Dispersion in Sediment-Laden Stream Flow
Publication: Journal of Engineering Mechanics
Volume 126, Issue 8
Abstract
A theory is developed to demonstrate the effects of sorptive exchange on the transport of a chemical in a sediment-laden open-channel flow. Based on the multiple-scale method of homogenization, a depth-averaged transport equation is deduced up to a long time-scale. The dispersion coefficient is the sum of a modified Taylor dispersion coefficient and a dispersion coefficient due to a finite rate of mass exchange between dissolved phase in the water column and sorbed phase on suspended particles. These coefficients are functions of the suspension number and the bulk solid-water distribution ratio. It is shown that, for sufficiently large particles and solid fractions, enhancement of the longitudinal dispersion coefficient due to the sorptive exchange can be significant and should be included in a comprehensive model.
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References
1.
Aris, R. (1956). “On the dispersion of a solute in a fluid flowing through a tube.” Proc., Royal. Soc., London, Ser. A, 235, 67–77.
2.
Aris, R. (1959). “On the dispersion of a solute by diffusion, convection and exchange between phases.” Proc., Royal Soc., London, Ser. A, Vol. 252, 538–550.
3.
Auriault, J. L. (1983). “Effective macroscopic description for heat conduction in periodic composites.” Int. J. Heat Mass Transfer, Oxford, U.K., 26(6), 861–869.
4.
Auriault, J. L., and Adler, P. M. (1995). “Taylor dispersion in porous media: Analysis by multiple scale expansions.” Adv. Water Resour., Essex, U.K., 18, 217–226.
5.
Bensoussan, A., Lions, J. L., and Papanicolaou, G. (1978). Asymptotic analysis for periodic structures, North-Holland, Amsterdam.
6.
Chase, R. R. P. (1979). “Settling behavior of natural aquatic particulates.” Limnology and Oceanography, 24, 417–426.
7.
Elder, J. W. (1959). “The dispersion of marked fluid in turbulent shear flow.” J. Fluid Mech., Cambridge, U.K., 5, 544–560.
8.
Engelund, F. (1970). “Instability of erodible beds.” J. Fluid Mech., Cambridge, U.K., 42, 225–244.
9.
Fischer, H. B. (1967). “The mechanics of dispersion in natural streams.”J. Hydr. Div., ASCE, 93(6), 187–216.
10.
Fischer, H. B. (1973). “Longitudinal dispersion and turbulent mixing in open-channel flow.” Annu. Rev. Fluid Mech., 5, 59–78.
11.
Fischer, H. B., List, E. J., Koh, R. C. Y., Imberger, J., and Brooks, N. (1979). Mixing in inland and coastal waters, Academic, San Diego.
12.
Hornung, U. (1997). Homogenization and porous media, Springer, New York.
13.
Johnson, R. G. (1974). “Particulate matter at the sediment-water interface in coastal environments.” J. Marine Res., 32, 313–333.
14.
Lee, C. K., Sun, C. C., and Mei, C. C. (1996). “Computation of permeability and dispersivities of solute or heat in periodic porous media.” Int. J. Heat Mass Transfer, Oxford, U.K., 39(4), 661–676.
15.
Liu, H. (1977). “Predicting dispersion coefficient of streams.”J. Envir. Engrg. Div., ASCE, 103(1), 59–69.
16.
Liu, H., and Cheng, A. H. D. (1980). “Modified Fickian model for predicting dispersion.”J. Hydr. Div., ASCE, 106(6), 1021–1040.
17.
Mauri, R. (1991). “Dispersion, convection, and reaction in porous media.” Phys. Fluids, 3(5), 743–756.
18.
Mei, C. C. (1992). “Method of homogenization applied to dispersion in porous media.” Transp. in Porous Media, Dordrecht, The Netherlands, 9, 261–274.
19.
Mei, C. C., and Auriault, J. L. (1989). “Mechanics of heterogeneous porous media with several spatial scales.” Proc., Royal Soc., London, Ser. A, 426, 391–423.
20.
Mei, C. C., and Auriault, J. L. (1991). “The effect of weak inertia on flow through a porous medium.” J. Fluid Mech., Cambridge, U.K., 222, 647–663.
21.
Mei, C. C., Auriault, J. L., and Ng, C. O. ( 1996). “Some applications of the homogenization theory.” Advances in Applied Mechanics, J. W. Hutshinson and T. Y. Wu, eds., Vol. 32, Academic, San Diego, 277–348.
22.
Ng, C. O. (1999). “Macroscopic equations for vapor transport in a multi-layered unsaturated zone.” Adv. Water Resour., Essex, U.K., 22(6), 611–622.
23.
Ng, C. O. (2000). “Chemical transport associated with discharge of contaminated fine particles to a steady open-channel flow.” Phys. Fluids, 12(1), 136–144.
24.
Ng, C. O., and Mei, C. C. (1996). “Homogenization method applied to soil vapor extraction in aggregated soils.” Phys. Fluids, 8(9), 2298–2306.
25.
Passioura, J. B. (1971). “Hydrodynamic dispersion in aggregated media 1. Theory.” Soil Sci., 111(6), 339–344.
26.
Raats, P. A. C. ( 1981). “Transport in structured porous media.” Flow and transport in porous media, A. Verruijt and F. B. J. Barrends, eds., Balkema, Rotterdam, The Netherlands, 221–226.
27.
Sayre, W. W. (1975). Dispersion of mass in open-channel flow, Colorado State University, Fort Collins, Colo.
28.
Schnoor, J. L. (1996). Environmental modeling, Wiley, New York.
29.
Schwarzenbach, R. P., Gschwend, P. M., and Imboden, D. M. (1993). Environmental organic chemistry, Wiley, New York.
30.
Taylor, G. I. (1953). “Dispersion of soluble matter in solvent flowing through a tube.” Proc., Royal Soc., London, Ser. A, 219, 186–203.
31.
Taylor, G. I. (1954). “The disperison of matter in turbulent flow through a pipe.” Proc., Royal Soc., London, Ser. A. 223, 446–468.
32.
Thibodeaux, L. J. (1996). Environmental chemodynamics, 2nd Ed., Wiley, New York.
33.
Vanoni, V. A. (1975). Sedimentation engineering, ASCE, New York.
34.
Wu, S. C., and Gschwend, P. M. (1986). “Sorption kinetics of hydrophobic organic compounds to natural sediments and soils.” Envir. Sci. and Technol., 20, 717–725.
35.
Zabawa, C. F. (1978). “Microstructure of agglomerated suspended sediments in northern Chesapeake Bay estuary.” Sci., 202, 49–51.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 126 • Issue 8 • August 2000
Pages: 779 - 786
History
Received: Apr 6, 1999
Published online: Aug 1, 2000
Published in print: Aug 2000
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