Asymptotic series for disparate mixtures

Abstract

The term “disparate mixture” here refers to a physical mixture composed of two distinct phases, where the physical properties of the phases are very dissimilar. It might be formed, e.g., from two immiscible gases or fluids, or from a soil-water compound. The calculation of fields in such a mixture is discussed, leading to the development of a pair of coupled asymptotic series (corresponding to the field point in one or the other of the phases). The specific problem of acoustic wave fields due to a point source in a two-fluid mixture illustrates the procedure. Questions of interest are: How does the mixture behave away from the limiting case, i.e., when the property ratio of the phases is very small but nonzero? How are successive terms in the series related to geometric length scales in the mixture (connectivity scales, inclusion size scales, matrix “gap” scales)? Preliminary results of applying the method to the reflection of plane waves from a flat interface are presented, and extensions to additional layered mixture models are indicated.