Effect of Surfactants on Drop Size Distributions in a Batch, Rotor-Stator Mixer

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Surfactants are often required to stabilize liquid-liquid dispersions produced by rotor-stator mixers. Since drops are deformed rapidly due to the high power input of these devices, the dynamic interfacial properties governed by the surfactant adsorption rate have a significant effect 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 in rotor-stator mixers.

The mean drop size and drop size distributions (DSD) of dilute dispersions produced by a batch rotor-stator mixer were studied. Silicone oils of various viscosities were dispersed in aqueous nonionic surfactant and aqueous methanol solutions. The aqueous methanol (clean) systems allowed comparison of surfactant-laden to surfactant-free systems with similar equilibrium interfacial tensions. The DSD were measured via a video microscopy/automated image analysis technique.

The equilibrium interfacial tension of clean and surfactant systems was measured, via a pendant drop technique, as a function of methanol and surfactant concentration, respectively. The dynamic surface tension of surfactant solutions was similarly measured. By fitting the data to the Langmuir adsorption isotherm and a long time approximation to the Ward Tordai equation, the adsorption parameters and surfactant diffusivities were obtained. This information, with an estimate of the drop deformation timescale, allowed estimation of the surface dilational modulus (Esd). This is a measure of the Marangoni stresses acting on the drop' surface due to interfacial tension gradients.

Trends observed in the mean drop size and DSD experimental results are explained in terms of the interfacial and rheological properties. Below the CMC, Esd peaks and the drop size increases with 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 was developed and modified to partially account for the effect of surfactants via an appropriately defined effective viscosity. Various model choices were systematically fit to the drop size data to select the most appropriate mechanistic correlation. Normalized experimental DSD data collapsed to a single log-normal volume distribution.