On the flow of fluids through inhomogeneous porous media due to high pressure gradients |
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| Institution: | 1. Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G2G1;2. Department of Mechanical Engineering, Texas A&M University, College Station, TX 77843, United States;1. ENGIE EPI, 1 Place Samuel de Champlain, 92930 La Défense Cedex, France;2. ENPC, Institut Navier, 6 & 8 avenue Blaise Pascal, 77455 Marne-la-Vallée, France;1. Center for Theoretical Physics, MIT, Cambridge, MA 02139, USA;1. Department of Mechanical Engineering, Aliabad Katoul Branch, Islamic Azad University, Aliabad Katoul, Iran;2. Energy Research Center, Aliabad Katoul Branch, Islamic Azad University, Aliabad Katoul, Iran;3. Centre for Cooperative Research on Alternative Energies (CIC energiGUNE), Basque Research and Technology Alliance (BRTA), Alava Technology Park, Albert Einstein 48, 01510 Vitoria-Gasteiz, Spain;4. IKERBASQUE Basque Foundation for Science, Plaza Euskadi 5, 48009 Bilbao, Spain;5. Department of Mechanical and Aeronautical Engineering, University of Pretoria, Pretoria 0002, South Africa;6. Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan |
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| Abstract: | Most porous solids are inhomogeneous and anisotropic, and the flows of fluids taking place through such porous solids may show features very different from that of flow through a porous medium with constant porosity and permeability. In this short paper we allow for the possibility that the medium is inhomogeneous and that the viscosity and drag are dependent on the pressure (there is considerable experimental evidence to support the fact that the viscosity of a fluid depends on the pressure). We then investigate the flow through a rectangular slab for two different permeability distributions, considering both the generalized Darcy and Brinkman models. We observe that the solutions using the Darcy and Brinkman models could be drastically different or practically identical, depending on the inhomogeneity, that is, the permeability and hence the Darcy number. |
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| Keywords: | Pressure-dependent viscosity Porous rigid solid Barus formula Brinkman model Darcy equation Inhomogeneity |
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