Wave propagation in a non-ideal dusty gas

•The propagation of small and finite amplitude waves through a non-ideal gas with dust particles is studied.•The effects of non-linearity leading to a distortion of the wave profile and the influence of the dust particles and Van der Waals excluded volume on wave motion and velocity gradient are discussed.•Propagation of weak wave in the medium are discussed and the analytical solution of the flow field are obtained up to the first order.•The solutions up to first order in the physical plane are obtained in case of expansion fans.•The numerical values of the shock trajectory are obtained considering effects of dust particles and Van der Waals excluded volume.

In this paper we have studied the behavior of wave motion as propagating wavelets and their culmination into shock waves in a non-ideal gas with dust particles. In the absence of non-ideal effect the gas satisfies an equation of state of Mie–Gruneisen type. An expansion wave resulting from the action of receding piston is considered and the solutions to this problem showing effects of dust particles and non-idealness are obtained. The propagation of weak waves is considered and the flow variables in the region bounded by the piston and the characteristic wave front are found out. The expansive action of a receding piston undergoing an abrupt change in velocity is discussed. Cases of central expansion fan and shock fronts are studied and the solutions up to first order in the physical plane are obtained. The effects of non-idealness and dust particles are discussed in each case.