DIFFUSION AND THE TORSION PARAMETER

The parameters describing the trapping kinetics of a linear model for diffusion, in solids involving a captured immobile phase of the diffus ing entity, can be determined by measuring mean residence times for ma tter in the systems and evaluating the exponents for the final exponen tial decay rates of the diffusing entity from various shaped solids. T he mean residence time for matter in a given region can be expressed i n terms of a ''torsion parameter'' S which in the case of Dirichlet bo undary conditions and cylindrical geometries, coincides with the torsi onal rigidity of the cylinder. The final decay rate is given by the fi rst eigenvalue mu of a Helmholtz problem. Expressions and inequalities are derived for these parameters S and mu for general linear boundary conditions and for geometries relevant to diffusion experiments.