Unifying thermodynamics, electrokinetics and Marangoni effects for highly charged nano-emulsion droplets


Surfactants are compounds that lower the surface tension between two liquids, between a gas and a liquid, or between a liquid and a solid. They are composed of molecules that spontaneously assemble to help form very small drops and bubbles. As a result, surfactants have extraordinarily widespread uses as cleaning, dispersing, emulsifying, foaming and anti-foaming agents, and their adsorption at fluid interfaces has been studied extensively. Specifically, ionic surfactants are particularly effective at stabilizing dispersions, since the charge provides an electro-steric barrier to drop coalescence, which would otherwise promote macroscopic phase separation by minimizing interfacial energy. A review of published reports reveals that the theory for rigid spherical nanoparticles has been well developed; nonetheless, its application to nano-drops remains questionable due to fluid mobility of the interface and of the surfactant molecules adsorbed there. In fact, at zero frequency, small drops with surface impurities are well known to behave as rigid spheres due to concentration-gradient-induced Marangoni stresses. However, at the megahertz frequencies of electroacoustic diagnostic instruments, the interfacial concentration gradients are dynamic, coupling electromigration, advection and diffusion fluxes.

In general, electrokinetic determinations of the charge of ionic surfactants infer anomalously low surface-charge densities as compared to adsorption isotherms for planar interfaces and micelles. So far, numerous explanations have been proposed to explain the discrepancies, but none of them are satisfactorily complete. Many electrokinetic measures of surface charge have been undertaken with electrokinetic models for rigid particles. On this account, McGill University researchers: Professor Reghan J. Hill and Gbolahan Afuwape (PhD candidate) proposed a new theory to address the shortcomings of rigid-sphere models. In particular, they focused on addressing a parameter space relevant to anionic surfactant-stabilized oil-water emulsions, using sodium-dodecylsulfate-stabilized hexadecane as a specific example. Their work is published in the Journal of Fluid Mechanics.

In their approach, the McGill University scientists detailed the general solution of a predominantly hydrodynamic problem for the flow in the bulk regions inside and outside a drop under megahertz electrical forcing. Next, they addressed the thin interfacial region where species, charge and momentum conservation principles are coupled, providing boundary conditions for the two bulk regions. Eventually, they computed the dynamic electrophoretic mobility, highlighting how the Marangoni effects manifest at the megahertz frequencies of electrokinetic-sonic-amplitude (ESA) measurements (used to measure drop size and charge).

The authors demonstrated that fluid mobility and fluctuating Marangoni stresses can have a profound influence on the magnitude and phase of the dynamic mobility. In addition, they showed that the drop interface transited from a rigid/immobile one at low frequency to a fluid one at high frequency. Overall, the model demonstrated an ability to unify electro-kinetics and equilibrium interfacial thermodynamics.

In summary, the study developed an approximate theoretical model for the dynamics of non-conductive, ionic-surfactant-stabilized nano-drops under oscillatory forcing. The model was advanced with several simplifying approximations for thin, highly charged interfaces. Most notably, the researchers neglected ion-concentration perturbations in the diffuse and bulk regions, and the exchange of surfactant between the interface and the immediately adjacent electrolyte. In a statement to Advances in Engineering, Professor Reghan J. Hill said with knowledge of how the interfacial tension varies with electrolyte composition, the particle radius might be adopted as the primary fitting parameter from an experimental measure of the dynamic mobility. Further, their theory was general enough that it might be applied to aerosols and bubbly dispersions. Professor Hill also noted that their approximate analytical model has since been verified by developing an intricate computational solution of the problem, the details of which are published in the Journal of Fluid Mechanics. This enables the model to be applied to nano-emulsions with the smallest of droplet sizes. Experimental tests of the theory, applied to nano-emulsions and nano-emulsion-doped hydrogels, have been submitted for publication with Gbolahan Afuwape.

About the author

Reghan J. Hill is an Associate Professor in the Department of Chemical Engineering, McGill University. He received a B.E. (1st class honours) in Chemical and Materials Engineering from the University of Auckland, and a Ph.D. in Chemical Engineering from Cornell University, under Professor D. L. Koch. His post-doctoral training was under Professors D. A. Saville and W. B. Russel at Princeton University. He has research interests in soft matter, and presently teaches courses on Principles of Chemical Engineering, Foundations of Soft Matter, and graduate courses in Heat and Mass Transfer and Chemical Reaction Engineering.

About the author

Mr. Gbolahan A. Afuwape is currently a Ph.D. candidate in the Department of Chemical Engineering, McGill University. He obtained his bachelor’s degree (2010) from the University of Lagos, Nigeria, and Master’s degree (2016) from McGill. His research focuses on electro-kinetics of highly charged droplets, polyelectrolytes, and hydrogel-nanocomposites, including rheological studies of polymers and nanocomposites.



Reghan J. Hill, Gbolahan Afuwape. Dynamic mobility of surfactant-stabilized nano-drops: unifying equilibrium thermodynamics, electrokinetics and Marangoni effects. Journal of Fluid Mechanics (2020), volume 895.

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