A new bound on the absorption coefficient of a two-phase medium

Abstract

The Doi bound on the effective absorption coefficient of a random two-phase medium is revisited in this brief note. Defects are created in one of the constituents, being absorbed by the other one, which thus act as a perfect sink. Use is made of a variational principle due to Rubinstein and Torquato. The trial dields generalize the ones, originally proposed by Doi, and hence the new bound is more restrictive than the original Doi's one for an arbitrary medium. In the particular case of an array of nonoverlapping array of spherical sinks, the new bound however coincides with Doi's and with the one, derived by Talbot and Willis. In passing, besides the known "particle-particle" bound, a curios new "surface-surface" bound is extracted. Though a bit weaker than the Doi's, this bound relies only upon the two-point "surface" statistics. In the dilute case it reproduces th classical Smoluchowski result.