Viscosity of surfactant stabilized emulsions

A new scaling parameter for the viscosity of surfactant stabilized emulsions is proposed. We suggest that the attractive force between emulsion droplets is caused by the small surfactant micelles in the continuous phase of an emulsion. The new scaling parameter will be referred to as the depletion flow number, Fld=4πηsa2am/kTϕm, and is defined as the ratio between the viscous energy needed to separate the droplets and the depletion energy that opposes this separation. Here ηs, a, am, and ϕm are the solvent viscosity, dispersed phase droplet radius, micelle radius, and micelle volume fraction, respectively. Fld is of the order of unity at the onset of shear thinning and is capable of explaining all previously observed effects of drop size, solvent viscosity, and surfactant concentration. With master curves which are obtained by using Fld as the running parameter, a relatively simple empirical model is constructed which can reproduce the viscosity curves of many previously reported in the literature.