Skip to main content
Log in

Sorptivity calculation for arbitrary diffusivity

  • Published:
Transport in Porous Media Aims and scope Submit manuscript

Abstract

An estimate of the sorptivity that requires only the knowledge of simple integrals of the soil-water diffusivity weighted by a power of the water content is present. The result is checked systematically for diffusivity functions with very different behaviours: power law, exponential and the two Fujita diffusivities. In all cases the error is always less than 1% regardless of whether or not the diffusivity increases rapidly with water content.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Braddock, R. D., Parlange, J.-Y., and Lisle, I. G., 1981, Properties of the sorptivity for exponential diffusivity and application to the measurement of the soil-water diffusivity,Soil. Sci. Soc. Am. J. 45, 705–709.

    Google Scholar 

  • Broadbridge, P. and White, I., 1988, Constant rate rainfall infiltration: A versatile nonlinear model. I. Analytic solutions,Water Resour. Res. 24, 145–154.

    Google Scholar 

  • Brooks, R. H. and Corey, A. J., 1964,Hydraulic properties of porous media, Hydrol. Paper #3, Colorado State University, Fort Collins, Colorado.

    Google Scholar 

  • Bruce, R. R. and Klute, A., 1956, The measurement of soil-water diffusivity,Soil Sci. Soc. Am. Proc. 20, 458–462.

    Google Scholar 

  • Brutsaert, W., 1968, The adaptability of an exact solution to horizontal infiltration,Water Resour. Res. 4, 785–789.

    Google Scholar 

  • Brutsaert, W., 1976, The concise formulations of diffusive sorption of water in a dry soil,Water Resour. Res. 12, 1118–1124.

    Google Scholar 

  • Dirksen, C., 1975, Determination of soil water diffusivity by sorptivity measurements,Soil Sci. Soc. Am. Proc. 39, 22–27.

    Google Scholar 

  • Elrick, D. E. and Robin, J. J., 1981, Estimating the sorptivity of soils,Soil Sci. 132, 127–133.

    Google Scholar 

  • Fujita, H., 1952a, The exact pattern of a concentration-dependent diffusion in a semi-infinite medium. I,Textile Res. J. 22, 757–760.

    Google Scholar 

  • Fujita, H., 1952b, The exact pattern of a concentration-dependentdiffusion on a semi-infinite medium. II,Textile Res. J. 22, 823–827.

    Google Scholar 

  • Heaslet, M. A. and Alksne, A., 1961, Diffusion from a fixed surface with a concentration-dependent coefficient,J. Soc. Indust. Appl. Math. 9, 585–596.

    Google Scholar 

  • Lockington, D., 1993, Estimating the sorptivity for a wide range of diffusivity dependence on water content,Transport in Porous Media 10, 95–101.

    Google Scholar 

  • Lockington, D., Parslow, J. and Parlange, J.-Y., 1988, Integral estimates of the sorptivity,Soil Sci. Soc. Am. J. 52, 903–908.

    Google Scholar 

  • Parlange, J.-Y., 1975, On solving the flow equation in unsaturated soils by optimization: Horizontal infiltration,Soil Sci. Soc. Am. Proc. 39, 415–418.

    Google Scholar 

  • Parlange, J.-Y., Barry, D. A., Parlange, M. B., and Haverkamp, R., 1992a, Note on the sorptivity for mixed saturated-unsaturated flow,Water Resour. Res. 28, 2529–2531.

    Google Scholar 

  • Parlange, J.-Y. and Braddock, R. D., 1980, An application of Brutsaert's and optimization techniques to the non-linear diffusion equations: The influence of tailing,Soil Sci. 129, 145–149.

    Google Scholar 

  • Parlange, J.-Y., Braddock, R. D., and Chu, B. T., 1980, First integrals of the diffusion equation; an extension of the Fujita solutions,Soil Sci. Soc. Am. J. 44, 908–911.

    Google Scholar 

  • Parlange, J.-Y., Braddock, R. D., and Lisle, I. G., 1980, Third order integral relation between sorptivity and soil-water diffusivity using Brutsaert's technique,Soil Sci. Soc. Am. J. 44, 889–891.

    Google Scholar 

  • Parlange, J.-Y., Haverkamp, R., Rand, R. H., Rendon, L., and Schmitz, G. H., 1987, Water movement in soils. The role of analytical solutions, inFuture Developments in Soil Science Research, Soil Sci. Soc. Am., Madison, Wisconsin, pp. 11–21.

    Google Scholar 

  • Parlange, M. B., Prasad, S. N., Parlange, J.-Y., and Römkens, M. J. M., 1992b, Extension of the Heaslet-Alksne technique to arbitrary soil-water diffusivities,Water Resour. Res. 28, 2793–2797.

    Google Scholar 

  • Parslow, J., Lockington, D., and Parlange, J.-Y., 1988, A new perturbation expansion for horizontal infiltration and sorptivity estimates,Transport in Porous Media 3, 133–144.

    Google Scholar 

  • Reichardt, K., Nielsen, D. R., and Biggar, J. W., 1972, Scaling of horizontal infiltration into homogeneous soils,Soil Sci. Soc. Am. Proc. 36, 241–245.

    Google Scholar 

  • Shampine, L. F., 1973, Some singular concentration dependent diffusion problems,ZAMM 53, 421–422.

    Google Scholar 

  • Spanier, J. and Oldham, K. B., 1987,An Atlas of Functions, Hemisphere Publishing Corp., New York.

    Google Scholar 

  • Sposito, G., 1990, Lie group invariance of the Richards equation, in J. H. Cushman (ed.),Dynamics of Fluids in Hierarchical Porous Media, Academic Press, London, pp. 327–347.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Parlange, J.Y., Barry, D.A., Parlange, M.B. et al. Sorptivity calculation for arbitrary diffusivity. Transp Porous Med 15, 197–208 (1994). https://doi.org/10.1007/BF00613278

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00613278

Key words

Navigation