STABILITY OF UNIFORMLY PROPAGATING SHS WAVES IN POROUS SOLIDS WITH MELTING AND FLOW OF REACTANTS

We formulate a two-dimensional model describing the combustion of poro us condensed phase materials in which a reactant melts and spreads thr ough the void space of a porous solid. The melt may completely fill th e pores, or some gas may remain in the pores. In each case, the volume fraction of melt is prescribed. In the limit of large activation ener gy, we analytically rind a one-dimensional basic state consisting of a uniformly propagating combustion wave with a planar reaction front an d a planar melting front. We find that the uniformly propagating solut ion with planar fronts is linearly unstable to traveling waves transve rse to the propagation direction of the basic state above some critica l Zeldovich number. The critical wave number associated with this crit ical Zeldovich number is generally unique and nonzero. However, the cr itical wave number can be zero for certain parameter values. For other special parameter values, the neutral stability curve may have two mi nima, so that two wave numbers lose stability at the same Zeldovich nu mber. Copyright (C) 1996 Elsevier Science Ltd.