Equilibrium Dynamics of Microemulsion and Sponge Phases

TL;DR

This paper investigates the dynamic structure factor of microemulsion and sponge phases, revealing oscillatory behavior in the intermediate scattering function at low viscosity, explained via fluid flow dynamics.

Contribution

It introduces a field-theoretic analysis of the structure factor showing oscillations at certain scales and viscosities, a novel insight into microemulsion dynamics.

Findings

Structure factor develops a non-zero frequency peak at low viscosity.

Intermediate scattering function oscillates in time under certain conditions.

Flow through a tube model explains the oscillatory behavior.

Abstract

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.