Effective one-dimensional description of confined diffusion biased by a transverse gravitational force
arXiv:1105.1879 · doi:10.1103/PhysRevE.84.011118
Abstract
Diffusion of point-like non interacting particles in a two-dimensional (2D) channel of varying cross section is considered. The particles are biased by a constant force in the transverse direction. We apply our recurrence mapping procedure, which enables us to derive an effective one-dimensional (1D) evolution equation, governing the 1D density of the particles in the channel. In the limit of stationary flow, we arrive at an extended Fick-Jacobs equation, corrected by an effective diffusion coefficient D(x), depending on the longitudinal coordinate x. Our result is an approximate formula for D(x), involving also influence of the transverse force. Our calculations are verified on the stationary diffusion in a linear cone, which is exactly solvable.
10 pages, 7 figures, submitted in Phys. Rev. E
References in corpus (10)
- Artificial Brownian motors: Controlling transport on the nanoscale
- Entropic transport: Kinetics, scaling and control mechanisms
- Biased diffusion in confined media: Test of the Fick-Jacobs approximation and validity criteria
- Entropic Stochastic Resonance
- Current in a three-dimensional periodic tube with unbiased forces
- Entropic particle transport: higher order corrections to the Fick-Jacobs diffusion equation
- Entropic particle transport in periodic channels
- Entropic stochastic resonance: the constructive role of the unevenness
- A channel Brownian pump powered by an unbiased external force
- Steering the potential barriers: entropic to energetic
Cited by in corpus (5)
- Thermal ratchet effect in confining geometries
- Transport coefficients for a confined Brownian ratchet operating between two heat reservoirs
- Giant enhancement of hydrodynamically enforced entropic trapping in thin channels
- Phase space reduction of the one-dimensional Fokker-Planck (Kramers) equation
- First-passage times in conical varying-width channels biased by a transverse gravitational force: Comparison of analytical and numerical results