Equilibrium Dynamics of Microemulsion and Sponge Phases

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 $k_0 < k {< \atop \sim} q$. 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, $G({\bf k}, t)$, {\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.