Continuum Mixture Modeling of Reactive Porous Media

Abstract

Despite extensive studies on granular energetic materials, the shock response of mixed-phase materials remains a controversial topic in the multiphase flow literature. Much debate has centered on the formulation and derivation of conservation equations for multiphase mixtures that, at the microscale, are statistical in nature. Many of these theories are based on a continuum approximation which averages thermal, mechanical, and chemical fields for a localized collection of materials representative of a heterogeneous mixture. This approach requires that the smallest resolved length scale be considerably larger than a typical particle or pore size in the mixture. This does not imply that processes at the microscale are negligible but, rather, that interactions associated with the discrete nature of the mixture are included as submodels. As one might expect, these relationships are crucial to prediction of initiation and growth of reaction in porous energetic materials.