Dispersion in steady and time-oscillatory flows through an eccentric annulus

A multiple-scale perturbation is conducted to derive an averaged equation for predicting the longtime solute transport in an eccentric annulus in which the uniaxial flow may oscillate periodically in time. A proof for the positiveness of the dispersivity is presented, implying that over a cycle of oscillation a solute cloud always broadens. For a steady flow driven by a fixed pressure gradient, increasing the eccentricity and annulus size gives rise to stronger dispersion. This relationship holds when the flow becomes unsteady. In the limit of slow oscillation, dispersion due to an oscillatory flow asymptotes to one-half of that by a steady flow. Increasing the oscillation frequency leads to a two-step decay of the dispersivity. The maximum dispersion in an oscillatory flow can be achieved in the limit of slow oscillation and large eccentricity, where dispersion can be O(10³) times larger than that in an otherwise concentric annulus.