Equilibrium Dynamics of Microemulsion and Sponge Phases

Abstract

The dynamic structure factor $G(\mathbf{k},\omega )$ 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 $k_0<k\genfrac{}{}{0ex}{}{<}{\sim }q$. 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, $G(\mathbf{k},t)$, {\it 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.

24 pages, LaTex, 11 Figures on request; J. Phys. II France 4 (1994) to be published

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