Abstract
This paper puts forward a perspective or opinion that we can demonstrate Darcy’s law is valid at any scale where fluid can be modeled/analyzed as a continuum. Darcy’s law describes the flow of a fluid through a porous medium by a linear relationship between the flow rate and the pore pressure gradient through the permeability tensor. We show that such a linear relationship can be established at any scale, so long as the permeability tensor is expressed as a function of adequate parameters that describe the pore space geometry, fluid properties, and physical phenomena. Analytical models at pore scale provide essential information on the key variables that permeability depends on under different flow regimes. Upscaling techniques based on the Lippman-Schwinger equation, pore network models, or Eshelby’s homogenization theory make it possible to predict fluid flow beyond the pore scale. One of the key challenges to validate these techniques is to characterize microstructure and measure transport properties at multiple scales. Recent developments in imaging, multiscale modeling, and advanced computing offer new possibilities to address some of these challenges.
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Data Availability Statement
No data, models, or code were generated or used during the study.
Acknowledgments
Some of the arguments made in this paper are inspired from a formal debate held by COS and BC and moderated by CA during the Biot-Bažant Conference on Engineering Mechanics and Physics of Porous Materials, held June 1–3, 2021. A recording of the debate is available in O’ Sullivan and Coasne (2021). We thank R. Hartkamp for providing the data for the molecular simulation snapshot in Fig. 1(a). We also thank Mr. Tokio Morimoto, who provided the images in Figs. 1(b and d). Some of the arguments presented in this paper originated from Chloé Arson’s project “BRITE Pivot Track: Micro-macro modeling of reactive flow and rock weathering enhanced by Artificial Intelligence,” which is funded by the US National Science Foundation (NSF) under grant CMMI No. 2135584. The financial support from the NSF is gratefully acknowledged.
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Published In
Journal of Engineering Mechanics
Volume 148 • Issue 11 • November 2022
Copyright
© 2022 American Society of Civil Engineers.
History
Received: Mar 29, 2022
Accepted: Jun 26, 2022
Published online: Aug 30, 2022
Published in print: Nov 1, 2022
Discussion open until: Jan 30, 2023
ASCE Technical Topics:
- Computer models
- Continuum mechanics
- Engineering fundamentals
- Engineering mechanics
- Flow (fluid dynamics)
- Fluid dynamics
- Fluid flow
- Fluid mechanics
- Foundations
- Geomechanics
- Geotechnical engineering
- Hydrologic engineering
- Linear functions
- Mathematical functions
- Mathematics
- Models (by type)
- Physical models
- Scale models
- Soil mechanics
- Soil properties
- Soil water
- Soil water movement
- Water and water resources
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