Pore penetration

The relationship between applied pressure (P) and the diameter of the smallest circular pore penetrated (d) by a liquid gas is given by the equation ... 

The estimation of the surface area of finely divided solid particles from solution adsorption studies is subject to many of the same considerations as in the case of gas adsorption, but with the added complication that larger molecules are involved whose surface orientation and pore penetrability may be uncertain. A first condition is that a definite adsorption model is obeyed, which in practice means that area determination data are valid within the simple Langmuir Equation 5.23 relation. The constant rate is found, for example, from a plot of the data, according to Equation 5.23, and the specific surface area then follows from Equations 5.21 and 5.22. The surface area of the adsorbent is generally found easily in the literature. 

Cevc, G., et al. 1998. Ultraflexible vesicles, transfersomes, have an extremely low pore penetration resistance and transport therapeutic amounts of insulin across the intact mammalian skin. Biochim... 

Figure 14.1 Schematic of olfactory sensillum and a generalized biochemical pathway of odor reception. A An olfactory sensillum includes 2-3 neurons surrounded by 3 support cells olfactory dendrites/cilia project up the fluid filled lumen of a cuticular hair. The sensillum lumen is isolated from hemolymph by a cellular barrier. Modified from Steinbrecht (1969) see Steinbrecht (1999) for more details. B Hydrophobic odor molecules enter the aqueous sensillum lumen via pores penetrating the cuticular hair wall. Hydrophilic OBPs are proposed to bind and transport odors to receptor proteins located in the neuronal membranes. ODEs (pathway I) in the sensellum lumen are proposed to degrade these odor molecules. Cytoplasm of support cells contain xenobiotic inactivating enzymes, such as glutathione-S-transferase (GST) (pathway I la) which may also serve to inactivate odor molecules (pathway lib). Interactions between OBPs and ORs and the function of SNMP are unclear. Modified from Rogers et al. (1999).

Fig. 4 shows two STM images of the surface structure of a carbon black. The sample exhibits a specific surface area, determined by N2 adsorption at 77 K, of 15.3 m g, which is almost coincident with its geometric area (16.9 m g ). Therefore, this is a nonporous carbon and its STM images should be expected to differ from those of the ACFs. As a matter of fact, this is what can be observed in Fig. 4. First, it is noted that the carbon black does not display any mesoporosity (Fig. 4a) such as that of the AFCs (Fig. 2). Second, at the micropore scale the carbon black porosity is also very poorly developed (Fig. 4b) in comparison with the pore development of ACFs (e.g.. Fig. 3a). In the former case (Fig. 4b), altough some trenches are also present, they are very shallow and, consequently, are simple topographic variations of a smooth surface and cannot be considered as pores penetrating deeply into the material as in Fig. 3a. Also, pores of the type shown in Fig. 3b for the ACFs were not normally seen on the carbon black surface. Hence, all these observations agree with the lack of adsorption capabilities of this material.

A simple variation on the method described above was used by Tullberg et al. (1989) to select B16 melanoma cells of increased invasive (and metastatic) ability. Filters with pores of 10 /.tm are employed to avoid a selection for pore penetration, and coated with a thick layer (approximately 1 fim) of Matrigel , a reconstituted BM derived from EHS tumors (see Chapter 4 for more details). Cells are plated on the coated filters at a density that is lower than that used for the migration selection, since in this case the time it takes for the cells to migrate can be considerably higher, and excessive growth on the upper side of the filter has to be prevented. Optimal conditions have to be empirically determined for each cell line. Cells that have invaded and passed to the underside of the filter are collected and expanded as described above, and further selections can be made to obtain a fairly homogenous cell population of increased invasive potential, from which clones can be derived. 

Practical determination of the porosities often suffers some difficulties. The most common method for determining the total porosity is the injection of a non-retained, pore-penetrating tracer substance (grey and small black circles in Fig. 2.5). In normal phase chromatography, toluene or 1,3,5-tri-tert-butylbenzene are often used, while in reversed phase chromatography uracil is the component of choice. 

Note that the first moment in this case is independent of any mass transfer and dispersion coefficients and thus equivalent to the retention time obtained for the ideal model (Eq. 6.50). The factor k is a modified retention factor that is zero for non-pore-penetrating tracers. It is connected to k (Eq. 2.1) by ... 

Brinker and coworkers [49] reported the synthesis of microporous silica membranes on commercial (membralox) y-alumina supports with pore diameters of 4.0 nm. Ageing of the silica sols was shown to be effective to form discrete membrane layers with an estimated thickness of 35 nm on top of the support and to inhibit pore penetration of the silica. Sols with gyration radii Rg < (radius of support pores) penetrate the support to a depth of about 3 im, which is the thickness of the y-alumina support layer. Minimization of the condensation rate during film formation was considered to decrease the width of the pore size distribution without changing the average pore radius, which was estimated to be 0.35 < Tp < 0.5 nm. The porosity of films deposited on dense supports was about 10% as calculated from refractive index measurements. 

For microporous membranes only the porous part of the surface (e) is available for penetration the solid is assumed not to accept molecules. For small molecules hitting the surface under not too low angles it is reasonable to assume a low value of the activation energy for pore penetration (this is process Fx in Fig. 9.21). A pessimistic estimate for microporous silica membranes using values of e = 0.01 and t - 0.01 yields at 300 K and 1 atm a collisional flux (of H2) which is at least one order of magnitude larger than the permeation (flux) values found by de Lange et al. [63]. 

Cumulative pore penetration curves are obtained by measuring the volume of mercury forced into the solid at difierent pressures. Figure 7.14 shows a typical mercury porosimeter and Fig. 7.1S a cumulative penetration curve. Derivative distribution data are also given in Fig. 7.15. Until recently, most porosimeters were limited to pressures of 3.5 x 10 atm. From Table... 

FIGURE 16.7 (a) Current and (b) potential difference profiles as a function of the relative pore penetration... 

FIGURE 16.9 Current profiles as a function of the relative pore penetration distance in a thin-layer cylindrical pore electrocatalyst. Only small polarizations and high-conductivity electrolytes are considered. ja = 1CT5 A cm 2. A4>0 = 0.10 V (grey line), A<1>0 = 0.15 V (dashed line), /0 = 10 7 A cm-2. A0 = 0.10 V (dotted line), A4>0 = 0.15 V (continuous line). 

Pores in composite materials are typically open, and form chains of pores, penetrating the whole matrix. Wood fiber is exposed to these pores. Hence, higher... 

Chromatographic processes can be classified according to the type of equilibration process involved, which is governed by the type of stationary phase. Various bases of equilibration are (1) adsorption, (2) partition, (3) ion exchange, and (4) pore penetration. 

The apparent permeability, a function of the proportion of pores penetrated by the mud filtrate, can be determined from the pore size distribution curve, absolute permeability and porosity of the rock material (Tan et al., 1996a). The methodology is based on a simple capillaric model which represents a porous medium by a bundle of parallel capillaries (Scheideggar, 1974). From the law of Hagen-Poiseuille, the absolute permeability of such a model is given by ... 

Hermia (1982) introduced the Filtration Laws, which aim to describe fouling mechanisms. The models are valid for unstirred, dead-end filtration (deposition without cake dismrbance due to shear and no gravity settling) and complete rejection of solute by the membrane (but obviously allowing pore penetration). Under conditions where permeate drag dominates, the effect of stirring may be negligible. The constant pressure filtration law is shown in equation (3.11). 

Colloids are retained effectively by UF due to the small pore sizes of the membranes, compared to MF. However, if colloids are very small, then pore penetration can occur. Kim et al (1993) found a higher colloid rejection in stirred conditions using silver sol. Particle penetration into the membrane was highest at low salt concentrations. In the absence of salt, particle-membrane interactions dominated, whereas at high salt concentrations aggregation enhanced rejection. 

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