Summary: Physica A 354 (2005) 95100
Random walk to freedom: The time of effusion
Yan LevinÃ, Marco A. Idiart, Jeferson J. Arenzon
Instituto de Fi´sica, Universidade Federal do Rio Grande do Sul, Caixa Postal 15051, CEP 91501-970,
Porto Alegre, RS, Brazil
Received 24 November 2004
Available online 7 April 2005
The problem of effusion is studied using Monte Carlo simulations and scaling analysis.
Particles confined to the interior of a container undergo a random walk with step size d. If a
hole is opened in one of the container walls, an outgoing diffusive current of particles will exit
through it. Effusion is exponentially fast with the characteristic time dependent on d, the
container volume, and the size of the pore. It is found that if the effusion time is properly
scaled, all the data can be collapsed onto one universal curve independent of the geometry of
container and the pore.
r 2005 Elsevier B.V. All rights reserved.
PACS: 82.39.Wj; 66.10.Cb; 87.15.Vv
Keywords: Diffusion; Effusion; Vesicle; Random walk; Mixed boundary value; Scaling function
The problem of determining the effusion time of solute through a pore of a vesicle
[1,2] is of great practical interest in a number of different contexts ranging from the