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Diffusion and the torsion parameter

Published online by Cambridge University Press:  17 February 2009

Alex McNabb  and
Grant Keady
Alex McNabb
Affiliation:
Department of Mathematics, Massey University, Palmerston North, New Zealand.
Grant Keady
Affiliation:
Mathematics Department, University of Western Australia, Nedlands, 6009, Western Australia.
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Abstract

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The parameters describing the trapping kinetics of a linear model for diffusion, in solids involving a captured immobile phase of the diffusing entity, can be determined by measuring mean residence times for matter in the systems and evaluating the exponents for the final exponential decay rates of the diffusing entity from various shaped solids. The mean residence time for matter in a given region can be expressed in terms of a “torsion parameter” S which in the case of Dirichlet boundary conditions and cylindrical geometries, coincides with the torsional rigidity of the cylinder. The final decay rate is given by the first eigenvalue μ of a Helmholtz problem. Expressions and inequalities are derived for these parameters S and μ for general linear boundary conditions and for geometries relevant to diffusion experiments.

Type
Research Article
Information
The ANZIAM Journal , Volume 35 , Issue 3 , January 1994 , pp. 289 - 301
Copyright
Copyright © Australian Mathematical Society 1994

References

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