Dynamic Density Functional theory for steady currents: Application to colloidal particles in narrow channels

TL;DR

This paper develops a theoretical framework using Dynamic Density Functional theory to analyze steady currents and density profiles of colloidal particles in narrow channels under external driving forces, accounting for interactions and potential barriers.

Contribution

It introduces a dynamic density functional approach for non-equilibrium steady states of interacting particles in one-dimensional potentials, extending previous equilibrium models.

Findings

Closed-form solutions for ideal gas in generic potentials

Numerical results for hard-rod interactions

Relevance for microfluidic device design

Abstract

We present the theoretical analysis of the steady state currents and density distributions of particles moving with Langevin dynamics, under the effects of an external potential displaced at 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 one-dimensional external potentials and the limits of strong and weak potential barriers. The ideal gas case is solved in a closed form for generic potentials and compared with the numerical results for hard-rods, with 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.