J. Phys. II France
Volume 3, Numéro 6, June 1993
Page(s) 829 - 849
DOI: 10.1051/jp2:1993170
J. Phys. II France 3 (1993) 829-849

Dynamics of spontaneous emulsification

R. Granek, R. C. Ball and M. E. Cates

Theory of Condensed Matter, Cavendish Laboratory, Madingley Road, Cambridge, CB3 0HE, Great-Britain

(Received 30 September 1992, accepted in final form 3 March 1993)

We present a model for spontaneous emulsification resulting from a transiently negative interfacial tension between water and oil regions, which may be achieved under conditions of strong adsorption of surfactant molecules to the interface. While our approach builds on a linear stability analysis, it addresses the essential non-linear coupling of surface growth to the diffusion flux of surfactants to the interface. We consider a large drop of oil of radius R embedded in a dilute surfactant solution and predict that undulations develop with a characteristic wavelength $\lambda^{*}$, which at long times t obeys $\lambda^{*}\sim t^{1/3}$. This suggests that the size of the droplets created spontaneously at the interface scales as $\xi_{\rm o}^{1/3}$, where $\xi_{\rm o}$ is a diffusion length which is comparable to R under steady state diffusion conditions. We discuss the regimes of applicability of our results to various experimental systems.

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