TECHNICAL PAPERS
Dec 1, 1985

Critique of Camp and Stein's RMS Velocity Gradient

Publication: Journal of Environmental Engineering
Volume 111, Issue 6

Abstract

The analysis of relative fluid motion by Camp and Stein, which led to their well‐known formulation of particle collision rate in flocculation, is examined using standard tools from continuum mechanics. As a result of certain apparent conceptual errors, including the notion that a three‐dimensional relative velocity field can be represented in general by a single velocity gradient, several recommendations are offered, including the abandonment of Camp and Stein's terms “absolute velocity gradient” and “root mean square (rms) velocity gradient.” Revisions in nomenclature and an alternate theory of particle collisions are discussed, as well as some implications of inhomogeneity in the turbulent flocculation problem.

Get full access to this article

View all available purchase options and get full access to this article.

References

1.
Aris, R., Vectors, Tensors and the Basic Equations of Fluid Mechanics, Prentice‐Hall, Inc., Englewood Cliffs, NJ, 1962.
2.
Batchelor, G. K., An Introduction to Fluid Dynamics, Cambridge University Press, Cambridge, England, 1967.
3.
Borisenko, A. I., and Tarapov, I. E., Vector and Tensor Analysis with Applications, translated from the Russian by Richard A. Silverman, Revised English ed., Dover Publications, Inc., New York, NY, 1979.
4.
Brodkey, R. S., “Fluid Motion and Mixing,” Mixing Theory and Practice, Vol. 1, V. W. Uhl and J. B. Gray, Eds., Academic Press, New York, NY, 1966, pp. 7–110.
5.
Camp, T. R., and Stein, P. C., “Velocity Gradients and Internal Work in Fluid Motion,” Journal of the Boston Society of Civil Engineers, Section, American Society of Civil Engineers, Vol. 30, Oct., 1943, pp. 219–237.
6.
Clark, M. M., “Turbulence Structure in a Small Mixing Vessel,” Proceedings of the June 25–27, 1984 National Conference on Environmental Engineering, ASCE, Univ. of Southern California, Los Angeles, CA.
7.
Cleasby, J. L., “Is Velocity Gradient a Valid Turbulent Flocculation Parameter?” Journal of Environmental Engineering, ASCE, Vol. 110, No. EE5, 1984, pp. 875–897.
8.
Fung, Y. C., A First Course in Continuum Mechanics, Prentice‐Hall, Inc., Englewood Cliffs, NJ, 1977.
9.
Mercier, S. R., “The Reactive Transport of Suspended Particles: Mechanisms and Modeling,” dissertation presented to the Massachusetts Institute of Technology, at Cambridge, MA, in 1984, in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
10.
Overbeek, J. T. G., “The Interaction Between Colloidal Particles,” Colloid Science, Vol. I, H. R. Kruyt, Ed., Elsevier Publishing Co., New York, NY, 1952, pp. 278–301.
11.
Saffman, P. G., and Turner, J. S., “On the Collision of Drops in Turbulent Clouds,” Journal of Fluid Mechanics, Vol. 1, No. 16, 1956, pp. 16–30.
12.
Sampson, K. J., and Ramkrishna, D., “Particle Size Correlations and the Effects of Limited Mixing on Agglomerating Particulate Systems,” Journal of Colloid and Interface Science, Vol. 104, No. 1, Mar., 1985, pp. 269–276.
13.
Spielman, L. A., “Hydrodynamic Aspects of Flocculation,” The Scientific Basis of Flocculation, K. J. Ives, Ed., Sijthoff and Noordhoff, Alpen an den Rijn, The Netherlands, 1978.
14.
Taylor, G. I., “Statistical Theory of Turbulence,” Proceedings of the Royal Society of London, Senes A : Mathematical and Physical Sciences, Vol. 151, Oct., 1935, pp. 430–437.
15.
Tennekes, H., and Lumley, J. L., A First Course in Turbulence, Massachusetts Institute of Technology Press, Cambridge, MA, 1972.
16.
Townsend, A. A., The Structure of Turbulent Shear Flow, Cambridge University Press, Cambridge, England.
17.
Valioulis, I. A., “Particle Collisions and Coalescence in Fluids,” dissertation presented to the California Institute of Technology, at Pasadena, CA, in 1983, in partial fulfillment of the requirements for the degree of Doctor of Philosophy.

Information & Authors

Information

Published In

Go to Journal of Environmental Engineering
Journal of Environmental Engineering
Volume 111Issue 6December 1985
Pages: 741 - 754

History

Published online: Dec 1, 1985
Published in print: Dec 1985

Permissions

Request permissions for this article.

Authors

Affiliations

Mark M. Clark, A. M. ASCE
Consulting Scientist, Tetra Tech, Inc., 1911 Fort Myer Drive, Suite 601, Arlington, VA 22209

Metrics & Citations

Metrics

Citations

Download citation

If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.

Cited by

View Options

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Media

Figures

Other

Tables

Share

Share

Copy the content Link

Share with email

Email a colleague

Share