Effect of surfactants and interfacial rheology on equilibrium drop size in turbulent liquid-liquid dispersions

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Surfactants are often required to stabilize liquid-liquid dispersions produced by high shear mixers. Due to the high power input, drops are deformed rapidly in the dispersion zone so the dynamic interfacial properties governed by the surfactant adsorption rate can have a significant impact on the resulting drop size. The objective of this work is to develop a fundamental link between surfactant adsorption dynamics, interfacial properties, and turbulent emulsification processes. To ensure constant bulk surfactant concentration during dispersion, equilibrium drop size for dilute dispersions produced by a batch rotor-stator mixer were studied. Silicone oils of various viscosity were dispersed in aqueous nonionic surfactant solutions. Drop size distributions (DSD) were measured via a video microscopy/automated image analysis technique. Equilibrium interfacial tension was measured via a pendant drop technique, as a function of surfactant concentration. The dynamic surface tension was similarly measured. The data were fit to the Langmuir adsorption isotherm and the long-times approximation to the Ward – Tordai equation and the adsorption parameters and surfactant diffusivities so obtained were employed, with an estimate of the drop deformation timescale, to estimate the surface dilational modulus (Esd) or Marangoni stress acting on the drop’ surface due to interfacial tension gradients. Trends observed in the measured equilibrium mean drop size and DSD are explained in terms of the interfacial and rheological properties. Below the CMC, Esd peaks and the drop size increases with bulk surfactant concentration, despite a decrease in equilibrium interfacial tension. Above the CMC, Marangoni stresses are small but the presence of the surfactant still modifies the rheology of the interface, increasing the effective viscosity of the drops. A comprehensive set of mechanistic models for drop size in turbulent flows, based on Kolmogorov-Hinze theory, was developed and modified to partially account for the effect of surfactants via an appropriately defined effective viscosity. The approach allows integration of surfactant phenomena into widely accepted correlations for drop size in surfactant free systems.