Simple Emulsions Stabilized by Surfactants

In the pioneering work of Demini6re et al. [39], the emulsion is modeled as a stack of monodisperse cells with characteristic size D. The total number of drops per unit volume, n, is related to the volume fraction cf) of the dispersed phase through the following relationship  

Because coalescence is a completely random process, the total number of coalescence events per unit time is assumed to be proportional to the total surface area A of the droplets  

co is defined as a coalescence frequency per unit surface area of the droplets. Considering Eqs. (5.5) and (5.6) and assuming that is constant (independent of T ), it can be concluded that the mean size in the emulsion increases with time according the following law  

The first kinetics measurements about coalescence were reported by Kabalnov and Weers in water-in-oil emulsions [40]. These authors measured the characteristic time at which the layer of free water formed at the bottom of the emulsions corresponded approximately to half of the volume of the dispersed phase. This time was assumed to be equal to t. By measuring r at different temperatures, the activation energy was deduced from an Arrhenius plot. Kabalnov and Weers were able to obtain the activation energy for a water-in-octane emulsion at / 50%, stabilized by the nonionic surfactant C12E5 (pentaethylene glycol mono n-dodecyl ether), above the phase inversion temperature (PIT), and found a value of 47 kgTr, Tr being the room temperature. 

Ifralan is a commercial nonionic surfactant essentially composed of a mixture of polyethylene glycols C12E5 and C10E5. In Eq. (5.12), a = 2 was adopted for Ifralan surfactant and a = 3 was adopted for SDS. (From [42].) 

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