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Electrokinetic spectra of dilute surfactant-stabilized nano-emulsions

Published online by Cambridge University Press:  09 September 2020

Reghan J. Hill Open the ORCID record for Reghan J. Hill [Opens in a new window]
Reghan J. Hill*
Affiliation:
Department of Chemical Engineering, McGill University, 3610 University Street, MontrealH3A 0C5, Canada
*
†Email address for correspondence: [email protected]
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Abstract

An electrokinetic model for a surfactant-stabilized nano-drop under oscillatory forcing is solved. This generalizes a model for which an analytical solution was recently proposed for large, highly charged drops. Calculations of the dynamic electrophoretic mobility and the accompanying electrostatic polarization for a single drop provide a theoretical foundation for interpreting electrokinetic sonic amplitude and complex-conductivity spectra for dilute surfactant-stabilized oil-in-water emulsions and bubbly liquids. The model is distinguished from earlier models by accounting for the internal fluid and interfacial dynamics at finite frequencies (${\sim }10^3\text {--}10^7\ \textrm {Hz}$). This dynamics accounts for the electro-migration, diffusion and advection of surfactant ions on the interface, and exchange of these ions with the immediately adjacent electrolyte. Surface gradients induce Marangoni stresses, which couple to the electrical and hydrodynamic stresses, modulating the magnitude and phase of the drop velocity and electrostatic polarization induced by the electric field. Of particular interest, for sodium dodecyl sulphate stabilized oil-in-water drops, is how the high surface-charge density manifests in a breakdown of the Smoluchowski-slip approximation, even for drops with very thin diffuse layers. More generally, the model furnishes dynamic mobilities for drops with arbitrary size and charge, thus permitting appropriate averaging for polydisperse systems. Such calculations may help to resolve long-standing challenges and controversy with regards to the surface-charge density of nano-drops and their macro-scale counterparts, and may pave the way to quantitative interpretations of more complex dynamic interfacial rheology and exchange kinetics, e.g. for Pickering emulsions.

JFM classification

Complex Fluids: Colloids Complex Fluids: Emulsions Drops and Bubbles: Electrohydrodynamic effects
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 902 , 10 November 2020 , A15
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

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