Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-06T10:14:22.875Z Has data issue: false hasContentIssue false
  • English
  • Français

Effect of boundary reaction on solute dispersion in pulsatile flow through a tube

Published online by Cambridge University Press:  26 April 2006

Bijoy S. Mazumder  and
Samir K. Das
Bijoy S. Mazumder
Affiliation:
Illinois State Water Survey, University of Illinois at Urbana-Champaign, 2204 Griffith Drive, Champaign, IL 61820, USA Present Address: Mathematics and Statistics Division, Indian Statistical Institute, 203 B.T. Road, Calcutta 700035, India.
Samir K. Das
Affiliation:
Central Water and Power Research Station, Pune 411024, India
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper examines the streamwise dispersion of passive contaminant molecules released in a time-dependent laminar flow through a tube in the presence of boundary absorption or a catalytic wall reaction, which causes a depletion of contaminant in the flow. A finite-difference implicit scheme has been used to solve the unsteady convective–diffusion equation for all time. Here it is shown how the mixing of the cross-sectionally integrated concentration of contaminant molecules is influenced by the frequency of pressure pulsation and the heterogeneous reaction at the boundary. The behaviour of the dispersion coefficient due to the shear effects of steady, oscillatory, and the combined action of steady and periodic currents have been examined separately. The comparison reveals that for all cases the dispersion coefficient asymptotically reaches a stationary state after a certain time and it decreases with the absorption parameter. The increased wall absorption causes negatively skewed deviations from Gaussianity.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 239 , June 1992 , pp. 523 - 549
Copyright
© 1992 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Anderson, D. A., Tannehill, J. C. & Pletcher, R. H., 1984 Computational Fluid Mechanics and Heat Transfer. Hemisphere.
Andersson, B. & Berglin, T., 1981 Dispersion of laminar flow through a circular tube. Proc. R. Soc. Lond. A 377, 251–268.Google Scholar
Aris, R.: 1956 On the dispersion of a solute in a fluid flowing through a tube. Proc. R. Soc. Lond. A 235, 67–77.Google Scholar
Arts, R.: 1960 On the dispersion of a solute in pulsating flow through a tube. Proc. R. Soc. Lond. A 259, 370–376.Google Scholar
Barton, N. G.: 1983 On the method of moments for solute dispersion. J. Fluid Mech. 126, 205–218.Google Scholar
Barton, N. G.: 1984 An asymptotic theory for dispersion of reactive contaminants in parallel flow. J. Austral. Math. Soc. B 25, 287–310.Google Scholar
Barton, N. G. & Stokes, A. N., 1986 A computational method for shear dispersion in parallel flow. In Computational Techniques and Applications, CTAC-85 (ed. J. Noye & R. May), pp. 345–355. North-Holland.
Chatwin, P. C.: 1970 The approach to normality of the concentration distribution of solute in a solvent flowing along a straight pipe. J. Fluid Mech. 43, 321–352.Google Scholar
Chatwin, P. C.: 1975 On the longitudinal dispersion of passive contaminant in oscillatory flows in tubes. J. Fluid Mech. 71, 513–527.Google Scholar
Fischer, H. B., List, E. J., Koh, R. C. Y., Imberger, J. & Brooks, N. H., 1979 Mixing in Inland and Coastal Waters. Academic.
Gill, W. N. & Ananthakrishnan, V., 1967 Laminar dispersion in capillaries: Part 4. The slug stimulus. AIChE J. 13, 801–807.Google Scholar
Gill, W. N., Ruckenstein, E. & Hsieh, H. P., 1975 Homogeneous models for porous catalysts and tubular reactors with heterogeneous reactions. Chem. Eng Sci. 30, 685–694.Google Scholar
Gill, W. N. & Sankarasubramanian, R., 1970 Exact analysis of unsteady convective diffusions. Proc. R. Soc. Lond. A 316, 341–350.Google Scholar
Gupta, P. S. & Gupta, A. S., 1972 Effects of homogeneous and heterogeneous reactions on the dispersion of a solute in the laminar flow between two plates. Proc. R. Soc. Lond. A 330, 59–63.Google Scholar
Güven, O., Molz, F. J. & Melville, J. G., 1984 An analysis of dispersion in a stratified aquifer. Wat. Resour. Res. 20, 1337–1354.Google Scholar
Holley, E. R., Harleman, D. R. F. & Fischer, H. B. 1970 Dispersion in homogeneous estuary flow. J. Hydraul. Div. ASCE 96, 1691–1709.Google Scholar
Jimenez, C. F. & Sullivan, P. J., 1984 Contaminant dispersion in some time-dependent laminar flows. J. Fluid Mech. 142, 57–77.Google Scholar
Lapidus, L. & Pinder, G. F., 1982 Numerical Solution of Partial Differential Equations in Science and Engineering. Wiley-Interscience.
Mazumder, B. S. & Das, S. K., 1989 Dispersion of contaminant in oscillatory flow through a pipe – computation of moments. Acta Mech. 80, 151–156.Google Scholar
Mehta, R. V., Merson, R. L. & Mccoy, B. J., 1974 Hermite polynomial representation of chromatography elution curves. J. Chromatogr. 88, 1–6.Google Scholar
Mukherjee, A. & Mazumder, B. S., 1988 Dispersion of contaminant in oscillatory flows. Acta Mech. 74, 107–122.Google Scholar
Okubo, A.: 1967 The effect of shear in an oscillatory current on horizontal diffusion from an instantaneous source. Intl J. Oceanol. Limnol. 1, 194–204.Google Scholar
Purnama, A.: 1988 Boundary retention effects upon contaminant dispersion in parallel flows. J. Fluid Mech. 195, 393–412.Google Scholar
Purtell, L. P.: 1981 Molecular diffusion in oscillating laminar flow in a pipe. Phys. Fluids 24, 789–793.Google Scholar
Sankarasubramanian, R. & Gill, W. N., 1973 Unsteady convective diffusion with interphase mass transfer. Proc. R. Soc. Lond A 333, 115–132.Google Scholar
Schlichting, H.: 1966 Boundary Layer Theory. McGraw-Hill.
Sexl, Th., 1930 Uber den von E. G. Richardson entdeckten ‘Annulareffekt’. Z. Phys. 61, 349.Google Scholar
Smith, R.: 1982 Contaminant dispersion in oscillatory flows. J. Fluid Mech. 114, 379–398.Google Scholar
Smith, R.: 1983a The contraction of contaminant distributions in reversing flows. J. Fluid Mech. 129, 137–151.Google Scholar
Smith, R.: 1983b Effects of boundary absorption upon longitudinal dispersion in shear flows. J. Fluid Mech. 134, 161–177.Google Scholar
Taylor, G. I.: 1921 Diffusion by continuous movements. Proc. Lond. Math. Soc. 20, 196–211.Google Scholar
Taylor, G. I.: 1953 Dispersion of solute matter in solvent flowing slowly through a tube. Proc. R. Soc. Lond. A 219, 186–203.Google Scholar
Uchida, S.: 1956 The pulsating viscous flow superposed on the steady laminar motion of incompressible fluid in a circular pipe. Z. Angew. Math. Phys. 7, 403–422.Google Scholar
Valentine, E. M. & Wood, I. R., 1977 Longitudinal dispersion with dead zones. J. Hydraul. Div. ASCE 103, 975–990.Google Scholar
Yasuda, H.: 1984 Longitudinal dispersion of matter due to the shear effect of steady and oscillatory currents. J. Fluid Mech. 148, 383–403.Google Scholar
Yasuda, H.: 1989 Longitudinal dispersion of suspended particles in oscillatory currents. J. Mar. Res. 47, 153–168.Google Scholar