Bolus Contaminant Dispersion for Oscillatory Flow in a Curved Tube

[+] Author and Article Information
Yahong Jiang

Department of Engineering Sciences and Applied Mathematics, Robert R. McCormick School of Engineering and Applied Science, Northwestern University, Evanston, IL 60208

James B. Grotberg

Biomedical Engineering Department, Robert R. McCormick School of Engineering and Applied Science, Northwestern University, Evanston, IL 60208; Also, Department of Anesthesia, Northwestern University Medical School, Chicago, IL 60611

J Biomech Eng 118(3), 333-340 (Aug 01, 1996) (8 pages) doi:10.1115/1.2796015 History: Received November 16, 1992; Revised August 10, 1995; Online October 30, 2007


The dispersion of a bolus of soluble contaminant in a curved tube during volume-cycled oscillatory flows is studied. Assuming a small value of δ (the ratio of tube radius to radius of curvature), the Navier-Stokes equations are solved by using a perturbation method. The convection-diffusion equation is then solved by expanding the local concentration in terms of the cross-sectionally averaged concentration and its axial derivatives. The time-averaged dimensionless effective diffusivity, 〈Deff /D〉, is calculated for a range of Womersley number α and different values of stroke amplitude A and Schmidt number Sc, where D is the molecular diffusivity of contaminant. For the parameter values considered, the results show that axial dispersion in a curved tube is greater than that in a straight tube, and that it has a local maximum near α = 5 for given fixed values of Sc = 1, A = 5 and δ = 0.3. Finally it is demonstrated how the time history of concentration at a fixed axial position can be used to determine the effective diffusivity.

Copyright © 1996 by The American Society of Mechanical Engineers
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