Mathematical model of gas-free combustion of a binary powder mixture with allowance Marangoni convection

Abstract

A macroscopic mathematical model has been developed for the gas-free combustion of a binary reaction mixture with allowance for thermocapillary convection of a low-melting reagent. The model includes equations as follows: mass balance of reaction substances, chemical transformation, melt motion, thermal conductivity. Melt formed during the melting of one of the components is believed to move in the porous carcass of the mixture due to thermocapillary forces. The dynamics of changes in temperature, chemical conversion depth, melt fraction and porosity are numerically calculated in a gasless combustion wave. Depending on the main parameters characterizing the process, conductive, convective, and mixed modes of synthesis front propagation are revealed. Analytical relationships are derived to estimate the combustion rate for these modes. An approximate criterion that reveals the synthesis mode from the structural and physicochemical parameters of the binary mixture is found.