Connection of microstructure to rheology in a microemulsion model

The rheological properties of self-assembling fluids are studied within the framework of a simple time-dependent Landau-Ginzburg model: In addition to the Langevin relaxation dynamics, the order parameter field is subject to a kinematic deformation process due to a shear velocity field. The Hamiltonian contains a Gaussian part which has proven to be important in the study of self-assembly, as well as phi(4) and phi(2)(del phi)(2) contributions. In the disordered phase and for low shear rate, the relevant rheological coefficients (excess viscosity, first and second normal stress coefficient) can be calculated perturbatively. The essential ingredient is the one-loop, self-consistent solution of the evolution equation for the quasistatic structure factor. In the case of steady shear, we find shear thinning behavior, a positive first, and a negative second normal stress difference for all values of the shear rate. For oscillatory shear, it turns out that the self-assembling structures give rise to viscoelastic behavior. Analytic results are derived for the Limiting cases of low and high frequency. For low steady shear, all results can be expressed in scaling form using the correlation lengths d and xi originally defined for microemulsion under equilibrium conditions and scaling functions already known from the pure Gaussian treatment. This suggests a class of experiments where neutron scattering data can be compared to viscosity results. For low to high shear rates, the one-loop equations have also been solved numerically, and we display the nonequilibrium structure factors arising from this approach.