Pores hydraulic radius

In Eq.lO the Boltzmann population is assumed. Although the model predictions and experimental data are consistent, it is very difficult to state firmly that the equilibrium population of the states has already been reached. The population depends exponentially on the energy, and this in turn depends on the square of the oid radius, thus it is extremely sensitive to the accepted radius value. The pore radii acting in annihilation processes need not be identical with. say. the hydraulic pore radius. Additional distortion of experimental s. R dependence can be due to the difference in the efficiency of registration of 2y and 3y annihilation events. However, the results presented abo e indicate that the model parameter AR = 0.19 nm allows us to accept the commonly used LN pore radius in annihilation experiments... 

The mean hydraulic pore radius RH (estimated by the MP method) varied between 3.2 and 7.0 A. This parameter was slightly affected by the surfactant/ precursor ratio (SAA/TEOS) but increased with the surfactant chain length X. 

The properties of gas flow in porous media depend on the ratio of the number of molecule-molecule collisions to that of the molecule-wall collisions. The Knudsen number Kn is a characteristic parameter defining different regions of this ratio. Its value is defined by Kn = Xl dp with X being the average free path length of the gas molecules and dp the characteristic pore diameter (sometimes the hydraulic pore radius is taken). 

Using the concepts of active gas-filling and kinetic specific surface S p, it is possible to determine the hydraulic pore or cell radius r, as ... 

Fig. 2 The o-P.s lifetime in the cylindrical pore at room temperature as a function of pore radius. In the model curve AR - 0.19 nm is assumed. The experimental points represent the peak value of the lifetime tjp and average hydraulic radius R. The triangles denote silica gels, dots - Vycor glasses, squares - melamine formaldehyde resins, diamond - Vycor glass with dextrane coating...

These techniques involving the measurement of membrane permeability to a fluid (liquid or gas) lead to a mean pore radius (usually the effective hydraulic radius Th) whose quantitative value is often highly ambiguous. The flux of a fluid through a porous material is sensitive to all structural aspects of the material [129]. Thus, in spite of the simplicity of the method, the interpretation of flux data, even for the simplest case of steady state, is subject to uncertainties and depends on the models and approximations used. 

Under the same printing conditions and taking the effective pore radius, void fraction, and tortuosity of a coated paper to be about 0.2 pm, 0.3 and 5, respectively, the calculated hydraulic impression becomes 0.2 pm. Thus, for coated papers the total amount of ink impressed is a small fraction of the amount of ink transferred to the paper during printing. In other words, the immobilization of ink is predominant in the transfer of ink to newsprint, while the free ink film split is predominant in the case of coated papers. 

Since the pressure at which the pore fluids are displaced from these fibers was greater than the rupture pressure of the fibers, another indirect method for determining pore size was investigated. Pappenheimer et al. [9], derived the relationship between the hydraulic flux of water through a membrane (which is dependent on the square of the equivalent pore radius) and the diffusion rate of tritiated water through the same membrane ... 

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 ... 

Example 3.4.4 The utility of equation (3.4.86) for the determination of the solvent flux through a porous membrane will be briefly illustrated with an example worked out by Cheryan (1987). For an XMIOOA ultrafQtration (UF) membrane, the mean pore diameter (= 2 x hydraulic mean pore radius) = 17.5 nm the number of pores/cm of the top membrane surface area (skin) = 3 x 10 = membrane... 

Miiller-Huber et al. (2015) modified this simple capillary channel model with a constant cross-sectional area by introducing a variable pore radius. The radius is variable along the charuiel axis following an exponential function as described for hydraulic permeability in Section 2.5.7. 

The model in this study takes into account the spatial differences, and predicts both the hydraulic conductivity and water retention. The model in Pig. 1 is the case of vertical one-dimensional flow. The model has two components. The branch plays the role of the water conduit and the node that of the water storage. It is hard to separate the two different types of pore size from the usual PSD(Pore Size Distribution) curve. The same pore radius is assigned to each component according to the PSD curve, which is given by the pore-size measurement by the porosimeter. The computation is based on the Monte Carlo method. 

The pore radius assigned to each component of the network model is generated random numbers from 0 to 1 according to the probability density given from the pore-size measurement. The numerical assumption of the occurrence of the pore size is important in this model. The water saturation and hydraulic conductivity computed depend on the spatial distribution of the pore radius. The pore radii larger than 30 Ha, which can not be measured by the mercury intrusion method, are approximated to appear at the same probability as 3CTJm given by the PSD curve of Toyoura sand. 

The procedures described so far have all required a pore model to be assumed at the outset, usually the cylinder, adopted on the grounds of simplicity rather than correspondence with actuality. Brunauer, Mikhail and Bodor have attempted to eliminate the over-dejjendence on a model by basing their analysis on the hydraulic radius r rather than the Kelvin radius r . The hydraulic radius is defined as the ratio of the cross-sectional area of a tube to its perimeter, so that for a capillary of uniform cross-section r is equal to the ratio of the volume of an element of core to... 

Water Transport. The dependence of the diffusive permeability of tritiated water Pq., (HTO) and hydraulic permeability LpAX on the lEC are presented in Figures 4 and 5. Both Pj and LpAX can be seen to increase exponentially as a function of lEC. Since the volume fraction of water, (J>, is also a linear function of the lEC, a similar exponential relation is obtained for these parameters vs. (J>. In terms of the pore model, the increase in either diffusion permeability or the hydraulic permeability may be caused by one or both of the following possibilities (a) an increase in the number of passageways, or (b) by increase in the radius of the pores. This question may be resolved by examining the g factor, defined as a ratio of two permeabilities (15) ... 

Figure 6. Separation factor-particle diameter tehavior as a function of packing diameter for the pore-partitioning model. Parameters are the same as in Figure 3 with the exception of the interstitial capillary radius which was computed from the hed hydraulic radius (Equation 11 (7.) with void fraction = 0.358).

---