Mode-Coupling Theory for the Rheology of Colloidal Glasses: Recent Progress

I describe recent progress in the development of constitutive models for the rheology of dense colloidal suspensions in the glassy regime. These start from a formal development of mode coupling theory (MCT) applied to a nonlinear Green-Kubo equation for interacting advected Brownian particles, which forms the basis of an integration through transients (ITT) approach. The physical content of the resulting MCT-ITT constitutive model is briefly outlined. That physics includes a strong dependence of material properties, such as relaxation times, on the preceding flow history. Then, a much simplified schematic version, developed recently, is discussed. This schematic model is tensorially acceptable to rheologists and appears to capture much of the physics of the full model. Finally, an informal ‘risk-assessment’, discussing the strengths and weaknesses of the MCT approximation, is presented.