Solutions are presented for the problem of the motion of a dusty gas contained between two coaxial cylinders which start to rotate impulsively from rest, following a formulation given by Saffman (1962). It is assumed that the relaxation time of the dust, τ, is small, and solutions are obtained by considering the ratio of the time scales, on which the gas velocity and the mass concentration of dust change, to be both large and small. In each of these two cases the following three sets of boundary conditions are considered: (1) both cylinders rotating with the same angular velocity; (2) and (3) one cylinder rotating with the other stationary. With the ratio of the time scales small and using boundary condition (1) a solution for the mass concentration of dust, f , is derived in closed form. In all other cases the solutions for f are derived numerically.
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