K. Z. Markov. On
the sink strength and permeability of microcracked arrays.
Proc. Roy. Soc. Lond. A (2003) 459, 1035–1051
The effective absorption coefficient (the sink strength or the trapping constant)
g of a statistically isotropic random array of penny-shaped cracks is considered.
The cracks are treated as oblate spheroids with vanishing aspect ratio. A variational
procedure, based on Rubinstein-Torquato's principle [J. Chem. Phys. 88,
6372-6380 (1988)] is employed which yields nontrivial lower bound on g using appropriate trial fields of `particle' and `surface' type. The bounds
include the crack density parameter for the array as well as the two-point correlation
function for the set of crack's centers. The bounds also provide useful and nontrivial
information concerning cracks competition at nondilute concentration. The straightforward
`transition' of the obtained results as upper bounds on the effective permeability
of an array of randomly distributed disk-like obstacles is finally indicated.
Keywords: microcracked media; absorption problem; permeability; variational
estimates; effective properties