Nonlinear rheology of dense colloidal dispersions: a phenomenological model and its connection to mode coupling theory

Rheological properties, especially 'shear-thinning', of dense colloidal dispersions are discussed on three different levels. A generalized phenomonological Maxwell model gives a broad framework connecting glassy dynamics to the linear and non-linear rheology of dense amorphous particle solutions. First principles mode coupling theory calculations for the time or frequency dependent shear modulus give quantitative results for dispersions of hard colloidal spheres in the linear regime. Schematic models extending mode coupling theory to the non-linear regime recover the phenomenology of the generalized Maxwell model, and predict universal features of flow curves, stress versus shear-rate.