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Development of the flow induced by a piston moving impulsively in a dusty gas

The flow resulting from the impulsive motion of a piston moving at constant speed in a dusty gas is studied analytically and numerically. An idealized equilibrium-gas approximation is used to discuss the effects of piston speed and mass concentration of dust particles on the eventually formed shock wave. The detailed time-dependent change of the flow structure is studied by solving the equations of motion numerically. A partly dispersed shock-wave structure is formed at a high piston speed and a fully dispersed shock at a low piston speed. Two situations are considered, where the particles striking the piston experience an elastic collision, or where they stick to its surface. Significant effects on the flow produced by particles that reflect from the piston surface are discussed and clarified.