Abstract
The parameters in Richards' equation are usually calculated from experimentally measured values of the soilwater characteristic curve and saturated hydraulic conductivity. The complex pore structures that often occur in porous media complicate such parametrization due to hysteresis between wetting and drying and the effects of tortuosity. Rather than estimate the parameters in Richards' equation from these indirect measurements, imagebased modelling is used to investigate the relationship between the pore structure and the parameters. A threedimensional, Xray computed tomography image stack of a soil sample with voxel resolution of 6 μm has been used to create a computational mesh. The CahnHilliardStokes equations for twofluid flow, in this case water and air, were applied to this mesh and solved using the finiteelement method in COMSOL Multiphysics. The upscaled parameters in Richards' equation are then obtained via homogenization. The effect on the soilwater retention curve due to three different contact angles, 0°, 20° and 60°, was also investigated. The results show that the pore structure affects the properties of the flow on the large scale, and different contact angles can change the parameters for Richards' equation.
Original language  English 

Article number  20170178 
Pages (fromto)  120 
Number of pages  20 
Journal  Proceedings of the Royal Society A: Mathematical, Physical, and Engineering Sciences 
Volume  473 
Issue number  2207 
Early online date  22 Nov 2017 
DOIs  
Publication status  Published  Nov 2017 
Bibliographical note
Electronic supplementary material is availableonline at https://dx.doi.org/10.6084/m9.figshare.c.3925807.
Funding. L.J.C. and N.K. are funded by BBSRC SARISA BB/L025620/1. K.R.D. is funded by ERC 646809DIMR. M.N., P.D.H. and T.S.G. are funded by BBSRC BB/J00868/1 and A.G.B. is funded by BB/L025825/1. The James Hutton Institute receives funding from the Scottish Government. T.R. is funded by BBSRC SARISA BB/L025620/1, EPSRC EP/M020355/1, ERC 646809DIMR, BBSRC SARIC BB/P004180/1 and NERC NE/L00237/1.
Acknowledgements. The authors acknowledge the use of the IRIDIS High Performance Computing Facility, and associated support services, in particular Ivan Wolton, at the University of Southampton, and the μVIS Centre at the University of Southampton for the provision of necessary software and highperformance computer support in the completion of the work. The authors also acknowledge S. D. Keyes, University of Southampton, for providing the images used for this work. The authors would like to thank Prof. Ian Sinclair and members of the ‘Rooty Team’ at the University of Southampton for helpful discussions related to this work. T.R. would like to acknowledge useful discussions with Prof. David Smith and Floyd Woodrow DCM MBE.
Keywords
 Journal Article
 imagebased modelling
 porous media
 Richards' equation
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Paul Hallett
 Biological Sciences, Aberdeen Centre For Environmental Sustainability  Chair in Soil Physics
Person: Academic