Equivalent diameter, pore

The limits of pore size corresponding to each process will, of course, depend both on the pore geometry and the size of the adsorbate molecule. For slit-shaped pores the primary process will be expected to be limited to widths below la, and the secondary to widths between 2a and 5ff. For more complicated shapes such as interstices between small spheres, the equivalent diameter will be somewhat higher, because of the more effective overlap of adsorption fields from neighbouring parts of the pore walls. The tertiary process—the reversible capillary condensation—will not be able to occur at all in slits if the walls are exactly parallel in other pores, this condensation will take place in the region between 5hysteresis loop and in a pore system containing a variety of pore shapes, reversible capillary condensation occurs in such pores as have a suitable shape alongside the irreversible condensation in the main body of pores. 

Fig. 3.3.5 Propagators for water flow at 2.93 mm3 s-1 through the fixed-bed reactor (a) spherical glass beads, pore diameter dp = 2 mm and (b) cylindrical pellets with average equivalent diameter of 2.2 mm.

Figure 28a shows the result of SAXS on sample BrlOOO. We used Guinier s formula (see eq. 6) for the small angle scattering intensity, I(k), from randomly located voids with radius of gyration, Rg. Although Guinier s equation assumes a random distribution of pores with a homogeneous pore size, it fits our experimental data well. The slope of the solid line in Fig. 28b gives R - 5.5 A and this value has been used for the calculated curve in Fig. 28a. This suggests a relatively narrow pore-size distribution with an equivalent spherical pore diameter of about 14A. Similar results were found for the other heated resin samples, except that the mean pore diameter changed from about 12 A for samples made at 700°C to about 15 A for samples made at 1100°C.

Indeed, it is easy to define the size (sizes) of simple particles (e.g., in the case of spherical globules or cylinders). But, for many real PSs, the form of particles and pores is complicated. The sizes of complicated particles or pores are expressed with equivalent diameters (sizes). The particular choice of an equivalent is directed by measuring the technique or other reasons. Following are some frequently used expressions for equivalent diameters [52] ... 

For equation 4.6 to be generally useful, an expression is needed for d m, the equivalent diameter of the pore space. Kozeny(5,6) proposed that d m may be taken as ... 

Table 10.1 Examples of soil pore classifications, with description of equivalent soil water phenomena and matric pressures a brief illustration of the soil system in those conditions is also given d represents the equivalent diameter of pores and is expressed in /tm, unless otherwise stated...

Table 6.8 presents the details of calculations for spherical particles with an equivalent diameter of 2.4mm. It may be observed that the pore diffusion considerably affects the process rate, particularly at higher temperatures. The external mass transfer plays a minor role. Their combination leads to a global effectiveness that drops from 75% to 35% when the temperature varies from 160 to 220°C. Based on the above elements the apparent reaction constant may be expressed by the following Arrhenius law ... 

Catalyst Type Pore Volume (cm3/g) Surface Area (m2/g) Equivalent Diameter (mm)... 

The computer-generated reconstruction in Fig. 19 is consistent with the mercury porosimetry result. The random 3-D network of Fig. 19 contains pore elements up to 3 p.m in diameter. The computer image, however, shows pore features up to 9 p.m in (equivalent) diameter. The imaged representation exhibits these large pore features due to overlapping of pores as the plane section passes close by pore junctions (nodes). A feature may thus contain elements of several pores and thereby appear enlarged in the plane of the section. This aggregation of pore sections is readily discernible in Fig. 19, just as it was in the previous illustrative example in Fig. 16. 

If in addition to the motionally restricted layers described above, the pores are totally filled with water, the amount of water added in excess of the restricted two layers will depend on the free equivalent diameter, ts, shown in Figure 5. If di, is the diameter of the bulk water cluster or aggregate (0826) at room temperature, then two ranges can be defined for the size of ta. 

In what follows we derive an empirical relation for the permeability, known as the Kozeny-Carman equation, which supposes the porous medium to be equivalent to a series of channels. The permeability is identified with the square of the characteristic diameter of the channels, which is taken to be a hydraulic diameter or equivalent diameter, d. This diameter is conventionally defined as four times the flow cross-sectional area divided by the wetted perimeter, and measures the ratio of volume to surface of the pore space. In terms of the porous medium characteristics. 

Airborne PM samples with an aerodynamic equivalent diameter of less than 10 microns (PMio) were collected with a high-volume sampler (DHA-80, Digitel) on cellulose nitrate filters with a diameter of 150 mm and a pore size of 3 pm. The total volume of air sampled for the collection of PM was about 4,500 m for the rural locations and 1,400 m for the sampling location in the city of Frankfurt am Main. 

The velocity U is defined as the ratio of the liquid s volume flow rate to the net cross section of all spacings between particles in the given layer of porous medium. It is obvious that U < Ug, since also includes the volume flow rate of liquid through the pores of particles. The constant k is known as permeability (its dimensionality is m ). In order to determine k, we must choose a certain model of porous medium. A low-permeable porous medium can be conceptualized as a medium consisting of a set of microchannels of diameter de (it is called hydraulic, or equivalent, diameter). This diameter is usually defined as... 

The accessible stationary phase surface is smaller in relation to the column volumes, which results in a lower loading capacity and smaller retention factors compared with fully porous materials with an equivalent diameter of diffusion pores. 

S is the ratio of the surface area of the medium to its pore volume and stands for equivalent diameter of the pores. The hydraulic (mean) radius m is defined as the ratio of the average pore cross-sectional area to the average wet perimeter, in line with the concept of the equivalent loads (as explained in Section III). All the geometrical parameters from Eq. (19) can be estimated for particulars of the porous media. For example, in the case of aligned fibers, hydraulic radius and equivalent diameter can be expressed by ... 

The catalysts for ammonia synthesis are porous particles with weenie and interlaced micro-pores. The active sites playing the role of surface catalysis are distributed on the internal surfaces formed by these micro-pores. The internal surface area of ammonia synthesis after reduction is about 10m -g -15m -g , and the external surface area is only 0.1 m g F So, the surface area playing the role of surface catalysis mainly is internal surface. The equivalent diameter of catalyst particles used in industrial ammonia reactor is between 1.5 mm and 13 mm, and the inhibition effect of diflfusion should be considered in real ammonia synthesis rates. When designing industrial reactor, the resistance of external diffusion can be neglected by increasing contact between gas flow and external sm-face of catalysts. The catalytic reaction processes for ammonia synthesis pertain to considerable internal diffusion process in most cases. 

Porosity data Specific volume of the sample (Vs), specific pore volume (Pp), and foam porosity (e), measured by pycnometry. Deq. Equivalent average pore diameter determined from SEM image analysis Deq). Foam porosity determined by X-ray microtomography S). 

In order to quantify these observations, the pore size distribution was calculated using image analysis techniques. The used image analysis algorithms are described elsewhere [8] and enable the statistical distribution of the equivalent diameter of the pores Z)eq to be assessed. For the sake of comparison, only macropores smaller than 500 tun were evaluated, i.e. ultramacropores observed only in the Al foam were not considered. 

Sometimes catalyst pores not covered by the liquid film are not filled with liquid due to evaporation phenomena caused by an excess of heat of reaction. If both reactants A and B have an appreciable vapor pressure at the working conditions, they can react as gaseous reactants after diffusing inside the catalyst pores. In this case inter-particle diffusion resistance is strongly reduced (at least 10 times) and the reaction rate can be very fast. These last phenomena are not significant in Slurry Reactors where the catalyst particles are always completely wetted and are much smaller - 0.1 mm (equivalent diameter) instead of 10-50 mm as in TBRs. 

Several recorded pulses from the same air bubble dissolving in an undersaturated 46 wt% sucrose/0.1 M NaCl solution at 26°C are shown in Figure 3. The bubble was reversed twice every second. All pulses are for the same flow direction and the pulse form reveals that the 22 pm equivalent diameter and 110 pm long mica pore is not completely smooth. The pulse width decreases with bubble size as expected. 

There are various methods devised for characterizing open pores for their size by regarding them as capillaries and determining their equivalent diameter from the rate of fluid flow through them or the extent to which liquid mercury can be forced into them. 

Mercury porosimetry (MP) is an extremely useful technique to characterize pore structure of materials (Giesche, 2006). This method measures an average diameter of open pores and its distribution, total volume of pores, specific surface, density, etc. Limitation of this method is that high pressures can distort the actual pore structure. Besides it does not give the actual size of pores or capillaries, but equivalent diameter of model cylindrical pores. Closed pores are inaccessible to mercury and cannot be studied. 

Spunbonded fabrics are effective filters in that they are layered stmctures of relatively fine fibers, the three-dimensional stmcture of which creates a torturous path. Even relatively thin spunbonded fabrics (eg, 0.2—0.25 mm) present a significant challenge to the passage of soil fines and are suitable for use in some filtration appHcations. The porosity of geotextile fabrics is classified by means of several procedures such as flux (volume flow/area per time) and equivalent opening size (EOS), which is a measure of the apparent pore size of the openings in the fabric. The flux measures the porosity to Hquid water, and the EOS measures the porosity to soHd particles of a known diameter. Literature is available on limitations of particular styles of fabrics within an apphcation (63). 

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