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Diffusive transport in networks built of containers and tubes.
MedLine Citation:
PMID:  16196709     Owner:  NLM     Status:  PubMed-not-MEDLINE    
Abstract/OtherAbstract:
We have developed analytical and numerical methods to study the transport of noninteracting particles in large networks consisting of M d -dimensional containers C1,...,C(M) with radii R(i) linked together by tubes of length l(ij) and radii a(ij) where i,j = 1,2,...,M. Tubes may join directly with each other, forming junctions. It is possible that some links are absent. Instead of solving the diffusion equation for the full problem we formulated an approach that is computationally more efficient. We derived a set of rate equations that govern the time dependence of the number of particles in each container, N1(t), N2(t),...,N(M)(t). In such a way the complicated transport problem is reduced to a set of M first-order integro-differential equations in time, which can be solved efficiently by the algorithm presented here. The workings of the method have been demonstrated on a couple of examples: networks involving three, four, and seven containers and one network with a three-point junction. Already simple networks with relatively few containers exhibit interesting transport behavior. For example, we showed that it is possible to adjust the geometry of the networks so that the particle concentration varies in time in a wave-like manner. Such behavior deviates from simple exponential growth and decay occurring in the two-container system.
Authors:
L Lizana; Z Konkoli
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Publication Detail:
Type:  Journal Article     Date:  2005-08-25
Journal Detail:
Title:  Physical review. E, Statistical, nonlinear, and soft matter physics     Volume:  72     ISSN:  1539-3755     ISO Abbreviation:  Phys Rev E Stat Nonlin Soft Matter Phys     Publication Date:  2005 Aug 
Date Detail:
Created Date:  2005-10-03     Completed Date:  2006-01-04     Revised Date:  -    
Medline Journal Info:
Nlm Unique ID:  101136452     Medline TA:  Phys Rev E Stat Nonlin Soft Matter Phys     Country:  United States    
Other Details:
Languages:  eng     Pagination:  026305     Citation Subset:  -    
Affiliation:
Department of Applied Physics, Chalmers University of Technology and Göteborg University, SE-412 96 Göteborg, Sweden.
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