Pore radius, average

The Washburn model is consistent with recent studies by Rye and co-workers of liquid flow in V-shaped grooves [49] however, the experiments are unable to distinguish between this and more sophisticated models. Equation XIII-8 is also used in studies of wicking. Wicking is the measurement of the rate of capillary rise in a porous medium to determine the average pore radius [50], surface area [51] or contact angle [52]. 

When the average pore radius decreases to r, the rate of filtration becomes ... 

The reference Pt-Ba/y-Al203 (1/20/100 w/w) catalyst shows surface area values in the range 140-160 m2/g, a pore volume of 0.7-0.8cc/g and an average pore radius close to 100 A (measured by N2 adsorption-desorption at 77 K by using a Micromeritics TriStar 3000 instrument). Slight differences in the characterization data are associated to various batches of the ternary catalyst [24,25],... 

To develop analytical models for processes employing porous catalysts it is necessary to make certain assumptions about the geometry of the catalyst pores. A variety of assumptions are possible, and Thomas and Thomas (15) have discussed some of these. The simplest model assumes that the pores are cylindrical and are not interconnected. Develop expressions for the average pore radius (r), the average pore length (L), and the number of pores per particle (np) in terms of parameters that can be measured in the laboratory [i.e., the apparent particle dimensions, the void volume per gram (Vg), and the surface area per gram (Sg). ... 

We will start by developing an expression for the average pore radius T. If we denote the mass of an individual catalyst particle by raP, simple geometric considerations indicate that the void volume per particle is given by... 

The Knudsen diffusion coefficient may be evaluated from equation 12.2.4 if the catalyst property values are used to estimate the average pore radius. From equation C of Illustration 6.2,... 

Porosimetry data can be graphed in a variety of ways and can be tailored to the purpose of the study. Plotting volume versus pore size will easily display the pore sizes observed in the sample. Pore size distributions can be calculated from the raw data and plotted to give the pore volume per unit radius interval. Other parameters can be calculated from porosimetry data, including average pore radius [40,48], surface area [7,39,40], pore surface area [6], particle size [40], and density [6,49]. 

Fig 1- Effect of the polymerization temperature on the pore size distribution. At the highest temperature (T+8) the average pore radius is 400 nm while at the lowest T the pores are much larger with an average pore radius of 850 nm... 

The Wheeler model thus provides an average pore radius, r and pore length, L, in terms of the experimentally determinable parameters v, and fj. The only adjustable parameter is the roughness factor, r. The usefulness of this model was demonstrated by Wheeler, who successfully predicted the reaction rates of several catalytic reactions of industrial importance. 

The paracellular permeation pathway in the intestinal cell monolayer models is often limited. Therefore these models are not suitable for predicting permeability of paracellularly absorbed compounds. The average pore radius in Caco-2 cells (<6 A) is more representative of the colon than the small intestine (8-13 A)and paracellular transport can be up to 100-fold lower in Caco-2 cells than in the small intestine. Investigation of a rat intestinal cell line 2/4/Al, which forms polarized cell mono-layers and has an average pore radius (9 A) more representative of the small intestine, showed improved prediction of oral absorption for incompletely absorbed drugs [24, 25]. 

In addition to the packed bed acting as an ultrafilter, the porous frits used at both ends of the column may act as very effective filtering devices. Thus a 2-vim porosity frit would have an average pore radius of 1 lun. Because of the tortuosity and relatively wide pore-size distribution present in frits, it would be safe to assume that it contains much smaller crevices which can entrap macromolecules. 

Here, Dk is in cm2/s, r the average pore radius (cm), MB the molecular weight of the gas (g/mol), and T the temperature in K. In the case of a narrow pore size distribution, die average pore radius can be estimated as follows (Froment and Bishoff, 1990) ... 

Step 2 Calculation. Determination of the average pore radius Rbi Only a uniform pore of Rbi is considered. Rb.,>i, a, and h can be considered to be equal to zero. Because B and D values are known from the first step, Rb,i can be immediately calculated from eq 6 by using available data of fi. 

Desig- nation Nominal Size Surface Area (m /g) Total Void Fraction Dt X 10s (cm2/sec) Average Tortuosity Factor t, Parallel-Path Pore Model r = 2K./5. (A) r Based on Average Pore Radius... 

Pore Volume, Surface Area, and Average Pore Radius of Si()> and Ni-SiOi... 

When the catalyst is a porous solid, most of the surface area of the catalyst is the surface area of the inner surface of the pores. Therefore, most of the reaction proceeds in the pore. Gas molecules are transferred to the outer surface of the catalyst by diffusion. Generally speaking, the diffusion is faster than the diffusion inside the pores. Gas molecules collide with the inner wall of the pore before they collide with another molecule for the porous catalyst having an average pore radius rp of a few nm. Such diffusion is called Knudsen diffusion and its diffusion constant D is given by ... 

The average pore radius of a catalyst particle is the average of the dominant pore radii as observed from the frequency plot of the catalyst. 

Mercury porosimetry measurements for a partially sintered alumina preform showed a bimodal pore size distribution with neck diameter Dn = 0.15 pm [Manurung, 2001], As a comparison with the pore sizes and distribution of the preform measured by porosimetry, SEM micrographs (Fig. 5.1) were taken before and after infiltration. Based on SEM examination, the pores in the preform before infiltration ranged in size from r 0.1-0.5 pm. Assuming an average pore radius of 0.3 pm, this radius is approximately four times larger than the pore-neck radius (Dn = 0.15 pm, so pore radius = 0.075 pm) determined by mercury porosimetry. 

Equation (5) holds for the catalyst used, as diffusion in the porous catalyst particle is of the Knudsen type (pore radius mean free path of the gas molecules). For this catalyst the average pore radius, f, calculated from the equation, for cylindrical pores... 

Kieselgel 60 a silica gel with an average pore radius 3.6 nm, obtained from Merck. 

The catalyst used in this study was triply-promoted 1 0, CaO and AlzO, iron supplied by United Catalyst Inc. Louisville, Kentucky, U.S.A. under the trade number "C 73-1-01 . Porosity is about 0.45 and average pore radius about 24 nm. To activate the catalyst, a 60-h reduction at 440°C in pure hydrogen at a space velocity of 1500 1/h was employed. By the end of this period, the activity had become constant. Long-term catalyst activity was checked frequently and, over the course of the study, remained constant. The percentage variation among runs made under identical conditions was within 4%. 

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