Investigation of the Flux–Concentration Relation for Horizontal Flow in Soils

George Kargas,Petros Kerkides,Paraskevi Londra

doi:10.3390/w11122442

Abstract

The objective of the present work is to investigate the flux–concentration (F(Θ)) relation, where Θ is the normalized soil volumetric water content for the case of one-dimensional horizontal flow, subject to constant concentration conditions. More specifically, the possibility of describing F(Θ) by an equation of the form F(Θ) = 1 − (1 − Θ)p+1 is examined. Parameter p is estimated from curve-fitting of the experimentally obtained λ(Θ) data to an analytic expression of the form (1 − Θ)p where λ is the well-known Boltzmann transformation λ = xt−0.5 (x = distance, t = time). The results show that the equation of (1 − Θ)p form can satisfactorily describe the λ(Θ) relation for the four porous media tested. The proposed F(Θ) function was compared with the limiting F(Θ) function for linear and Green–Ampt soils and to the actual F(Θ) function. From the results, it was shown that the proposed F(Θ) function gave reasonably accurate results in all cases. Moreover, the analytical expression of the soil water diffusivity (D(Θ)) function, as it was obtained by using the equation for λ(Θ) of the form (1 − Θ)p, appears to be very close to the experimental D(Θ) data (root mean square error (RMSE) = 0.593 m2min−1).

Highlights

For a rational and productive irrigation water application, one needs to know well how water infiltrates into the soil, and how the soil moisture profiles evolve
It is noticeable that the values of S and λi depend strongly on the soil type, and theythe experimental monitoring of the entering the column obtained, tend to decreaseprocess, as soilsa continuous become finer in texture
It is shown that the analytical expressions of the soil hydraulic diffusivity D(θ) and soil sorptivity S approach the experimental ones well

Summary

Introduction

For a rational and productive irrigation water application, one needs to know well how water infiltrates into the soil, and how the soil moisture profiles evolve. This can be achieved by solving the appropriate Richards’ equation, which is feasible only when major soil hydraulic properties are known, together with the initial and boundary conditions imposed in each case. F(Θ) expresses the relation of soil water flux–density with the normalized volumetric soil water content, and can be used in an attempt to elucidate further the flow phenomena in unsaturated soils, both in the horizontal (absorption, as well as desorption) and in the vertical cases. The form of the F for the case of horizontal absorption and the normalized volumetric soil water content is given by the following equations:

Objectives

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Results

Conclusion