Analysis of the Princen and Kiss Equation To Model the Storage Modulus of Highly Concentrated Emulsions

The universality of the model proposed by Princen and Kiss is analyzed in the case of highly concentrated water-in-oil emulsions containing dispersed-phase volume fractions (phi) ranging from 0.89 to 0.97. Although Princen and Kiss equation has been rigorously established for a two-dimensional system and involves no adjustable parameter, the model for a tridimensional system, which is an extrapolation of the 2D model, requires the introduction of a phenomenological linear function E(phi) to account for experimental deviations. As mentioned by Princen and Kiss themselves, there is no satisfactory theoretical derivation of E(phi). Indeed, in this paper we point out that the linear dependence in phi of E(phi) is a consequence of the particular set of experimental data exploited by Princen and Kiss. Another choice of experimental data could have led to propose other mathematical functions since at very high volume fraction, sortie experimental data found in the literature show a more rapid increase of the storage modulus G' with phi than predicted by Princen land Kiss equation, which tends to underestimate the values of G'. Finally, for the studied highly concentrated emulsions, the dispersed-phase volume fraction dependence of storage modulus is discussed.