Gravity induced separation in "liquid flames"

We study the structure of a combustion wave propagating through a heterogeneous powder mixture which initially forms a hard matrix. The matrix is destroyed by the propagating combustion wave, due, e.g., to melting of some of the components of the mixture. Thus, a liquid bath is formed, in which processes such as heat and mass transfer as well as chemical reactions determine the structure of the combustion wave, its propagation velocity and the composition of the reaction product. The liquid bath is a suspension containing particles, either liquid or solid, which may either be reactive or inert. Under the influence of gravitational forces there is the possibility of relative motion of the individual components of the mixture. This may result in separation of the components under the influence of an external force field, such as gravity, if the densities of the components differ from one another. Separation is opposed by a friction force. To gain an understanding of the phenomena associated with relative motion and separation during the propagation of the combustion wave, topics which heretofore have not been considered, we formulate and analyze a relatively simple mathematical model of "liquid flame" combustion in a gravitational force field. We determine the structure of uniformly propagating combustion waves and describe the possibility of multiplicity of such solutions. We also consider nonstationary waves and show that "shock" type solutions, with jumps in the composition of the sample, are possible.