J. Phys. II France
Volume 4, Number 8, August 1994
Page(s) 1375 - 1391
DOI: 10.1051/jp2:1994205
J. Phys. II France 4 (1994) 1375-1391

Equilibrium dynamics of microemulsion and sponge phases

G. Gompper and M. Hennes

Sektion Physik der Ludwig-Maximilians-Universität München, Theresienstr. 37, 80333 München, Germany

(Received 13 April 1994, received in final form 19 April 1994, accepted 29 April 1994)

The dynamic structure factor $G({\bf k},\, \omega)$ is studied in a time-dependent Ginzburg-Landau model for microemulsion and sponge phases in thermal equilibrium by field-theoretic perturbation methods. In bulk contrast, we find that for sufficiently small viscosity $\eta$, the structure factor develops a peak at non-zero frequency $\omega$, for fixed wavenumber k with $k_0 < k \lesssim q$. Here, $2\pi/q$ is the typical domain size of oil- and water-regions in a microemulsion, and $k_0 \sim \eta q^2$. This implies that the intermediate scattering function, $G({\bf k},\,t)$, oscillates in time. We give a simple explanation, based on the Navier-Stokes equation, for these temporal oscillations by considering the flow through a tube of radius $R \simeq\pi/q$, with a radius-dependent tension.

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