Heterogeneous flame propagation in the self-propagating high-temperature synthesis (SHS) process in multi-layer foils for three components system: Theory and experimental comparisons

A theory for the heterogeneous flame propagation in the self-propagating high-temperature synthesis (SHS) process that proceeds in multi-layer foils, consisting of alternating layers of constituents, has been extended to three-component systems, by describing a premixed mode of bulk flame propagation supported by a non-premixed reaction that proceeds at the layer surface of a constituent with higher melting-point. The formulation allows for finite rate Arrhenius reaction at the layer surface, temperature-sensitive Arrhenius mass diffusion in the liquid phase, and existence of intermixed region between constituent layers. It is confirmed that thickness ratio of the constituent layers is related to mixture ratio and that thickness ratio of the intermixed region and the constituent layer is related to degree of dilution. Results show that the burning velocity first increases, reaches the maximum, and then decreases rapidly, with decreasing alloy layer thickness, that the decrease in the burning velocity can be attributed to the increase in the substance in the intermixed region between constituent layers, playing a role of diluent, and that the increase in the activity and/or amount of the less-active component in the alloy suppresses the burning velocity. A preheating effect for the burning velocity is also predicted. In experimental comparisons, it has been demonstrated that the analytical results agree with available experimental data in the literature, indicating that the present formulation has captured the essential features of the adiabatic, heterogeneous SHS process.