Force-driven transport through periodic entropy barriersN. Laachi1, M. Kenward1, E. Yariv2 and K. D. Dorfman1
1 Department of Chemical Engineering and Materials Science, University of Minnesota - Twin Cities 421 Washington Ave. SE, Minneapolis, MN 55455, USA
2 Faculty of Mechanical Engineering, Technion, Israel Institute of Technology - Technion City 32000, Israel
received 3 August 2007; accepted in final form 11 October 2007; published December 2007
published online 2 November 2007
We analyze the transport of a point-size Brownian particle under the influence of a constant and uniform force field through a slowly varying periodic channel whose cross-sectional area variations represent effective "entropy barriers." Using generalized Taylor-Aris dispersion (macrotransport) theory for spatially periodic media, we compute the mean velocity and effective diffusion coefficient (dispersivity) describing the long-time global transport of the particle. Systematic asymptotic perturbation analysis illuminates the transport process occurring in the strong-field limit, notably the role of the mean-squared channel roughness. The results thus obtained compare favorably with Brownian dynamics simulations over the full range of driving forces.
05.60.Cd - Classical transport.
02.50.Ey - Stochastic processes.
05.40.Jc - Brownian motion.
© Europhysics Letters Association 2007