Viscosity models for multiple emulsions

The viscous behavior of multiple emulsions is investigated. Expressions are derived for the viscosity of dilute and concentrated multiple emulsions where the multiple emulsion droplet itself contains many internal droplets. Such systems are often referred to as Type-B and Type-C multiple emulsions in the literature (in Type-B systems, the multiple emulsion droplet contains several small internal droplets; in Type-C systems, the multiple emulsion droplet contains a large number of small internal droplets; in Type-A systems (not considered here), there is present only one internal droplet, that is, these systems consist of “core–shell” droplets). According to the proposed viscosity models, the relative viscosity of multiple emulsions of Types B and C depends on four variables: volume fraction of internal droplets within a multiple emulsion droplet (φPE), volume fraction of total dispersed phase in the whole multiple emulsion (φME), ratio of primary-emulsion matrix viscosity to multiple-emulsion matrix viscosity (K21), and ratio of internal droplet viscosity to primary-emulsion matrix viscosity (K32). With the increase in any of these variables (φPE, φME, K21, or K32), the viscosity of the multiple emulsion generally increases. The predictions of the proposed models are compared with three sets of experimental data on the viscosity of multiple emulsions.