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Viscous transport in eroding porous media

Published online by Cambridge University Press:  22 April 2020

Shang-Huan Chiu ,
M. N. J. Moore  and
Bryan Quaife Open the ORCID record for Bryan Quaife [Opens in a new window]
Shang-Huan Chiu*
Affiliation:
Department of Scientific Computing, Florida State University, Tallahassee, FL 32306, USA
M. N. J. Moore
Affiliation:
Department of Mathematics and Geophysical Fluid Dynamics Institute, Florida State University, Tallahassee, FL 32306, USA
Bryan Quaife*
Affiliation:
Department of Scientific Computing and Geophysical Fluid Dynamics Institute, Florida State University, Tallahassee, FL 32306, USA
*
‡Present address: Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, NJ 07102, USA
† Email address for correspondence: [email protected]
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Abstract

Transport of viscous fluid through porous media is a direct consequence of the pore structure. Here we investigate transport through a specific class of two-dimensional porous geometries, namely those formed by fluid-mechanical erosion. We investigate the tortuosity and dispersion by analyzing the first two statistical moments of tracer trajectories. For most initial configurations, tortuosity decreases in time as a result of erosion increasing the porosity. However, we find that tortuosity can also increase transiently in certain cases. The porosity-tortuosity relationships that result from our simulations are compared with models available in the literature. Asymptotic dispersion rates are also strongly affected by the erosion process, as well as by the number and distribution of the eroding bodies. Finally, we analyze the pore size distribution of an eroding geometry. The simulations are performed by combining a boundary integral equation solver for the fluid equations, a second-order stable time-stepping method to simulate erosion, and high-order numerical methods to stably and accurately resolve nearly touching eroded bodies and particle trajectories near the eroding bodies.

JFM classification

Low-Reynolds-number flows: Boundary integral methods Low-Reynolds-number flows: Porous media Mathematical Foundations: Computational methods
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 893 , 25 June 2020 , A3
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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