The approach to steady state in microemulsions under shear flow

We present an analytical study of the dynamical process of the approach to steady state for a driven diffusive system represented by the microemulsion phase of a ternary mixture. The external applied field is given by a “plane Couette” shear flow and the problem is studied within the framework of a time-dependent Ginzburg–Landau model. A Fokker–Planck equation for the probability distribution of the concentration fluctuations is developed in a self-consistent one-loop approximation and solved exactly, giving an analytical expression for the dynamic correlation functions of the system. For comparison to experimental work, we also show grey-scale plots of the scattering function at different times during the dynamical process for two different shear rates.