those of de Vries. The third bending energy term accounts for the extra (positive or negative) interfacial tension of the surface of revolution with respect to the planar state  

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The Kabalnov-Wennerstrom theory predicts that the sharpness of the transition from unstable to stable emulsions is controlled by the value of When the surfactants are compared in a homologous series, k increases and ao decreases with the surfactant chain length. Accordingly, the sharpness of transition from unstable to stable systems is expected to increase with the surfactant chain length. 

The stability of emulsions containing nonionic surfactants is minimum at the HLB temperature where the interfacial tension reaches a minimum. The coalescence is enhanced at low interfacial tensions because deformation of the droplets can occur more easily. Thermal fluctuations on the surfactant monolayers may increase, producing a hole in the thin film that separates the drops. This hole may heal and the droplets will not coalesce, or it may propagate in the film, producing its final rupture, as described by the Kabalnov-Wennerstrom theory [67,74]. A linear dependence in the Arrhenius plot [logarithm of the macroemulsion lifetime, ln(T,/2) as a function of the inverse of temperature] is predicted. The activation energy of the film rupture can be calculated from the slope of such a plot [67,74]. 

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