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On Analytical Solutions of Advective Transport by Infiltration–Redistribution Gravitational Flow

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Abstract

Contaminant transport in the upper layers of soil during the multiple cycles of short infiltration and prolonged redistribution is investigated. Analytical solutions for the two typical problems encountered in agricultural engineering are derived. The first problem considers the penetration of fertilizer initially applied at the soil surface. The second one is the propagation of contaminant injected with the applied water. Explicit analytical expressions for the solute concentration are obtained under assumptions of one-dimensional gravitational flow and advective solute transport under equilibrium conditions. The properties of the solute penetration are analyzed for the case of contaminant initially applied at the soil surface and picked up by the water flow during ten infiltration–redistribution cycles.

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References

  • W.J. Bond J.R. Phillips (1990) ArticleTitleApproximate solutions for cation transport during unsteady, unsaturated soil water flow Water Resour. Res. 26 2195–2205 Occurrence Handle10.1029/90WR00988

    Article  Google Scholar 

  • P. Broadbridge I. White (1988) ArticleTitleConstant rate rainfall infiltration: a versatile nonlinear model, 1, analytical solution Water Resour. Res. 24 145–154 Occurrence Handle10.1029/WR024i001p00145

    Article  Google Scholar 

  • Brooks, R. H. and Corey, A. T. (1964) Hydraulic properties of porous media, Hydrol. Pap. 3, Colo. State Univ., Fort Collins.

  • G. Dagan E. Bresler (1979) ArticleTitleSolute dispersion in unsaturated heterogeneous soil at field scale I: Theory Soil Sci. Soc. Am. J. 43 461–467 Occurrence Handle10.2136/sssaj1979.03615995004300030008x

    Article  Google Scholar 

  • W.R. Gardner (1958) ArticleTitleSome steady state solutions of unsaturated moisture flow equations with application to evaporation from a water table Soil Sci. 85 228–232 Occurrence Handle10.1097/00010694-195804000-00006

    Article  Google Scholar 

  • P. Indelman I. Touber-Yasur B. Yaron G. Dagan (1998) ArticleTitleStochastic analysis of water flow and pesticides transport in a field experiment J. Contam. Hydrol. 32 77–97 Occurrence Handle10.1016/S0169-7722(97)00084-3

    Article  Google Scholar 

  • Lessoff, S. C., Indelman, P. and Dagan, G. (2002) Solute transport in infiltration–redistribution cycles in heterogeneous soils. In: Raats, P., Smiles, D., and Warrick, A. (eds.), Heat and Mass Transfer in the Natural Environment – A Tribute to J.R. Philip: In Geophysical Monograph Series, Volume 129. Environmental Mechanics: Water, Mass and Energy Transfer in the Biosphere. American Geophysical Union, Washington D.C., pp. 133–144.

  • S.C. Lessoff P. Indelman (2004) ArticleTitleAnalytical model of solute transport by unsteady unsaturated gravitational infiltration J. Contam. Hydrol. 72 85–107 Occurrence Handle10.1016/j.jconhyd.2003.10.008

    Article  Google Scholar 

  • J.R. Philip (1992) ArticleTitleExact solutions for redistribution by nonlinear convection-diffusion J. Aust. Math. Soc. Ser. B 33 363–383 Occurrence Handle10.1017/S0334270000007098

    Article  Google Scholar 

  • J.R. Philip J.H. Knight (1991) ArticleTitleRedistribution from plane, line, and point sources Irrig. Sci. 12 169–180 Occurrence Handle10.1007/BF00190520

    Article  Google Scholar 

  • D.E. Smiles K. Perroux S. Zegelin P. Raats (1981) ArticleTitleHydrodynamic dispersion during constant rate absorption of water by soil Soil Sci. Soc. Am. J. 45 453–458 Occurrence Handle10.2136/sssaj1981.03615995004500030001x

    Article  Google Scholar 

  • M.T. Genuchten Particlevan (1980) ArticleTitleA closed-form equation for predicting the hydraulic conductivity of unsaturated soils Soil Sci. Am. J. 44 892–898 Occurrence Handle10.2136/sssaj1980.03615995004400050002x

    Article  Google Scholar 

  • A.W. Warrick D.O. Lomen A. Islas (1990) ArticleTitleAn analytical solution to Richards’ equation for a draining soil profile Water Resour. Res. 26 253–258 Occurrence Handle10.1029/89WR01693

    Article  Google Scholar 

  • J.L. Wilson L.W. Gelhar (1981) ArticleTitleAnalysis of longitudinal dispersion in unsaturated flow 1. the analytical method Water Resour. Res. 17 122–130

    Google Scholar 

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Authors and Affiliations

  1. Technion-Faculty of Civil and Environmental Engineering, Technion City, Haifa, 32000, Israel

    A. Levin & P. Indelman

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  1. A. Levin
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  2. P. Indelman
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Correspondence to A. Levin.

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P. Indelman - (deceased)

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Levin, A., Indelman, P. On Analytical Solutions of Advective Transport by Infiltration–Redistribution Gravitational Flow. Transp Porous Med 65, 177–192 (2006). https://doi.org/10.1007/s11242-005-6101-8

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  • DOI: https://doi.org/10.1007/s11242-005-6101-8

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