Non-equilibrium relaxation and near-arrest dynamics in colloidal suspensions

In this work we propose a theory to describe the irreversible diffusive relaxation of the local concentration of a colloidal dispersion that proceeds toward its stable thermodynamic equilibrium state, but which may in the process be trapped in metastable or dynamically arrested states. The central assumption of this theory is that the irreversible relaxation of the macroscopically observed mean value (n) over bar (r, t) of the local concentration of colloidal particles is described by a diffusion equation involving a local mobility b*(r, t) that depends not only on the mean value (n) over bar (r, t) but also on the covariance sigma(r, r'; t) equivalent to <(delta n(r, t)delta n(r', t))over bar> of the fluctuations delta n(r, t) equivalent to n(r, t)-(n) over bar (r, t). This diffusion equation must hence be solved simultaneously with the relaxation equation for the covariance sigma(r, r'; t), and here we also derive the corresponding relaxation equation. The dependence of the local mobility b*(r, t) on the mean value and the covariance is determined by a self-consistent set of equations involving now the spatially and temporally non-local time-dependent correlation functions, which in a uniform system in equilibrium reduces to the self-consistent generalized Langevin equation (SCGLE) theory of colloid dynamics. The resulting general theory considers the possibility that these relaxation processes occur under the influence of external fields, such as gravitational forces acting in the process of sedimentation. In this paper, however, we describe a simpler application, in which the system remains spatially uniform during the irreversible relaxation process, and discuss the general features of the glass transition scenario predicted by this non-equilibrium theory.