Influence of the Dispersed Phase Distribution on the Electrical Conductivity of Liquid O/W Model and Dairy Emulsions

Abstract

The influence of the dispersed phase volume fraction (0.01 ⩽ φ ⩽ 0.4) and emulsification parameters (8 ⩽ P ⩽ 76 MPa and 35 ⩽ T ⩽ 100°C) on the relative electrical conductivity (σs/σ2s) of dairy model emulsions, reconstituted milk and creams, and commercial chocolate milks was studied. This study was based both on the use of statistically analyzed experimental designs and classical conductivity models of dispersed systems (Rayleigh-Wiener, Bruggeman, and Böttcher-Landauer). Furthermore, a simple approximation, based on Eveson's work on the relative viscosity of dispersed systems and derived from the Rayleigh-Wiener equation, was also proposed. This equation describes the electrical conductivity of dispersed systems composed of n classes of dispersed droplets, σsσ2s = Πi=1n(n - φ(i - 1))(σr1s + 2) + 2φ(σr1s - 1)(n - φ(i - 1))(sigma;r1s + 2) - φ(σr1s - 1) , with σr1s = σ1s/σ2s, and where σs, σ1s, and σ2s are, respectively, the conductivities of the whole dispersion, the dispersed phase, and the continuous medium. This equation, which is applicable to all systems composed of n different size classes of dispersed particles, represents the link between the Rayleigh-Wiener equation, only valid for monodispersed systems, and that of Bruggeman, valid for infinitely polydispersed systems. The use of the experimental design indicated that only the dispersed phase volume fraction, which explained 94% of the total variance, had a statistically significant effect on the model emulsion σs/σ2s ratio. Emulsification factors were found to have no measurable effect on the conductivity. A comparison with theoretical equations revealed that if all experimental data (with the exception of chocolate milks) fell on lines corresponding to the above four models, for φ ⩽ 0.15, only the model of Bruggeman and the above equation for n = 3 or 4 allowed a satisfactory description of the conductive behavior of this type of emulsion for the whole domain of φ studied. Moreover, the number n = 3 or 4 of different fraction sizes is a theoretical number as it is clear that the fat globule size distribution of a dairy emulsion is both continuous and polydispersed.