EOS of Mixtures: Phase Transformation and Explosive Reaction

Mixture equations of state are developed to model the freezing of water to ice VII, and the transformation of solid explosive reactants to gaseous reaction products. In each case there is a single reaction variable, w, the mass fraction of the initial phase, that proceeds from unity (initial phase, i=1) to zero (second phase, i=2). Common temperature and pressure between the two phases is assumed. Each phase is also assumed to be represented in terms of pi(Vi,T) and ei(Vi,T), where pi, Vi, T, and ei are the pressure, specific volume, temperature, and specific internal energy, respectively. Three independent equations are formed: (1) p1 = p2; (2) wV1 + (1−w)V2 = V; and (3) we1 + (1−w)e2 = e. These equations determine V1, V2, and T given the total specific volume V, the total specific internal energy e, and w. Three specific forms for pi(Vi,T) and ei(Vi,T) are used.