As function of pore size

Pore size distribution—distribution of the volume of the pores as function of pore size. 

Moreover, isopiestic water sorption data and dynamic vapor sorption (Soboleva et al., 2011) provide information on water uptake as a function of relative humidity in the surrounding gas phase. This information, if combined with pore size distribution data, could help determine the wetting angle in pores or the Gibbs energy of water sorption as functions of pore size. 

Figure 3.39. Typical value.s for the diffusion coefficient as a function of pore size.

Spry and Sawyer (1975) developed a model using the principles of configurational diffusion to describe the rates of demetallation of a Venezuelan heavy crude for a variety of CoMo/A1203 catalysts with pores up to 1000 A. This model assumes that intraparticle diffusion is rate limiting. Catalyst performance was related through an effectiveness factor to the intrinsic activity. Asphaltene metal compound diffusivity as a function of pore size was represented by... 

Fig. 56. Model computation for the demetallation rate as a function of pore size and time on stream for first-order kinetics and configurational diffusion of a 12.5-A-diameter metal-bearing molecule (Rajagopalan and Luss, 1979).

If all the pores are equally accessible, only those for which r is greater than y cos 6 p will be filled, i.e. each pressure increment causes a group of smaller pores to be filled and a cumulative pore volume as a function of pore size can be determined, as illustrated in Figure 5.9. 

Table 8.3. Molecular Weight as a Function of Pore Size in Gels...

Fig. 2. (a) Volume fraction of fully functional pores as a function of pore size for various preparation conditions, (b) Order parameter indicating the fraction of imprinted pores that are fully functional. Curves correspond to the same preparation conditions as in Fig. 1. 

For the pure alumina sample the chosen model for computing cumulative surface area. SedB, cumulative volume Fedn and surface area and volume distribution as a function of pore size is a cylinder closed at one end. This choice is motivated by the type IV shape of the isotherm and by the E type hysteresis. In the case of the cylinder model closed at one end, the relevant branch of the isotherm is the adsorption. The calculation is carried out from the saturation pressure down to the pressure corresponding to the hysteresis loop s closing. The cumulative specific surface area, SadB, is close to both 5bet and St values for the pure mesoporous material, X(0) (Table 1). 

In Fig. 9a and 9b the orders of magnitude of the different diffusion coefficients and the activation energy for diffusion are given as a function of pore size [36], For diffusion in micropores (<2 nm in diameter), the diffusivity can vary over several orders of magnitude, depending on the size and nature of the diffusing species and the microporous media. Diffusion in micropores is often referred to as configurational diffusion. 

Electro-osmotic flow rate is not a function of pore size, but is directly related to the applied electrical charge. Power requirements are as high as 100 volts and 40 amperes. Typical flow volume is of the order of several gallons per hour. 

The pore pressure is directly responsible for the molecular layering and the pore filling. Having described the pore pressure, we now address the molecular layering process. This process can be described by any appropriate equation. If there is no or weak fluid—fluid interaction, we can use the BET-type equation, while if the fluid-fluid interaction is strong we can use the modified Hill-de Boer equation as suggested by Do and Do [63] to calculate the adsorbed film thickness t. In these equations the affinity constant is a function of pore size and the pressure involved in those equations is the pore pressure. 

Figure 12.3 Integral adsorption enthalpy and corresponding immersion enthalpy as a function of pore size, as calculated by DFT for the filling of a sUt-shaped pore by a monoatomic fluid. (Adapted fi om [72].)...

Vogel, H.J. 1997. Morphological determination of pore connectivity as a function of pore size using serial sections. Eur. J. Soil Sci. 48 365-377. 

Hsu et al. [88], during measurement of the thermal conductivity of porous partially stabilized zirconia, used a two-flux radiation model to infer the effective radiative extinction coefficient as a function of pore size. They present a correlation of the data of the form... 

In the case of nitrogen physisoiption at 77 K, the pore condensation phenomenon takes place in materials exhibiting pores larger than 2nm (mesopores). At a given temperature, the condensation pressure is a function of pore size. Considering three mesoporous solids having the same pore size but with different pore shapes, such as cylindrical, spherical, and slit-like, indicate whether pore condensation pressure would also be a function of pore shape. Justify your answer. 

Along with vapor pressure, condensation rate is also an important parameter in membrane stability. The condensation rate is a measure of the liquid membrane s ability to replenish its liquid content and is especially important when the membrane is used with backside pumping. Condensation rates were measured as a function of pore size for the aqueous LiBr liquid membrane. Figure 6 illustrates the dependence of condensation rate on pore size. These results, along with die vapor pressure results, indicate that polymer supports with small pore diameters should be used to optimize aqueous membrane stability. 

Figure 9.2 demonstrates the volume of mercury intruded into a sample as a function of pore size. In the flrst part of the curve, the mercury Alls the spaces between the particles—inter-particle void. The particle density equals the ratio... 

Water flux and %rejection as a function of pore size rating of membranes used in cross-how systems. Source Amicon. 

Cranston and Inkley (1957) provided tables for R,2, kj2 and the critical relative pressure as a function of pore size. They also tabulated (r - ti2)/r for the second term in the RHS of eq. (3.10-25). 

In this section predictions are made using the model to demonstrate the different transport behaviours with varying pore size and temperature. Figure 5.11 predicts the permeability P as a function of pore size d for the different transport mechanisms, described earlier, with Equation (5.21) as the definition for W. For activated diffusion AE = IWI and for surface diffusion AEs = aq = aW. The results represent the permeability within a single pore. In reality there will be a distribution of pore sizes, and therefore the transition... 

As explained earlier, the permeability for surface diffusion is dominated by the surface concentration and therefore the model predicts a peak at which the heat of adsorption is maximized. The permeability for Knudsen diffusion increases as a cubic function of pore size (see Equations 5.16 and 5.17) since the diffusivity depends linearly on the pore size d and the concentration depends on the volume of the pore (assuming cylindrical pores). 

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