Skip to main content Accessibility help
Hostname: page-component-888d5979f-9v52d Total loading time: 0.192 Render date: 2021-10-25T16:16:30.989Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": true, "newCiteModal": false, "newCitedByModal": true, "newEcommerce": true, "newUsageEvents": true }

Electrokinetic spectra of dilute surfactant-stabilized nano-emulsions

Published online by Cambridge University Press:  09 September 2020

Reghan J. Hill*
Department of Chemical Engineering, McGill University, 3610 University Street, MontrealH3A 0C5, Canada
Email address for correspondence:


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 Papers
© The Author(s), 2020. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)


de Aguiar, H. B., de Beer, A. G. F., Strader, M. L. & Roke, S. 2010 The interfacial tension of nanoscopic oil droplets in water is hardly affected by SDS surfactant. J. Am. Chem. Soc. 132 (7), 21222123.CrossRefGoogle ScholarPubMed
Barchini, R. & Saville, D. A. 1996 Electrokinetic properties of surfactant-stabilized oil droplets. Langmuir 12 (6), 14421445.CrossRefGoogle Scholar
Baygents, J. C. & Saville, D. A. 1991 Electrophoresis of drops and bubbles. J. Chem. Soc. Faraday Trans. 87 (12), 18831898.CrossRefGoogle Scholar
Booth, F. 1951 The cataphoresis of spherical fluid droplets in electrolytes. J. Chem. Phys. 19 (11), 13311336.CrossRefGoogle Scholar
Borwankar, R. P. & Wasan, D. T. 1988 Equilibrium and dynamics of adsorption of surfactants at fluid-fluid interfaces. Chem. Engng Sci. 43 (6), 13231337.CrossRefGoogle Scholar
Bouchemal, K., Briancon, S., Perrier, E. & Fessi, H. 2004 Nano-emulsion formulation using spontaneous emulsification: solvent, oil and surfactant optimisation. Intl J. Pharm. 280 (1), 241251.CrossRefGoogle ScholarPubMed
Delacey, E. H. B. & White, L. R. 1981 Dielectric response and conductivity of dilute suspensions of colloidal particles. J. Chem. Soc. Faraday Trans. 2 77, 20072039.CrossRefGoogle Scholar
Djerdjev, A. M. & Beattie, J. K. 2008 Electroacoustic and ultrasonic attenuation measurements of droplet size and $\zeta$-potential of alkane-in-water emulsions: effects of oil solubility and composition. Phys. Chem. Chem. Phys. 10, 48434852.CrossRefGoogle ScholarPubMed
Gupta, A., Eral, H. B., Hatton, T. A. & Doyle, P. S. 2016 Nanoemulsions: formation, properties and applications. Soft Matt. 12 (11), 28262841.CrossRefGoogle ScholarPubMed
Hashemnejad, S. M., Badruddoza, A. Z. M., Zarket, B., Ricardo Castaneda, C. & Doyle, P. S. 2019 Thermoresponsive nanoemulsion-based gel synthesized through a low-energy process. Nat. Commun. 10 (1), 2749.CrossRefGoogle ScholarPubMed
Hill, R. J. & Afuwape, G. 2020 Dynamic mobility of surfactant stabilized nano-drops: unifying equilibrium thermodynamics, electro-kinetics and Marangoni effects. J. Fluid Mech. 895, A14.CrossRefGoogle Scholar
Hill, R. J., Saville, D. A. & Russel, W. B. 2003 Electrophoresis of spherical polymer-coated colloidal particles. J. Colloid Interface Sci. 258 (1), 5674.CrossRefGoogle Scholar
Hollingsworth, A. & Saville, D. 2003 A broad frequency range dielectric spectrometer for colloidal suspensions: cell design, calibration, and validation. J. Colloid Interface Sci. 257, 6576.CrossRefGoogle Scholar
Hunter, R. J. 2001 Foundations of Colloid Science. Oxford University Press.Google Scholar
Hunter, R. J. & O'Brien, R. W. 1997 Electroacoustic characterization of colloids with unusual particle properties. Colloids Surf. A 126 (2), 123128.CrossRefGoogle Scholar
Kim, K., Choi, S. Q., Zasadzinski, J. A. & Squires, T. M. 2011 Interfacial microrheology of DPPC monolayers at the air–water interface. Soft Matt. 7, 77827789.CrossRefGoogle Scholar
Kong, L., Beattie, J. K. & Hunter, R. J. 2001 Effects of nonionic surfactant and sodium dodecyl sulfate layers on electroacoustics of hexadecane/water emulsions. Colloid Polym. Sci. 297, 678687.CrossRefGoogle Scholar
Kralchevsky, P. A., Danov, K. D., Broze, G. & Mehreteab, A. 1999 Thermodynamics of ionic surfactant adsorption with account for the counterion binding: effect of salts of various valency. Langmuir 15, 23512365.CrossRefGoogle Scholar
Mangelsdorf, C. S. & White, L. R. 1992 Electrophoretic mobility of a spherical colloidal particle in an oscillating electric field. J. Chem. Soc. Faraday Trans. 88 (24), 35673581.CrossRefGoogle Scholar
Marinova, K. G., Alargova, R. G., Denkov, N. D., Velev, O. D., Petsev, D. N., Ivanov, I. B. & Borwankar, R. P. 1996 Charging of oil-water interfaces due to spontaneous adsorption of hydroxyl ions. Langmuir 12, 20452051.CrossRefGoogle Scholar
O'Brien, R. W. 1986 The high-frequency dielectric dispersion of a colloid. J. Colloid Interface Sci. 113 (1), 8193.CrossRefGoogle Scholar
O'Brien, R. W. 1988 Electro-acoustic effects in a dilute suspension of spherical particles. J. Fluid Mech. 190, 7186.CrossRefGoogle Scholar
O'Brien, R. W. 1990 The electroacoustic equations for a colloidal suspension. J. Fluid Mech. 212, 8193.CrossRefGoogle Scholar
O'Brien, R. W. & White, L. R. 1978 Electrophoretic mobility of a spherical colloidal particle. J. Chem. Soc. Faraday Trans. 2 74, 16071626.CrossRefGoogle Scholar
O'Brien, R. W., Cannon, D. W. & Rowlands, W. N. 1995 Electroacoustic determination of particle size and zeta potential. J. Colloid Interface Sci. 173 (2), 406418.CrossRefGoogle Scholar
Ortiz, D. G., Pochat-Bohatier, C., Cambedouzou, J., Bechelany, M. & Miele, P. 2020 Current trends in pickering emulsions: particle morphology and applications. Engineering 6 (4), 468482.CrossRefGoogle Scholar
Press, W. H., Teukolsky, S. A., Vetterling, W. T. & Flannery, B. P. 1988 Numerical Recipes in C The Art of Scientific Computing Second Edition. Cambridge University Press.Google Scholar
Prosser, A. J. & Franses, E. I. 2001 Adsorption and surface tension of ionic surfactants at the air–water interface: review and evaluation of equilibrium models. Colloids Surf. A 178 (1–3), 140.CrossRefGoogle Scholar
Russel, W. B., Saville, D. A. & Showalter, W. R. 1989 Colloidal Dispersions. Cambridge University Press.CrossRefGoogle Scholar
Schnitzer, O. & Yariv, E. 2014 Nonlinear electrophoresis at arbitrary field strengths: small-Dukhin-number analysis. Phys. Fluids 26 (122002), 120.CrossRefGoogle Scholar
Schnitzer, O., Frankel, I. & Yariv, E. 2014 Electrophoresis of bubbles. J. Fluid Mech. 753, 4979.CrossRefGoogle Scholar
Taylor, T. D. & Acrivos, A. 1964 On the deformation and drag of a falling viscous drop at low Reynolds number. J. Fluid Mech. 18 (3), 466476.CrossRefGoogle Scholar
Temkin, S. 2005 Suspension Acoustics. Cambridge University Press.CrossRefGoogle Scholar
Wuzhang, J., Song, Y., Sun, R., Pan, X. & Li, D. 2015 Electrophoretic mobility of oil droplets in electrolyte and surfactant solutions. Electrophoresis 36 (19), 24892497.CrossRefGoogle ScholarPubMed
Yang, F., Wu, W., Chen, S. & Gan, W. 2017 The ionic strength dependent zeta potential at the surface of hexadecane droplets in water and the corresponding interfacial adsorption of surfactants. Soft Matt. 13 (3), 638646.CrossRefGoogle ScholarPubMed
Zdrali, E., Chen, Y., Okur, H. I., Wilkins, D. M. & Roke, S. 2017 The molecular mechanism of nanodroplet stability stability. ACS Nano 11, 1211112120.CrossRefGoogle Scholar
Zdrali, E., Etienne, G., Smolentsev, N., Amstad, E. & Roke, S. 2019 The interfacial structure of nano- and micron-sized oil and water droplets stabilized with SDS and Span80. J. Chem. Phys. 150, 204704.CrossRefGoogle ScholarPubMed
Cited by

Send article to Kindle

To send this article to your Kindle, first ensure is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the or variations. ‘’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Electrokinetic spectra of dilute surfactant-stabilized nano-emulsions
Available formats

Send article to Dropbox

To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

Electrokinetic spectra of dilute surfactant-stabilized nano-emulsions
Available formats

Send article to Google Drive

To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

Electrokinetic spectra of dilute surfactant-stabilized nano-emulsions
Available formats

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *