Mechanics of Fluid Flow Through a Porous Medium
By a porous medium, we mean a material consisting of a solid matrix with an interconnected void. We suppose that the solid matrix is either rigid (the usual situation) or it undergoes small deformation. The interconnectedness of the void (the pores) allow
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Mechanics of Fluid Flow Through a Porous Medium
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Introduction
By a porous medium, we mean a material consisting of a solid matrix with an interconnected void. We suppose that the solid matrix is either rigid (the usual situation) or it undergoes small deformation. The interconnectedness of the void (the pores) allows the flow of one or more fluids through the material. In the simplest situation (“single-phase flow”), the void is saturated by a single fluid. In “two-phase flow,” a liquid and a gas share the void space. In a natural porous medium, the distribution of pores with respect to shape and size is irregular. Examples of natural porous media are beach sand, sandstone, limestone, rye bread, wood, and the human lung (Fig. 1.1 and Table 1.1). Manmade porous media include ceramics, composite materials, and high-porosity metallic foams. On the pore scale (the microscopic scale), the flow quantities (velocity, pressure, etc.) will be clearly irregular. But in typical experiments, the quantities of interest are measured over areas that cross many pores, and such space-averaged (macroscopic) quantities change in a regular manner with respect to space and time, and hence are amenable to theoretical treatment. How we treat a flow through a porous structure is largely a question of distance—the distance between the problem solver and the actual flow structure (Bejan 2004a, b). When the distance is short, the observer sees only one or two channels, or one or two open or closed cavities. In this case, it is possible to use conventional fluid mechanics and convective heat transfer to describe what happens at every point of the fluid- and solid-filled spaces. When the distance is large so that there are many channels and cavities in the problem solver’s field of vision, the complications of the flow paths rule out the conventional approach. In this limit, volume-averaging and global measurements (e.g., permeability, conductivity) are useful in describing the flow and in simplifying the description. As engineers focus more and more on designed porous media at decreasing pore scales, the problems tend to fall between the extremes noted above. In this intermediate range, the challenge is not only to describe coarse porous structures, but also to optimize D.A. Nield and A. Bejan, Convection in Porous Media, DOI 10.1007/978-1-4614-5541-7_1, # Springer Science+Business Media New York 2013
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1 Mechanics of Fluid Flow Through a Porous Medium
Fig. 1.1 Top: Examples of natural porous materials: (a) beach sand, (b) sandstone, (c) limestone, (d) rye bread, (e) wood, and (f) human lung (Collins 1961, with permission from Van Nostrand Reinhold). Bottom: Granular porous materials used in the construction industry, 0.5-cm-diameter Liapor® spheres (left) and 1-cm-size crushed limestone (right) (Bejan 1984)
flow elements, and to assemble them. The resulting flow structures are designed porous media (see Bejan et al. 2004; Bejan 2004b). The usual way of deriving the laws governing the macroscopic variables is to begin with the s
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