Dispersion cylindrical pore

To represent the elasticity and dispersion forces of the surface, an approach similar to that of Eqs. (3) and (4) can be taken. The waU molecules can be assumed to be smeared out. And after performing the necessary integration over the surface and over layers of molecules within the surface, a 10-4 or 9-3 version of the potential can be obtained [54,55], Discrete representation of a hexagonal lattice of wall molecules is also possible by the Steele potential [56], The potential is essentially one dimensional, depending on the distance from the wall, but with periodic variations according to lateral displacement from the lattice molecules. Such a representation, however, has not been developed in the cylindrical pore... 

Spontaneous wetting of the external surface of a solid is associated with zero contact angle, otherwise some work is necessary for complete wetting to be achieved. In the case of a powder we must also consider the penetration of liquid into the small channels inside and between the aggregates of the dry powder, and this is theoretically spontaneous only when 0 < 90° (assuming a hypothetical cylindrical pore). It may therefore be assumed that for the powder to be dispersed in the liquid as fine particles it is necessary for 0 < 90°, and that only when 0 = 0 would we expect the whole wetting process to be spontaneous—i.e.,... 

The adsorption process is, in this case, described with the help of a potential in between a perfect cylindrical pore of infinite length but finite radius, rp [18]. The calculation is made with the help of a model similar to those developed by Horvath-Kawazoe for determining the MPSD [18], which includes only the van der Waals interactions, calculated with the help of the L-J potential. In order to calculate the contribution of the dispersion and repulsion energies, Everett and Powl [45] applied the L-J potential to the case of the interaction of one adsorbate molecule with an infinite cylindrical pore consisting of adsorbent molecules (see Figure 6.20), and obtained the following expression for the interaction of a molecule at a distance r to the pore wall [18]... 

The Kelvin equation takes into account molecule/solid and intermolecular interactions using contact angle and surface tension, respectively. However, the Kelvin approach is not appropriate for de.scription of adsorption on small mesopores. Saam and Cole developed the thermodynamic theory with the average molecular potential for liquid helium in a cylindrical pore in order to understand unusual properties of liquid helium[19,20]. Findenegg et al have applied the Saam-Cole theory to elucidate fluid phenomena near the critical temperature[21]. The Saam-Cole theory includes the molecule/solid interaction in a form of the sum of the dispersion pair interactions. The Saam-Cole theory is fit for description of adsorption phenomena in regular mesopores[22j. 

Thermoporometry. This method is based on the observation that the equilibrium conditions of solid, liquid and gaseous phases of a highly dispersed pure substance are determined by the curvature of the interface (s) (10,17). In the case of a liquid (in this work, pure water) contained in a porous material (the membrane), the solid-liquid interface curvature depends closely on the size of the pores. The solidification temperature therefore is different in each pore of the material. The solidification thermogram can be translated into a pore size distribution of the membrane with the help of the equations derived by Brun (17). For cylindrical pores, with water inside the pores, it leads to the following equations ... 

Lindstrom and Boersma (1971) pioneered the prediction of breakthrough curves from equivalent cylindrical pore size distributions, determined by either the water retention or mercury porosimetry methods. The model developed by these authors includes the effects of bothintra- and interpore dispersion. In general, dispersion due to differences in tube size has a much greater influence on the shape and position of the breakthrough curve than mixing within tubes due to microscopic velocity profiles (Rao et al., 1976). For completeness, however, it is preferable to include both effects. Lindstrom and Boersma (1971) defined a CDE for each tube, so that C/C0 for the bundle as a whole is given by ... 

The frequency dispersion of porous electrodes can be described based on the finding that a transmission line equivalent circuit can simulate the frequency response in a pore. The assumptions of de Levi s model (transmission line model) include cylindrical pore shape, equal radius and length for all pores, electrolyte conductivity, and interfacial impedance, which are not the function of the location in a pore, and no curvature of the equipotential surface in a pore is considered to exist. The latter assumption is not applicable to a rough surface with shallow pores. It has been shown that the impedance of a porous electrode in the absence of faradaic reactions follows the linear line with the phase angle of 45° at high frequency and then... 

For porous electrodes, an additional frequency dispersion appears. First, it can be induced by a non-local effect when a dimension of a system (for example, pore length) is shorter than a characteristic length (for example, diffusion length), i.e. for diffusion in finite space. Second, the distribution characteristic may refer to various heterogeneities such as roughness, distribution of pores, surface disorder and anisotropic surface structures. De Levie used a transmission-line-equivalent circuit to simulate the frequency response in a pore where cylindrical pore shape, equal radius and length for all pores were assumed [14]. 

Considering the bed as an assemblage of randomly oriented cylindrical pores isuggests Y, 1/V 2, which is dose to the experimental values derived from dispersion measurements for gases at low Reynolds number. More detailed investigation reveals that the bed tortuosity (1/Yi) is related to the voidage. Wicke has suggested ... 

Fig. 2.6.8 Time-of-flight dispersion curves versus the encoding position of gas flowing through a cylindrically symmetrical glass phantom with large pores on the order of 1-cm diameter, obtained with slice selective inversion of magnetization. The flow direction changes twice as the gas is flowing from inlet to outlet. Slices parallel (upper) and perpen-...

The determination of the distance dependence of the steric repulsion between latex particles by measuring the osmotic pressure of dispersions at different volume fractions was first accomplished by Ottewill and coworkers (Barclay et ai, 1972 Cairns et al., 1976 Ottewill, 1976 1980). The apparatus used to make these measurements is shown in Fig. 13.4. The cell body was cylindrical in shape. Mercury was used as a piston in the cell. The dispersion was layered onto the top of the mercury and its level adjusted until it was just proud of the top of the cell. A millipore filter, of 0-2 pm mean diameter pore size, was placed centrally over the dispersion. A stainless steel top, fitted with a uniform bore capillary, completed the pressure cell. 

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