On dynamics of imploding shock waves in a mixture of gas and dust particles

In this paper, the generalized analytical solutions for one-dimensional adiabatic flow behind the imploding shock waves propagating in a dusty gas are obtained using the geometrical shock dynamics theory. The dusty gas is assumed to be a mixture of a perfect gas and spherically small solid particles, in which solid particles are continuously distributed. Shock jump relations given by Anand for a dusty gas are taken into consideration to explore the effects due to an increase in (i) the propagation distance from the centre of convergence, (ii) the mass fraction of solid particles in the mixture and (iii) the ratio of the density of solid particles to the initial density of the gas, on the shock velocity, pressure, temperature, density, velocity of mixture, speed of sound, adiabatic compressibility of mixture and the change-in-entropy across the shock front. The results provided a clear picture of whether and how the presence of solid particles influences the flow field behind the imploding shock front.