Skip to main content
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 141
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Fu, Xudong Gao, Ran and Wu, Zi 2016. Additional longitudinal displacement for contaminant dispersion in wetland flow. Journal of Hydrology, Vol. 532, p. 37.

    Luo, Jing Huai, Wenxin and Wang, Ping 2016. Contaminant transport in a three-zone wetland: Dispersion and ecological degradation. Journal of Hydrology, Vol. 534, p. 341.

    Wang, Ping and Chen, G.Q. 2016. Hydraulic dispersion of diurnal reactive constituents in an open channel eutrophic flow. Journal of Hydrology, Vol. 537, p. 200.

    Wang, Ping and Chen, G.Q. 2016. Transverse concentration distribution in Taylor dispersion: Gill’s method of series expansion supported by concentration moments. International Journal of Heat and Mass Transfer, Vol. 95, p. 131.

    Wu, Zi Fu, Xudong and Wang, Guangqian 2016. On spatial pattern of concentration distribution for Taylor dispersion process. Scientific Reports, Vol. 6, p. 20556.

    Aminian, Manuchehr Bernardi, Francesca Camassa, Roberto and McLaughlin, Richard M. 2015. Squaring the Circle: Geometric Skewness and Symmetry Breaking for Passive Scalar Transport in Ducts and Pipes. Physical Review Letters, Vol. 115, Issue. 15,

    Mohammed, F. J. Strunin, D. V. Ngo-Cong, D. and Tran-Cong, T. 2015. Asymptotics of averaged turbulent transfer in canopy flows. Journal of Engineering Mathematics, Vol. 91, Issue. 1, p. 81.

    Ngo-Cong, D. Mohammed, F.J. Strunin, D.V. Skvortsov, A.T. Mai-Duy, N. and Tran-Cong, T. 2015. Higher-order approximation of contaminant transport equation for turbulent channel flows based on centre manifolds and its numerical solution. Journal of Hydrology, Vol. 525, p. 87.

    Wu, Zi and Chen, G.Q. 2015. Axial diffusion effect on concentration dispersion. International Journal of Heat and Mass Transfer, Vol. 84, p. 571.

    Wu, Zi Fu, Xudong and Wang, Guangqian 2015. Concentration distribution of contaminant transport in wetland flows. Journal of Hydrology, Vol. 525, p. 335.

    Zeng, L. Wu, Zi Fu, Xudong and Wang, Guangqian 2015. Performance of the analytical solutions for Taylor dispersion process in open channel flow. Journal of Hydrology, Vol. 528, p. 301.

    Bolster, Diogo Méheust, Yves Le Borgne, Tanguy Bouquain, Jérémy and Davy, Phillipe 2014. Modeling preasymptotic transport in flows with significant inertial and trapping effects – The importance of velocity correlations and a spatial Markov model. Advances in Water Resources, Vol. 70, p. 89.

    Haynes, P. H. and Vanneste, J. 2014. Dispersion in the large-deviation regime. Part 1: shear flows and periodic flows. Journal of Fluid Mechanics, Vol. 745, p. 321.

    Saini, Anju Katiyar, V. K. and Pratibha, 2014. Effects of first-order chemical reactions on the dispersion coefficient associated with laminar flow through the lungs. International Journal of Biomathematics, Vol. 07, Issue. 02, p. 1450021.

    Wang, P. Li, Z. Huai, W.X. Chen, B. Li, J.S. Hayat, T. Alsaedi, A. and Chen, G.Q. 2014. Indicators for environmental dispersion in a three-layer wetland: Extension of Taylor's classical analysis. Ecological Indicators, Vol. 47, p. 254.

    Wu, Zi and Chen, G. Q. 2014. Approach to transverse uniformity of concentration distribution of a solute in a solvent flowing along a straight pipe. Journal of Fluid Mechanics, Vol. 740, p. 196.

    Wu, Zi and Chen, G.Q. 2014. Analytical solution for scalar transport in open channel flow: Slow-decaying transient effect. Journal of Hydrology, Vol. 519, p. 1974.

    Chen, Bin 2013. Contaminant transport in a two-zone wetland: Dispersion and ecological degradation. Journal of Hydrology, Vol. 488, p. 118.

    Jung, Youngjai and Seo, Il Won 2013. Time-split Mixing Model for Analysis of 2D Advection-Dispersion in Open Channels. Journal of The Korean Society of Civil Engineers, Vol. 33, Issue. 2, p. 495.

    Anmala, Jagadeesh and Kapoor, Vivek 2012. Mixing and Bimolecular Reaction Kinetics in a Plane Poisseulle Flow. Flow, Turbulence and Combustion, Vol. 88, Issue. 3, p. 387.


The approach to normality of the concentration distribution of a solute in a solvent flowing along a straight pipe

  • P. C. Chatwin (a1)
  • DOI:
  • Published online: 01 March 2006

Taylor (1953, 1954a) showed that, when a cloud of solute is injected into a pipe through which a solvent is flowing, it spreads out, so that the distribution of concentration C is eventually a Gaussian function of distance along the pipe axis. This paper is concerned with the approach to this final form. An asymptotic series is derived for the distribution of concentration based on the assumption that the diffusion of solute obeys Fick's law. The first term is the Gaussian function, and succeeding terms describe the asymmetries and other deviations from normality observed in practice. The theory is applied to Poiseuille flow in a pipe of radius a and it is concluded that three terms of the series describe C satisfactorily if Dt/a2 > 0·2 (where D is the coefficient of molecular diffusion), and that the initial distribution of C has little effect on the approach to normality in most cases of practical importance. The predictions of the theory are compared with numerical work by Sayre (1968) for a simple model of turbulent open channel flow and show excellent agreement. The final section of the paper presents a second series derived from the first which involves only quantities which can be determined directly by integration from the observed values of C without knowledge of the velocity distribution or diffusivity. The latter series can be derived independently of the rest of the paper provided the cumulants of C tend to zero fast enough as t → ∞, and it is suggested, therefore, that the latter series may be valid in flows for which Fick's law does not hold.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *