Porous media fibrous materials

An example of heat transfer through a porous medium is heat transfer through a layer of granular insulating material. This material will be saturated with air, i.e., the space between the granules of insulating material is entirely filled with air, and this air will flow through the insulation material as a result of the temperature difference imposed on the material, i.e., there will be a free convective flow in the porous material. Even when a fibrous insulation is used, the flow in the insulation can be... 

Natural convective flows in porous media occur in a number of important practical situations, e.g., in air-saturated fibrous insulation material surrounding a heated body and about pipes buried in water-saturated soils. To illustrate how such flows can be analyzed, e.g., see [20] to [22], attention will be given in this section to flow over the outer surface of a body in a porous medium, the flow being caused purely by the buoyancy forces resulting from the temperature differences in the flow. The simplest such situation is two-dimensional flow over an isothermal vertical flat surface imbedded in a porous medium, this situation being shown schematically in Fig. 10.25. 

Porosity is one of the most important continuum-scale parameters. It is defined as the fraction of the total volume that comprises void space e = Woid/ ktotai-Equivalently, the solid volume fraction ((f) = 1 - e) is generally used for fibrous materials or other open structures. The term microporosity implies that the particles in a porous medium are themselves porous, usually at a much smaller scale. A common example is porous catalyst in a packed-bed reactor. 

Fibrous porous materials are widely used in modern industry and engineering applications, such as heat exchangers, filters, catalysts, and fuel cell electrodes. The main technical challenge for the fibrous porous medium is to determine the velocity of the flow in the media. If we know the velocity of the fluid flow in the fibrous porous media, we can determine the important technical features of the media, such as the rate of change of temperature of the medium, the rate of change of concentration of substance, etc.. In most cases, the flow in the fibrous porous media is very slow and obeys Darcy s law [1], that relates the flow rate to the pressure gradient ... 

As mentioned in Chapter 2, when textile materials are immersed in the dye solution, the rate at which the dye is taken up is dependent upon the extent to which the liquor is agitated, and tends to approach a maximum value when the stirring is vigorous. This phenomenon, unfortunately, cannot be described in any simple fashion within fibrous assembhes, because of the extreme complexity of defining the flow of liquor through the textile materials. The dyeing of fibres, yams or cloth can be treated as mass transfer in a porous medium, defined by convective dispersion eqiratioa ... 

Many different types of filters are available commercially. They can be broadly classified into two types with, however, some overlap. Fibrous filters are composed of mats of fi bets that may be ntade of cellulose, quartz, glass, polymeric materials, or metals. Porous membrane filters are usually composed of thin films of polymeric materials 0.05 to 0.2 mm thick sufficiently porous for air to How through under pressure. Pore size is controlled in the manufacturing process and ranges from 0.02 to 10 /rm, A significant fraction of the panicles may be caught on the upstream surface of the filter, but some particles may also penetrate and be caught inside the pores of the medium as well. 

Filtration is the process of separating particles in suspension from a carrier fluid, which we here generally take to be a liquid, by passing the fluid through a permeable material called the filter medium. As noted in the introduction to Section 8.3, the filter may be a porous granular or fibrous medium, and the separated solids may be collected as a cake on the surface or be retained within the pores of the medium. 

Obvious uniformity is found in simple form with plain-weave metal cloth of light gauge wire. As the gauge of the wire becomes heavier and the weave is changed to a twilled or Dutch-type weave, we have a more elaborate medium that is generally used for filtration. The nature of the holes is more complex and more difficult to recognize with the unaided eye. Woven fabrics become more complicated due to the flexible nature of yams, and therefore it is more difficult to try to define the size of the hole in a woven fabric. The same is tme for media with random stmcture, such as felts, paper, fibrous and porous material. 

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