A First-Principles Constitutive Equation for Suspension Rheology

Using mode-coupling theory, we derive a constitutive equation for the nonlinear rheology of dense colloidal suspensions under arbitrary time-dependent homogeneous flow. Generalizing previous results for simple shear, this allows the full tensorial structure of the theory to be identified. Macroscopic deformation measures, such as the Cauchy-Green tensors, thereby emerge. So does a direct relation between the stress and the distorted microstructure, illuminating the interplay of slow structural relaxation and arbitrary imposed flow. We present flow curves for steady planar and uniaxial elongation and compare these to simple shear. The resulting non-linear Trouton ratios point to a tensorially nontrivial dynamic yield condition for colloidal glasses.