Beyond the Dynamic Density Functional theory for steady currents. Application to driven colloidal particles in a channel

Abstract

Motivated by recent studies on the dynamics of colloidal solutions in narrow channels, we consider the steady state properties of an assembly of non interacting particles subject to the action of a traveling potential moving at a constant speed while the solvent is modeled by a heat bath at rest in the laboratory frame. Since the description, we propose here, takes into account the inertia of the colloidal particles it is necessary to consider the evolution of both positions and momenta and study the governing equation for the one-particle phase-space distribution. We first derive the asymptotic form of its solutions as an expansion in Hermite polynomials and their generic properties, such as the force and energy balance and then we particularize our study to the case of an inverted parabolic potential barrier. We obtain numerically the steady state density and temperature profile and show that the expansion is rapidly convergent for large values of the friction constant and small drifting velocities. The present results on the one hand confirm the previous studies based on the dynamic density functional theory (DDFT) when the friction constant is large, on the other hand display effects such as the presence of a wake behind the barrier and a strong inhomogeneity in the temperature field which are beyond the DDFT description.

21 pages, 7 figures To appear in Journal of Chemical Physics

References in corpus (12)

• Dynamic Density Functional Theory of Fluids
• Dynamical density functional theory and its application to spinodal decomposition
• Screened hydrodynamic interaction in a narrow channel
• Depletion forces in non-equilibrium
• Driven low density granular mixtures
• Dynamic density functional study of a driven colloidal particle in polymer solutions
• Mean-field dynamical density functional theory
• Fluid-like behavior of a one-dimensional granular gas
• Dynamic Density Functional theory for steady currents: Application to colloidal particles in narrow channels
• Theory of thermostatted inhomogeneous granular fluids: a self-consistent density functional description
• Inelastic hard-rods in a periodic potential
• Multiple time-scale approach for a system of Brownian particles in a non-uniform temperature field

Cited by in corpus (10)

• Classical dynamical density functional theory: from fundamentals to applications
• Nonlinear response and emerging nonequilibrium micro-structures for biased diffusion in confined crowding environments
• Pseudospectral methods for density functional theory in bounded and unbounded domains
• Dynamics of localized particles from density functional theory
• Self-propulsion against a moving membrane: enhanced accumulation and drag force
• Interacting particles in a periodically moving potential: Traveling wave and transport
• Novel structure formation of a phase separating colloidal fluid in a ratchet potential
• Stochastic dynamics and thermodynamics around a metastable state based on the linear Dean-Kawasaki equation
• Current reversal in interacting colloids under time-periodic drive
• Symmetric exclusion processes on a ring with moving defects