A self- similar solution of a shock propagation in a mixture of a non-ideal gas and small solid particles

Similarity solutions are obtained for unsteady, one-dimensional self-similar flow behind a strong shock wave, driven by a moving piston, in a dusty gas. The dusty gas is assumed to consist of a mixture of small solid particles and a non-ideal gas, in which solid particles are continuously distributed. It is assumed that the equilibrium flow-condition is maintained and variable energy input is continuously supplied by the piston. Solutions are obtained under both the isothermal and adiabatic conditions of the flow-field. The spherical case is worked out in detail to investigate to what extent the flow-field behind the shock is influenced by the non-idealness of the gas in the mixture as well as by the mass concentration of the solid particles, by the ratio of density of the solid particles to the initial density of the mixture and by the energy input due to moving piston. A comparison is also made between isothermal and adiabatic cases.