Dynamical properties of colloidal systems: 1. Derivation of stochastic transport equations

To describe dynamical properties of a system of interacting Brownian particles stochastic transport equations are derived for the positions of the particles and their concentration fluctuations. This is achieved by an expansion of the Langevin equation for the momenta in terms of the reciprocal of the friction coefficient. As a by-product this procedure gives a new derivation of the generalized Smoluchowski equation. Using a local equilibrium approximation for the configurational distribution function a mode-mode coupling equation is derived for the local concentration, which still depends on the random forces of the solvent. For the interaction free case the relation to the ordinary diffusion approach is established.