Permeability of microporous carbon preforms
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I.
PERMEABILITY is an overall transport parameter widely used in macroscopic descriptions of fluid flow through porous structures in many engineering applications, such as flow of interdendritic melt during solidification,[1] infiltration of metallic melts through particulate or fibrous ceramic preforms,[2] and resin impregnation during polymer composite fabrication.[3] For a Boussinesq’s fluid, Darcy’s law[4] gives r f0
vsuperficial 5 ε vinfiltration ^k& Dp 5 mf z
INTRODUCTION
mf ]u 5 2¹p 2 u 2 r f0 [bT (T 2 T 0) ]t k 1 bC (C 2 C 0)]g
[1]
where k is the (porous) medium permeability. This parameter allows one to treat the fluid-solid system as a quasicontinous medium. A number of empirical relationships have been derived for packed[5] and fibrous beds,[6] and bundles of aligned fibers,[7] including correction factors for nonspherical shapes and misalignment of the fibers, as well. There is, however, no reliable equation[8] that could predict the permeability for a given microporous structure. The approach, therefore, has been to extract this value from experimental measurements. Assuming steady-state conditions and ignoring buoyancy effects, for unidirectional flow, Darcy’s relationship becomes uz 5 2
k ]p mf ]z
[2]
which can be easily solved, assuming a linear dependence for the pressure. z2 5 2
^k& Dpt mf
[3]
where z
1 1 ' ^k& z
* k1 dz 0
The average permeability ^k&, therefore, can be extracted from experimental measurements of flow rate vs applied pressure gradient on a representative sample. Obviously, permeability is expected to depend on the microstructural details of the channels, such as size, shape, volume fraction, and distribution of interconnected porosities. There are two techniques available to characterize porous structures: mercury porosimetry and quantitative metallography. During mercury porosimetry, the porous preform is immersed into a mercury bath and the volume of mercury, intruded into the preform, is measured as a function of applied hydrostatic pressure. This information is then used to obtain the incremental intrusion volume (per unit weight) of the porous specimen as a function of the pore diameter, assuming that the pores are cylindrical in shape. The data can then be processed to determine the pore-size distribution. Knowing the bulk density and the total intruded volume, the skeletal density is determined assuming a continuous porosity, i.e., no isolated pores exist in the specimen. Metallography of the preforms can also be used to obtain a detailed quantitative description of pore volume fraction, as well as pore shape and size distribution. The purpose of this research was to quantitatively examine the interconnected microchannels by these two techniques and identify the microstructural parameters that best describe the experimentally determined permeability through microporous carbon preforms.
or II. S.K. DATTA, formerly Graduate Student, Chemical Engineering Department, Cleveland State University, is Project Engineer, Thermal Treatment Center, Inc., Wickliffe, OH 4
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