Steady-state reactant flux into a medium containing spherical sinks

A detailed analysis is presented for determining the reactant flux into a composite material containing randomly-located, reactive spherical centers. The governing equations are configurationally averaged assuming the spheres are distributed according to a hard-sphere potential. The resulting infinite hierarchy of coupled equations is truncated using physical consideratiosn of screening and diluteness of the particulate phase. A general asymptotic solution is obtained valid to order c for all bounded and semi-infinite domains. The solution reproduces the mean-field result and includes the previously-neglected effects of sphere-boundary interactions. These interactions dominate the effect of two-sphere interactions which affect the solution at order c^(3/2) ln c. Explicit consideration is given tot he case in which the domain is spherical or semi-infinite and a solution obtained for each. The solutions obtained generally predict an enhanced reactant flux relative to the mean-field result. The solution is illustrated by application to the problem of coal ash vaporization.