ON THE EFFECT OF BACKGROUND VOIDAGE ON COMPRESSIVE SOLITARY WAVES IN COMPACTING MEDIA

The effect of background voidage on the necessary conditions for the e xistence of compressive solitary wave solutions in the two-phase fluid flow of a medium compacting under gravity is investigated. It is assu med that K = K-0 phi(n)(1 - phi)(-p) and xi + 4/3 eta = (xi + 4/3 eta) (0) phi(-m)(1 - phi)(q), where K is the permeability of the medium, xi + 4/3 eta is the effective viscosity of the solid matrix and phi is t he voidage. It is shown that for compressive solitary wave solutions t o exist, which satisfy certain boundary conditions, it is necessary th at the background voidage 40 and the exponent n lie in two regions of the (phi(0), n)-plane when 0 less than or equal to p < 1, and that thi s reduces to one region when p greater than or equal to 1. Necessary c onditions on the exponent m are also derived. Solitary wave solutions for specific values of n, m, p, q and phi(0) are obtained numerically and compared.