The effect of secondary motion on axial transport in oscillatory tube flow

In oscillatory flows through systems of branched or curved tubes, Taylor dispersion is modified both by the oscillation and by the induced secondary motions. As a model for this process, We examine axial transport in an annular region containing an oscillatory axial and steady secondary (circumferential) flow. Two complementary approaches are used: an asymptotic analysis for an annulus with a narrow gap (δ) and for large values of the secondary flow Peclet number ( P ); and a numerical solution for arbitrary values of δ and P . The results exhibit a form of resonance when the secondary-flow time equals the oscillation period, giving rise to a prominent maximum in the transport rate. This observation is consistent with preliminary numerical results for oscillatory flow in a curved tube, and can be explained physically.