Surface Area, Porosity, and Permeability

Some very interesting and important phenomena involve small particles and their surfaces. For example, S02 produced from mining and smelting operations that extract metals such as Cu and Pb from heavy metal sulfide ores, can be oxidized to S03 in the atmosphere, thus contributing to acid rain problems. 

Here the reaction rate depends not only on the concentration of the S02 but also on the surface area of any catalyst available, such as airborne dust particles. The efficiency of a catalyst depends upon its specific surface area, Asp, defined as the ratio of surface area to mass [30], Accordingly, this property is frequently used as a basis for comparing different kinds of catalysts, or catalyst supports, and for diagnosing practical problems in catalysts being used in a process (since both agglomeration and poisoning reduce Asp). The specific surface area of the airborne dust particles, considering n spheres of density p and radius R, would be  

Asp= ( particles)(area/particle) / ( partides)(mass/particle) 

Emulsions, Foams, and Suspensions Fundamentals and Applications. Laurier L. Schramm Copyright 2005 WILEY-VCH Verlag GmbH Co. KGaA, Weinheim ISBN 3-527-30743-5 

Example. Consider two 1 g samples of silica spheres, in one sample the spheres are 1mm diameter, in the other they are 1 pm diameter. The total mass of each is the same (density 2 g/cm3), do they also have the same amount of surface area  

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The specific surface area depends on both the size and shape and is distinctively high for colloidal-sized species. This is important in the catalytic processes used in many industries for which the rates of reactions occurring at the catalyst surface depend not only on the concentrations of the feed stream reactants, but also on the surface area of catalyst available. Since practical catalysts are frequently supported catalysts, some of the surface area is more important than the rest. Also, given that the supporting phase is usually porous, the size and shapes of the pores may influence the reaction rates as well. The final rate expressions for a catalytic process may contain all of these factors surface area, porosity, and permeability. 

A modelling approach that could fulfil this need is based on the stationary-state approximation to coupled fluid flow and water-rock interaction (Lichtner 1985, 1988). This model represents the chemical evolution of an open, flow-through system as a sequence of relatively long-lived stationary states of the system, which are linked in time by short-lived transients. The basis for the model is the observation that within a representative elemental volume of a rock-water system, the aqueous concentration of any particular species is generally much less than its concentration in minerals. Long periods of time are therefore necessary to dissolve, or precipitate, minerals such that the spatial distribution of mineral abundances, surface area, porosity and permeability is altered significantly. Each time interval represents a stationary state of the system, in which fluid composition, reaction rates and the distribution of primary and alteration minerals vary only as a function of position in the flow path, not of time. 

The performance of the hollow-fiber dialyzers depends on many fiber properties such as fiber dimension, surface area, porosity and water permeability. 

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. 

In this study, the author examined the interrelationship among permeability Ar, porosity 0, specific surface area s, and residual water saturation S r for carbonate reservoirs of USSR. Parameters influencing the permeability most were included, whereas unnecessary ones were not used. 

Figure 6 also shows Smith s [10] values on silica. The surface area in this earlier study was 1 m /g sand determined by BET technique. In our study, the surface area was 0.123 mVg sand determined by BET technique. (The surface area calculated from permeability and porosity gave a 0.119 m /g value using equations from Pirson [14].) Therefore, Smith s mg/g values were divided by 8.13 in Figure 6. 

In the past 10 years, electrospun nanofibrous membranes have been spotlighted as an effective filter media to capture fine particles. In addition to the basic studies of electrospinning process to better understand the membrane construction process, researchers from all over the world focus on the study of the relationships between the structure characteristics of electrospun nanofibrous membranes (fiber diameter, pore size, porosity, surface area, etc.) and filtration performances (filtration efficiency, pressure, air permeability, etc.). In this chapter, recent advances in fabricating nanofibrous filter media via electrospinning process have been reviewed. In particular, filtration performances and relevant mechanical properties are discussed in detail. It is interesting that the electrospun nanofibrous membranes have been able to outperform conventional nonwoven membranes fabricated essentially by using the meltblown or spunbonded process. 

Surface Area and Permeability or Porosity. Gas or solute adsorption is typicaUy used to evaluate surface area (74,75), and mercury porosimetry is used, ia coajuactioa with at least oae other particle-size analysis, eg, electron microscopy, to assess permeabUity (76). Experimental techniques and theoretical models have been developed to elucidate the nature and quantity of pores (74,77). These iaclude the kinetic approach to gas adsorptioa of Bmaauer, Emmett, and TeUer (78), known as the BET method and which is based on Langmuir s adsorption model (79), the potential theory of Polanyi (25,80) for gas adsorption, the experimental aspects of solute adsorption (25,81), and the principles of mercury porosimetry, based on the Young-Duprn expression (24,25). 

All packing materials produced at PSS are tested for all relevant properties. This includes physical tests (e.g., pressure stability, temperature stability, permeability, particle size distribution, porosity) as well as chromatographic tests using packed columns (plate count, resolution, peak symmetry, calibration curves). PSS uses inverse SEC methodology (26,27) to determine chromatographic-active sorbent properties such as surface area, pore volume, average pore size, and pore size distribution. Table 9.10 shows details on inverse SEC tests on PSS SDV sorbent as an example. Pig. 9.10 shows the dependence... 

This is very important as several other properties are dependent upon it. If the porosity is too high, the article will be weak and will not retain liquid. The pore structure should also be taken into account. When a ceramic material is hred, although the internal surface area decreases as the material approaches zero porosity, the mean radius of the pores increases. Thus, when the internal surface area is 3 mVg the mean pore radius may be of the order of 10 m, while when the internal surface has dropped to 0-5 mVg the mean pore radius may be about 4-5 x 10 m. The mean pore radius may reach a value as high as 9 x 10 m as the ware approaches zero porosity during firing. It is thus obvious that at some point the pores must start to close up. This closing of the pores with the approach of vitrification is borne out by results of permeability measurements. 

High performance monolithic columns were prepared from styrene and divinyl-benzene (PSDVB, 200 pm i.d.) (Oberacher et al., 2004). The monoliths possess 5-300 nm pores with porosity of ca. 50% and 20% for external and internal pores, respectively, with specific surface areas of 30-40 m2/g. The column showed permeability K= 3.5 x 10 15m2 in water and slightly less in acetonitrile. The pore size... 

Karathanasis AD, Johnson DMC, Matocha CJ (2005) Biosolid colloid mediated transport of copper zinc and lead in waste-amended soils. J Environ Qual 34 1153-1164 Kieffer B, Jove CF, Oelkers EK, Schott J (1999) An experimental study of the reactive surface area of the Fontainebleau sandstone as a function of porosity, permeability, and fluid flow rate. Geochim Cosmochim Acta 63 3525-3534... 

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