Measurement of Porosity

Porosity can be measured indirectly via the particle and bulk densities as described by equation 5.2. This is the same method as currently used in many commercial instruments for surface area measurement by permeability in that a known mass of powder is packed into a known volume (i.e. the bulk density is known) and the porosity is evaluated from the knowledge of particle density. 

It is also possible to measure porosity by permeametry as described in section 2.5. Finally, there is also the possibility of measuring porosity of bulk powders directly by air or liquid displacement of the voids but this is not likely to be very accurate and there are, to the best of my knowledge, no standard procedures or commercial instruments available for such measurements. 

In conclusion to this section on porosity of bulk powders, it seems that the indirect method of calculating its value from other powder properties, namely the bulk and particle densities, is adequate for most practical applications. The fact whether or not the porosity should include the internal pores of the particles is taken care of by selection of a suitable method for particle density measurement (section 2.4). Care must be taken to avoid a possible confusion between the definitions of porosity and void ratio. 

An alternative approach to measurement of lignin distribution is to assess variation in the porosity of wood which has been hydrolyzed to form a lignin skeleton (Donaldson 1987). Hydrolysis with sulfuric acid is particularly useful because of the swelling that occurs. This magnifies areas of the cell wall such as the S3 layer or the compound middle lamella which would otherwise be too small to measure. 

Wood which has been hydrolyzed in 72% sulfuric acid for 3h at 70°C is washed exhaustively in water, dehydrated in acetone, and embedded in Spurr resin. Measurements of refractive index are made in the same way as described above. In addition, an assessment of porosity is carried out as follows For sections mounted in glycerol, o.p.d. is measured in the regions to be compared, e.g., S3 and S2. These measurements are then converted to effective thickness values using the following equation  

Relative porosity can then be determined by comparing the effective thickness of two regions, e.g., S3 and S2, using the following equation  

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NMR has proven to be a valuable tool for formation evaluation by well logging, downhole fluid analysis and laboratory rock characterization. It gives a direct measure of porosity as the response is only from the fluids in the pore space of the rock. The relaxation time distribution correlates with the pore size distribution. This correlation makes it possible to estimate permeability and irreducible water saturation. When more than one fluid is present in the rock, the fluids can be identified based on the difference in the fluid diffusivity in addition to relaxation times. Interpretation of NMR responses has been greatly advanced with the ability to display two distributions simultaneously. 

S. Anferova, V. Anferov, D. G. Rata, B. Bliimich, J. Arnold, C. Clauser, P. Blunder, H. Raich 2004, (A mobile NMR device for measurements of porosity and pore size distribution of drilled core samples), Concepts Magn. Reson. Part B 23B (1), 26-32. 

Relation 9.77 is usually called the Washburn equation [55,237], One should consider it as a special case of the fundamental Young-Laplace equation [3,9-11], Washburn was the first to propose the use of mercury for measurements of porosity. Now, it is a common method [3,8,53-55] of psd measurements for a range of sizes from several hundreds of microns to 3 to 6 nm. The lower limit is determined by the maximum pressure, which is applied in a mercury porosimeter the limiting size of rWl = 3 nm is achieved under PHg = 4000 bar. The measurements are carried out after vacuum treatment of a sample and filling the gaps between pieces of solid with mercury. Further, the hydraulic system of a device performs the gradual increase of PHg, and the appropriate intmsion of mercury in pores of the decreasing size occurs. 

Powder densification can be followed with measurements of porosity and force by means of the Heckel or Athy/Heckel equation [1] ... 

Kleinberg et al. (2005) and Takayama et al. (2005) show that NMR-log measurement of sediment porosity, combined with density-log measurement of porosity, is the simplest and possibly the most reliable means of obtaining accurate gas hydrate saturations. Because of the short NMR relaxation times of the water molecules in gas hydrate, they are not discriminated by the NMR logging tool, and the in situ gas hydrates would be assumed to be part of the solid matrix. Thus the NMR-calculated porosity in a gas-hydrate-bearing sediment is apparently lower than the actual porosity. With an independent source of accurate in situ porosities, such as the density-log measurements, it is possible to accurately estimate gas hydrates saturations by comparing the apparent NMR-derived porosities with the actual reservoir porosities. Collett and Lee (2005) conclude that at relatively low gas... 

The other measure of porosity, i, is only that fraction of volume between the particles... 

Various techniques, such as intrusion methods, image analysis and weight determinations are used to provide estimates of the porosity and the distribution of pore sizes within a tissue scaffold. This preliminary study of the structural features of particulate-leached PCL scaffolds has shown that reliable measures of porosity can be obtained from simple weighing measurements (Buoyancy method). 

A second criticism that can be levelled at the use of nitrogen adsorption manometry is the measurement of porosity in the upper mesopore range. Indeed, accurate pressure measurements in the region close to the saturation pressure are difficult and can be influenced by small variations in temperature (e.g. due to a decrease in level of liquid nitrogen in the cryostat). In such cases, the use of a constant level cryostat can be useful. Errors made in this pressure region greatly affect the calculation of pore size as the BJH calculation introduces a log pressure term. 

A wide range of manufacturing operations calling for measurement of properties as diverse as hot tear strength (for moldings extracted from heated molds), compression modulus (as a measure of porosity), coefficient of friction (for surface-treated components such as latex gloves and windscreen wiper blades) and adhesion strength (for rubber-to-fabric or rubber-to-metal bonds)... 

Rough SL, Bridgewater J, Wilson DI (2002) In situ measurements of porosities and permeabilities of alumina pastes. J Powder Technology 123 262-274... 

A change of signal strength by a factor of 2 is 6 dB and by a factor of 10 is 20 dB. The attenuation of the ultrasound depends on frequency for example, at 5 MHz in a composite laminate, the attenuation could be in the range of 1.5—2dB/mm, whereas at 1 MHz the values could be half of that. The values are subject to the specifics of the fibers, resin, fiber-to-resin ratio, ply type, and layup. They are also subject to the specifics of the ultrasonic inspection equipment. Because consolidation is compromised by porosity, the attenuation will increase. The measurement of porosity level by ultrasonic attenuation is used for acceptance of the composite product. Calibration curves must be developed for the specific equipment, and the level of dB loss as a function of porosity for each thickness of composite established. A typical criterion is that less than 2% porosity is acceptable for manufacturing processes. Greater than 4% porosity can result in a significant knockdown in performance. 

Permeability, which characterizes the ability of rocks to allow the movement of fluids contained in their pores, is one of the most important parameters describing the porous media. Normally, in order to measure the permeability, the sample must have a simple geometric shape (e.g. cylinder or cube) and certain dimensions. On the other hand, measurements of porosity, pore-size distribution, and specific surface area do not require special geometric dimensions. The correlations among permeability and other easier-to-measure parameters, therefore, have been studied theoretically and experimentally. In practice, the most often reported correlation is that between the permeability and porosity The coefficient of correlation for porosity-permeability relationship varies from sample to sample, with a better correlation if the porosity used in the calculation is measured when a core contains the irreducible fluid. Porosity does not reflect the number and width of fractures, the pore sizes and topological structure, whereas the specific surface area does. Thus, it appears advisable to relate permeability simultaneously to porosity, specific surface area, irreducible water/oil saturation, grain size/pore size/throat size distribution, tortuosity, etc. 

Maehara T, Yonamine A, Sonegawa T, Itoh N (2000) Measurement of porosity of porous silicon using x-ray refraction effect Jpn J Appl Phys 39 3649-3656 Mazumder S, Sen D, Sastry PUM, Chitra R, Sequeira A, Chandrasekaran KS (1998) Small angle x-ray scattering of porous silicon at two different wavelengths. J Phys Condens Mater 10(44) 9969-9974... 

Permeability. The rate of flow of a fluid (usually air) through a porous ceramic material per unit area and unit pressure gradient. This property gives some idea of the size of the pores in a body -whereas the measurement of porosity (q.v.) evaluates only the total pore volume. From the permeability of a compacted powder the specific surface (q.v.) of the powder can be deduced. B.S. 1902 Pt. 3.9 describes a gas permeability test applicable to refractory materials, as does ASTM C577. The ASTM C866 test for the filtration rate of whiteware clays depends on their water permeability. See blaine test carman equation lea and nurse... 

Porosimeter. A term variously applied to apparatus for the measurement of POROSITY (q.v.) or of pore-size... 

Roge, B., Fahr, A., Giguere, J.S.R., and McRae, K.I. (2003) Nondestructive measurement of porosity in thermal barrier coatings. J. Therm. Spray Technol, 12 (4), 530-535. 

Figure 6.10 shows how the permeability of cement paste increases with the tvic ratio. At first it increases slowly and beyond wIc = 0.5 it increases rapidly. The permeability may therefore be regarded as an indirect and partial measure of porosity. Considering the components of cement-based composites it may be assumed that the permeability is determined more by matrix properties than by aggregate ones. Particularly, the matrix/aggregate interface may have the largest content of pores and microcracks which affect the overall permeability (cf. Chapter 7). 

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