Mass-time and space-time fractional partial differential equations of water movement in soils: theoretical framework and application to infiltration

Su, Ninghu (2014) Mass-time and space-time fractional partial differential equations of water movement in soils: theoretical framework and application to infiltration. Journal of Hydrology, 519 (Part B). pp. 1792-1803.

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Abstract

This paper presents mass-time fractional partial differential equations (fPDEs) formulated in a material coordinate for swelling–shrinking soils, and space-time fPDEs formulated in Cartesian coordinates for non-swelling soils. The fPDEs are capable of incorporating mobile and immobile zones or without immobile zones. As an example of the applications, the solutions of the fPDEs are derived and used to construct equations of infiltration. New equations of cumulative infiltration into soils, which are either swelling or nonswelling and with mobile or immobile zones are presented, and published data are used to demonstrate the use of the new equations and derive the parameters. The transport exponent, u, for soils with mobile and immobile zones are given. The transport exponent is the criteria for defining flow patterns: for u < 1, the flow process is sub-diffusion as compared to u = 1 for classic diffusion and u > 1 for super-diffusion.

Item ID: 35707
Item Type: Article (Research - C1)
ISSN: 0022-1694
Keywords: water movement in soils; mass-time and space-time fractional partial; differential equations; swelling and non-swelling soils; infiltration; mobile and immobile zones; transport exponent
Funders: Australian Department of Industry, Reef Rescue Research and Development Program, Distinguished Espert of Ningxia Programme
Projects and Grants: Australian Department of Industry ACSRF01065, Reef Rescue Research and Development Program RRRD004
Date Deposited: 16 Oct 2014 00:15
FoR Codes: 01 MATHEMATICAL SCIENCES > 0102 Applied Mathematics > 010207 Theoretical and Applied Mechanics @ 30%
04 EARTH SCIENCES > 0404 Geophysics > 040403 Geophysical Fluid Dynamics @ 30%
05 ENVIRONMENTAL SCIENCES > 0503 Soil Sciences > 050305 Soil Physics @ 40%
SEO Codes: 96 ENVIRONMENT > 9609 Land and Water Management > 960905 Farmland, Arable Cropland and Permanent Cropland Water Management @ 33%
96 ENVIRONMENT > 9614 Soils > 961402 Farmland, Arable Cropland and Permanent Cropland Soils @ 34%
96 ENVIRONMENT > 9609 Land and Water Management > 960999 Land and Water Management of Environments not elsewhere classified @ 33%
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