Abstract
The dynamic structure factor
G(k,ω)
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
η
, the structure factor develops a peak at non-zero frequency
ω
, for fixed wavenumber
k
with
k
0
<k
<
∼
q
. Here,
2π/q
is the typical domain size of oil- and water-regions in a microemulsion, and
k
0
∼η
q
2
. This implies that the intermediate scattering function,
G(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≃π/q
, with a radius-dependent tension.