A two-fluid continuum model has been employed to investigate the formation of the lamellar structures in these materials. In this model, particle migration is related to the particle contribution to the normal stresses induced by the applied field and by the shear flow. Using naive approximations for these stresses, the model successfully predicts the formation of lamellar structures, and presumably the onset of a slow transient rheological response, for field strengths above a "critical" value. However, the naive approximations result in several other predictions that do not agree with experimental observations. Most notably, the predicted shear rheology is predicted to be insensitive to the applied field strength and the volume fraction dependence of the critical field strength does not agree with that observed experimentally.
We employ particle-level simulations to determine more accurate representations of the particle contributions to the stress, as functions of the applied field strength, shear rate, particle concentration, and shear history. Results for the normal stress components provide improved information to describe both the onset of lamella formation, as well as the long-time structure. Results for the deviatoric stress components provide information about the conventional field-induced rheology as well as its transient behavior.