Dispersion in unsteady Couette–Poiseuille flows

The paper presents the longitudinal dispersion of passive contaminant released in an incompressible viscous fluid flowing between two infinite parallel flat walls, in which the flow is driven by the application of both periodic pressure gradient and the oscillation of upper plate in its own plane with a constant velocity. A finite difference implicit scheme has been adopted to solve the unsteady convection-diffusion equation for all time period based on Aris method of moments. The dispersion coefficients are obtained for three different flow situations: steady, periodic and the combined effect of steady and periodic Couette–Poiseuille flows, separately. The results show that oscillation of upper plate produces more dispersion than the pulsation of pressure gradient and their combined action leads to a further increase of dispersion. Also plate oscillation has stronger effect on velocity distribution and on dispersion coefficient than the pressure pulsation. There is a remarkable difference in the behaviour of dispersion coefficient depending on whether the ratio of two frequencies arising from the oscillations of pressure gradient and the upper plate possesses a proper fraction or not.