Unsteady convective diffusion in a rotating parallel plate channel

The paper presents an exact analysis of the dispersion of a passive contaminant in a viscous fluid flowing in a parallel plate channel driven by a uniform pressure gradient. The channel rotates about an axis perpendicular to its walls with a uniform angular velocity resulting in a secondary flow. Using a generalized dispersion model which is valid for all time, we evaluate the longitudinal dispersion coefficientsKi (i=1, 2, ...) as functions of time. It is shown thatK1=0 andK3,K4, ... decay rapidly in comparison withK2. ButK2 decreases with increasing α (the dimensionless rotation parameter) for values of α upto approximately α=2.2. ThereafterK2 increases with further increase in α and its value gets saturated for large values of α (say, 500) and does not change any further with increase in α. A physical explanation of this anomalous behaviour ofK2 is given.