Chemicals in the Environment, Dispersive Transport

  • John S. GulliverEmail author


Dispersion is the enhanced mixing of material through spatial variations in velocity. When it is of interest (when we are not keeping track of the three-dimensional mixing), dispersion is typically one or two orders of magnitude greater than turbulent diffusion. The process of dispersion is associated with a spatial mean velocity, the assumption of plug flow, and a velocity profile. The means used in association with diffusion, turbulent diffusion, and dispersion are identified in Table 6.1.


Velocity Profile Dispersion Coefficient Turbulent Diffusion Plug Flow Longitudinal Dispersion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The movement of a constituent with movement of the fluid.


The spreading of fluid constituents through the motion inherent to atoms and molecules.

Diffusion coefficient

A coefficient that describes the tendency of molecules to spread a constituent mass.

Dirac delta

An impulse of a given quantity (mass) that occurs over an infinitely short time or space.


The process of mixing caused by a variation in velocity and transverse diffusion or turbulent diffusion.

Dispersion coefficient

A coefficient that can describe the mixing caused by a transverse velocity profile and transverse diffusion or turbulent diffusion. A dispersion coefficient means that some sort of spatial mean velocity is being used to describe the flow. Then, the mixing lateral or longitudinal to the spatial mean velocity due to a combination of a velocity profile and diffusion or turbulent diffusion is described by the dispersion coefficient. The coefficient’s location in the mass transport equation is similar to diffusion coefficients, and the units are similar.

Laminar flow

Flow that has no turbulent eddies, where the fluid flows in laminas and diffusion creates the mixing of the fluid.

Turbulent diffusion

The mixing of fluids through turbulent eddies created by convection.

Turbulent diffusion coefficient

A coefficient that comes from the multiplication of two turbulent velocities of the flow, divided by density of the fluid. The coefficient’s location in the mass transport equation is similar to diffusion coefficients, and the units are similar, so it is called a “turbulent diffusion coefficient.”


Primary Literature

  1. 1.
    Taylor GI (1953) Dispersion of soluble matter in solvent flowing slowly through a tube. Proc R Soc Lond Ser A 219:186CrossRefGoogle Scholar
  2. 2.
    Taylor GI (1954) The dispersion of matter in turbulent flow through a pipe. Proc R Soc Lond Ser A 223:446CrossRefGoogle Scholar
  3. 3.
    Elder JW (1959) The dispersion of marked fluid in turbulent shear flow. J Fluid Mech 5:544CrossRefGoogle Scholar
  4. 4.
    Crank J (1975) The mathematics of diffusion, 2nd edn. Oxford University Press, OxfordGoogle Scholar
  5. 5.
    Gulliver JS (2007) An introduction to chemical transport in the environment. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  6. 6.
    Freeze RA, Cherry JA (1979) Groundwater. Prentice-Hall, Englewood CliffsGoogle Scholar
  7. 7.
    Koch DL, Brady JF (1985) Dispersion in fixed beds. J Fluid Mech 154:399CrossRefGoogle Scholar
  8. 8.
    Gelhar L, Welty C, Rehfeldt KR (1992) A critical-review of data on field-scale dispersion in aquifers. Water Resour Res 28(7):1955CrossRefGoogle Scholar
  9. 9.
    Fisher HB (1973) Longitudinal dispersion and turbulent mixing in open-channel flow. Ann Rev Fluid Mech 5:59CrossRefGoogle Scholar
  10. 10.
    Karikhoff SW, Brown DS, Scott TA (1979) Sorption of hydrophobic pollutants on natural sediments. Water Res 13:241CrossRefGoogle Scholar
  11. 11.
    Lehman WJ, Reehl WF, Rosenblatt DH (1990) Handbook of chemical property estimation. American Chemical Society, Washington, DCGoogle Scholar

Books and Reviews

  1. Fisher HB, List JE, Koh RCY, Imberger J, Brooks NH (1979) Mixing in inland and coastal waters. Academic, San DiegoGoogle Scholar
  2. Kreyszig E (1982) Advanced engineering mathematics, 4th edn. Wiley, New YorkGoogle Scholar
  3. Levenspiel O (1962) Chemical reaction engineering. Wiley, New YorkGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  1. 1.Department of Civil EngineeringUniversity of MinnesotaMinneapolisUSA

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