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 (j) 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(j) to account for experimental deviations. As mentioned by Princen and Kiss themselves, there is no satisfactory theoretical derivation of E(j). Indeed, in this paper we point out that the linear dependence in j of E(j) 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, some experimental data found in the literature show a more rapid increase of the storage modulus G 0 with j than predicted by Princen and Kiss equation, which tends to underestimate the values of G 0 . Finally, for the studied highly concentrated emulsions, the dispersed-phase volume fraction dependence of storage modulus is discussed.

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An approach based on percolation theory is associated to the rigorousness of the two-dimensional (2D) model of close-packed, monodisperse, cylindrical emulsions established by Princen, to obtain an equation to model the dispersed-phase volume fraction (ϕ) dependence of the storage modulus (G′) of highly concentrated emulsions. A first-order Taylor expansion of this general percolation model leads to an expression similar to the three-dimensional (3D) model proposed by Princen and Kiss for real polydisperse emulsions, with a more satisfactory derivation of the function E(ϕ). Finally, the robustness of this model is tested against different experimental data collected from the literature.

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The effects of the formulation and dispersed-phase weight fraction on rheological properties of highly concentrated water-in-oil emulsions are reported. Because the surfactant concentration is kept constant, emulsion characteristics may be represented on a formulation−composition bidimensional map. The formulation variable is the hydrophilic−lipophilic balance (HLB) number of the nonionic surfactant or surfactant mixture which ranges from 4.3 to 10. Highly concentrated water-in-dodecane emulsions are prepared using a semibatch process, with a dispersed-phase weight fraction ranging from 0.90 to 0.98. Two major effects are observed in relation to the formulation influence: First, elastic modulus (G′) remarkably decreases in the vicinity of optimum formulation whenever the affinity of the surfactant for the oil and water phases is exactly balanced (HLB = 10.5). Second, the elastic modulus value passes through a maximum, concomitant to a minimum drop size, at some distance of the so-called optimum formulation (HLB = 7.7). Hence, the use of a bidimensional formulation−composition map allows one to control and to modulate the final rheological properties of highly concentrated emulsions.