General Multi-Species Dynamical Density Functional Theory

We extend our recent study on the dynamics of single-species colloidal fluids in the full position-momentum phase space to the dynamics of multi-species colloidal fluids. We include both inertia and the full hydrodynamic interactions, which strongly influence the non-equilibrium properties of the system. For many-particle systems, the number of degrees of freedom prohibit a direct solution of the underlying stochastic equations and a reduced model is necessary. Under minimal assumptions, we derive a dynamical density functional theory (DDFT), i.e. a reduction to the dynamics of the reduced one-body distribution. Via computations based on spectral methods extended to integral operators, we demonstrate the excellent agreement between this DDFT and the full Langevin equations for a range of multi-species systems. In suitable limits we recover existing DDFTs (which neglect inertia and/or hydrodynamic interactions) and we investigate the resulting corrections to these DDFTs.