ABSTRACT:
In this talk we present some recent results on the stochastic modelling of the dynamics of colloidal fluids including inertia and hydrodynamic interactions, two effects which strongly influence the nonequilibrium properties of the system. We derive a general dynamical density functional theory (DDFT) which shows very good agreement with full Langevin dynamics. In suitable limits, we recover existing DDFTs and a Navier-Stokes-like equation with additional non local terms. Furthermore, we show rigorously that in the overdamped limit, the one particle distribution function satisfies a nonlinear, non-local Smoluchowski-like equation.