First-Principles Constitutive Equation for Suspension Rheology

We provide a detailed derivation of a recently developed first-principles approach to calculating averages in systems of interacting, spherical Brownian particles under time-dependent flow. Although we restrict ourselves to flows which are both homogeneous and incompressible, the time-dependence and geometry (e.g. shear, extension) are arbitrary. The approximations formulated within mode-coupling theory are particularly suited to dense colloidal suspensions and capture the slow relaxation arising from particle interactions and the resulting glass transition to an amorphous solid. The delicate interplay between slow structural relaxation and time-dependent external flow in colloidal suspensions may thus be studied within a fully tensorial theory.