Dynamic density functional theory for steady currents: Application to colloidal particles in narrow channels

We present the theoretical analysis of the steady state currents and density distributions of particles moving with Langevin dynamics, under the effects of periodic external potentials, with dependence on only one direction, which are displaced at a constant rate. The dynamic density functional (DDF) formalism is used to introduce the effects of the molecular interactions, from the equilibrium Helmholtz free energy density functional. We analyzed the generic form of the DDF for external potential with one-dimensional dependence, and discuss the limits of strong and weak potential barriers. The ideal gas case is solved in a closed form and compared with the numerical results for hard-rods in one dimension, using the exact equilibrium free energy. The results may be of relevance for microfluidic devices, with colloidal particles moving along narrow channels, if external driving forces have to compete with the Brownian fluctuations and the interaction forces of the particles. (C) 2003 American Institute of Physics.