December 1, 2020
A porous medium is a solid with voids distributed more or less uniformly throughout the bulk of the body.
The basic characteristic of this medium is porosity. The bulk porosity Π of a material is defined as the ratio of void volume Vv to body volume V0, Π = Vv/V0. Since the remaining portion Vs of the total volume of the material is in the form of a solid “skeleton”, then
For example, the porosity of porous materials with the skeleton formed by spherical particles with diameter dp can be found from the relation
where Np is the number of particles per unit volume. These spheres can be arranged in various ways (Figures 1a and b). The cubic arrangement of spheres of the same diameter is characterized by a porosity of 0.476, while at a denser, rhombic, packing the porosity reduces to 0.259 (theoretically, this is the minimum porosity of packing of uniform spheres without deformation of the solid). The real porosity generally is estimated using its relation to density ρΣ = ρ0(1−Π) or Π = 1(ρΣ/ρ0), where ρΣ and ρ0 are the densities of the medium and of the solid material forming its skeleton, respectively.
Permeability (or gas permeability) is the property which gives a measure of the gas flow through a porous medium exposed to a pressure difference. The superficial velocity V of fluid flow depends on permeability and pressure gradient in accordance with a modified Darcy equation
Here, superficial velocity v is defined as the volumetric flow rate of the fluid per unit cross section of the medium. The coefficent α allows for friction losses that are characterized by the fluid viscosity η and the structure of a porous matrix. The coefficient of inertia β takes into account the losses associated with expansion, constriction, and bends in the pore channels; these losses are approximately proportional to ρV2.
The modified Darcy equation is universal and describes isothermal liquid and gas flow in any porous solids without allowance for capillary forces. The influence of capillary forces (an increase in viscosity) is observed in water at the pore sizes dp < 1 μm. As a consequence, the ratio of water to gas flow rates for identical pressure difference may be either proportional to the ratio of their viscosities at high dp or decrease by nearly a factor of 20 for porous channels of small diameter.
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