Novel shear modulus equations for concentrated emulsions of two immiscible elastic liquids with interfacial tension

Abstract

Starting from the shear modulus equation for a dilute emulsion system of two immiscible liquids with interfacial tension, four new equations have been developed for the shear modulus of concentrated emulsions using a differential scheme. The continuous phase and the dispersed droplets are treated as elastic liquids in the derivation. Out of the four models developed in the paper, two models predict the relative shear modulus (ratio of emulsion modulus to continuous phase modulus) to be a function of three variables: elastocapillary number, modulus ratio (dispersed phase modulus to continuous phase modulus) and volume fraction of dispersed phase. The remaining two models include an additional parameter, i.e. the maximum packing volume fraction of droplets. The proposed models are evaluated using three sets of experimental data on high frequency shear modulus of concentrated polymer-thickened oil-in-water emulsions.