COMBUSTION OF POROUS SAMPLES WITH MELTING AND FLOW OF REACTANTS

We formulate and analyze a model describing the combustion of porous c ondensed materials in which a reactant melts and spreads through the p ores of the sample. Thus there is liquid motion relative to the porous solid matrix. Our model describes the cases when the melt either fill s all the pores or when some gas remains in the pores. In each case th e melt occupies a prescribed volume fraction of the mixture. We employ both analytical and numerical methods to find uniformly propagating c ombustion waves, to analyze their stability and to determine behavior in the instability region. The principal physical conclusion which fol lows from our analysis is that the flow of the melted component can re sult in nonuniform composition of the product. Unlike models which do not take into account the relative motion of the components, this mode l exhibits a dependence of the structure of the product on the mode of propagation of the combustion front. Thus, if the initial mixture is uniform, models which do not allow for relative motion necessarily lea d to uniform structure of the product, while in the model employed her e the structure can be nonuniform. We observe that the structure of un iformly propagating combustion waves depends on whether the refractory or melting component is in excess in the initial mixture. We determin e how various parameters of the system affect stability and find a pul sating instability of the uniformly propagating solutions. We also per form numerical simulations in order to (i) study the dynamical behavio r of the combustion wave in the instability region, (ii) obtain a desc ription of the melt flow on the scale of the entire sample rather than on the scale of the combustion wave, i.e. to study the evolution of t he liquid melt layer which may occupy only a part of the product regio n. We show, in particular, that a transition to relaxation oscillation s may occur closer to the threshold of instability than in gasless sol id fuel combustion. Our numerical and analytical results are in qualit ative agreement.