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Evaporation-Induced Capillary Siphoning Through Hydraulically Connected Porous Domains: The Vedernikov–Bouwer Model Revisited

  • A. R. KacimovEmail author
  • Yu. V. Obnosov
  • D. Or
Article
  • 28 Downloads

Abstract

Evaporation-driven wicking of soil water through porous domains with contrasting hydraulic properties is studied analytically by conformal mappings and compared to numerical solutions. Initially, the connected rectangular domains are fully saturated. The first rectangle, Gp, is comprised of a coarse-textured porous medium with large permeability and low capillary forces. Evaporation-induced capillary flow pulls water horizontally across the domains to the surface of fine-textured rectangular domain, Gz, through an interfacial hydraulic exchange region that shrinks with time. The flow field in Gz is 2-D and is analytically expressed by the Vedernikov–Bouwer model that assumes a constant hydraulic conductivity for pressure heads higher than the air-entry value. The rate of 1-D drop of the phreatic surface in Gp is proportional to the evaporation rate (decreasing with time) from the Gz surface. The complex potential domain Gw “shrinks” with time, and at any time instance, it is conformally mapped onto Gz via two auxiliary planes using the Schwarz–Christoffel and Mobius transformations. The resulting Cauchy problem for an integro-differential equation with respect to an affix of the conformal mapping is solved using numerical algebra routines. A similar capillary coupled flow problem was numerically simulated using HYDRUS2D considering 2-D flow in both Gp and Gz. New insights into process dynamics are gained from a solution of an auxiliary optimization for a vertical imbibition in a column brought in contact with a water table where particle size (linking capillarity and permeability) is used as a control variable and counter-gravity front propagation dynamics as criteria.

Keywords

Counter-gravity imbibition Stages of evaporation 2-D potential flow Complex potential HYDRUS simulations 

Abbreviations

GA

Green–Ampt

PK-77

Reference to the last (Russian) edition of the Polubarinova-Kochina (1977) book

SEF

Supplementary Electronic File

VB

Vedernikov and Bouwer

Notes

Acknowledgements

This work was funded by a grant from the Sultan Qaboos Higher Center for Culture and Science – Diwan of Royal Court and the Research Council of Oman (TRC) [RC/AGR/SWAE/17/01], SQU Grant IG/CAMS/SWAE/18/01 and by the subsidy allocated to Kazan Federal University for the state assignment in the sphere of scientific activities, Project No. 1.12878.2018/12.1. Helpful comments by three anonymous referees are greatly appreciated.

Data Sharing

The Mathematica codes (Sects. 2, 4) and HYDRUS project (Sect. 3) are open files and available to the referees and readers upon request.

Supplementary material

11242_2019_1285_MOESM1_ESM.pptx (4.1 mb)
Supplementary material 1 (PPTX 4188 kb)

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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of Soils, Water and Agricultural EngineeringSultan Qaboos UniversityMuscatSultanate of Oman
  2. 2.Institute of Mathematics and MechanicsKazan Federal UniversityKazanRussia
  3. 3.Department of Environmental Systems ScienceETH ZurichZurichSwitzerland

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