Adiabatic thermal explosion of a gas-solid mixture

The critical conditions of the adiabatic explosion problem of a gas-solid (dusty gas) mixture is presented. The definitions used for the homogeneous gas to determine criticality are used here for the gas-solid mixture. This work showed that the classical definition of the critical point can be adopted and modified to determine the critical condition in gamma-eta and gamma-theta domains. It was also found that using the definition of criticality as an inflection point in the critical trajectory in the theta-eta plane gives the same results as given by the classical definition of criticality. It is interesting to see that the critical and maximum points in the gas temperature-concentration domain could coincide. It was found that the presence of a solid produces more than one critical temperature. The limiting cases of the problem are also offered. The numerical solution showed that the supercritical trajectory shows a thermal runaway for the gas over the solid at the end of reaction.