EQUILIBRIUM DYNAMICS OF MICROEMULSION AND SPONGE PHASES

The dynamic structure factor G(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 k0 < k less than or similar to q. Here, 2pi/q is the typical domain size of oil- and water-regions in a microemulsion, and k0 approximately etaq2. This implies that the intermediate scattering function, G(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 congruent-to pi/q, with a radius-dependent tension.