Directed transport of a Brownian particle in a periodically tapered tube
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TICAL, NONLINEAR, AND SOFT MATTER PHYSICS
Directed Transport of a Brownian Particle in a Periodically Tapered Tube Yu. A. Makhnovskiia,*, V. Yu. Zitsermanb, and A. E. Antipovc a
Topchiev Institute of Petrochemical Synthesis, Russian Academy of Sciences, Leninskii pr. 29, Moscow, 119991 Russia Joint Institute for High Temperatures, Russian Academy of Sciences, Izhorskaya ul. 13, Bldg. 2, Moscow, 125412 Russia cMoscow State University, Moscow, 119992 Russia *email: [email protected]
b
Received November 11, 2011
Abstract—The problem of the motion of a Brownian particle in a periodically tapered tube induced by a timeperiodic longitudinal force with zero mean is considered. Under the action of this force, the particle is shown to drift in a direction opposite to the constant load force applied to it. Analytical solutions for the drift velocity, the stopping force (the load causing the effect to disappear), and the efficiency of converting the energy introduced by perturbations into directed motion have been obtained at a large amplitude of the driv ing force, when the effect being discussed is maximal. In the range of its applicability extending from zero to asymptotically large force switching frequencies (proportional to the amplitude of the driving force), these solutions are in good agreement with the results of Brownian dynamics simulations. DOI: 10.1134/S1063776112090075
1. INTRODUCTION The drift of particles is generally believed to be induced by the directed action of either stationary macroscopic forces or temperature, chemical poten tial, etc. gradients. Comparatively recently, using a number of phenomena as an example, it has been found that the origin of the drift can also be completely different: in spatially periodic systems with broken mirror symmetry, directed motion can result from reg ularly or randomly repeated nonequilibrium perturba tions (the ratchet effect). By nonequilibrium perturba tions we mean the externally generated processes destroying the equilibrium (detailed balance): chemi cal reactions involving particles; photostimulated conformation transitions in them; the actions of ran dom or regular electric fields (with zero mean), etc. These perturbations should be distinguished from equilibrium fluctuations (thermal noise), which are unavoidable due to the contact with the environment, but they do not lead to any drift per se in accordance with the second law of thermodynamics. The particle transport induced by fluctuations was first discussed by Smoluchowski [1] and Feynman [2] when analyzing the possibility of “rectifying” Brown ian motion. Subsequently, studies were carried out in different directions. For example, in solidstate phys ics, a new class of transport phenomena was studied in detail using the appearance of a direct electric current under the action of a highfrequency electromagnetic field in media without any symmetry center (the pho tovoltaic effect) [3]. In recent years, the main empha sis has been shifted to the realm of intracellular trans
port mechanisms
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