Pore density, relationship porosity

Relationship Between Pore Density, N, and Porosity, Pr. EquatIons 25 (In the case of the circularly growing pore), 20, and 35 relate the pore density and porosity. The theoretical relations between N and porosity Fr thus obtained are shown In Figure 24 with the value of as a parameter. Evidently, N decreases monotonical with an Increase In Fr. Open circles, closed circles and rectangles In the figure Indicate experimental data points for regenerated cellulose. Here, the radii of the secondary particles S are calculated from the particles observed In the dry membranes sl by Equation 37. 

Surface pore diameters were measured by visual inspection of the line profiles of 50 pores of each membrane. All membranes have a wide pore size distribution. The deviation between 20 % and 40% from the average value is noticeable in most cases and is higher for membranes with larger pores (or higher MWCOs). The pore density was obtained by observing several AFM images from different sample areas of the same membrane and counting the number of pores in a unit area. Smface porosity is defined as the ratio of the pore area to the total area of the membrane. The porosity is low and varies between 0.6% and 7%. No relationship between MWCO and porosity was found. 

As already noted with respect to coal density, the porosity of coal decreases with carbon content (Figure 9.3) (King and Wilkins, 1944) and has a minimum at approximately 89% carbon coals followed by a marked increase in porosity. The nature of the porosity also appears to vary with carbon content (rank) for example, the macropores are usually predominant in the lower carbon (rank) coals while higher carbon (rank) coals contain predominantly micropores. Thus, pore volume can be calculated from the relationship ... 

The decrease in the fiber diameter of fabric resulted in a decrease in porosity and pore size, but an increase in fiber density and mechanical strength. The microfiber fabric made of PCLA (1 1 mole ratio) was elastomeric with a low Young s modulus and an almost linear stress-strain relationship under the maximal stain (500%) in this measurement. 

Based on Equation 10.3, chemical mobility differs from water mobility by a factor of 1 + (pb/x)Xd. This factor is also known as the retardation factor. The larger the retardation factor, the smaller is the velocity of the chemical species in relationship to the velocity of water. Note, however, that the retardation factor contains a reactivity factor (Kd) and two soil physical parameters, bulk density (pb) and porosity (t). The two parameters affect retardation by producing a wide range of total porosity in soils as well as various pore sizes. Pore size regulates the nature of solute flow. For example, in very small pores, solute movement is controlled by diffusion, while in large pores, solute flow is controlled by mass flow. 

The porosity of solid samples can be quantitatively studied by mercury poro-simetry. The total volume, specific surface area of the pores, bulk density, and particle size can be determined in 1.8 nm-300 pm pore size and 15 nm-3 mm particle size. The principle of the method is that there is a relationship between the pressure of mercury and the size of the pores filled with mercury. The pressure of mercury (p) required for its introduction into the pores of a given radius (r) can be expressed by Washburn s equation ... 

For adsorbents with sufficiently laig e porosities (often referred to as mesoporous systems) isotherms can exhibit hysteresis between the adsorption and desorption branches as illustrated schematically in figure 1. A classification of the kinds of hysteresis loops has also been made. It is generally accepted that such behavior is related to the occurrence of capillary condensation - a phenomenon whereby the low density adsorbate condenses to a liquid like phase at a chemical potential (or bulk pressure) lower than that corresponding to bulk saturation. However, the exact relationship between the hysteresis loops and the capillary phase transition is not fully understood - especially for materials where adsorption cannot be described in terms of single pore behavior. 

As cracking proceeds the load is carried by a smaller area. Additionally, even in an uncracked state, the load carried by boundaries is magnified due to porosity in the material. The relationship between porosity P and mean boundary traction is not simple, as it will depend on the morphology of the pores. Thus, (r)will depend on porosity and crack density in the form... 

As the amount of water present in a rock is influenced by the porosity, the resistivity provides a measure of its porosity. For example, in granular materials in which there are no clay minerals, the relationship between the resistivity, p, on the one hand and the density of the pore water, p, , the porosity, n, and the degree of saturation, S on the other, is as follows ... 

Although it seems straightforward, estimating 5ga at the field scale is difficult. One approach is to establish relationships between and field hydrostrati-graphic properties such as permeability and porosity. Arthur (1996) proposed a relationship among porosity, dry density, and pore radius to determine S. y Smith and Schafer (1999) also proposed a method relating porosity, permeability, and tortuosity. For the purposes of the analysis presented here, the approach of Arthur (1996) was used with constant parameter values taken from the input file for I PA... 

Compressional wave velocities versus bulk density for the series of acid-catalyzed TEOS xerogels investigated by Murtagh el al. [31], The solid lines correspond to the relationship predicted from a fused silica-porosity composite assuming either spherical- or needle-shaped pores. Gel values fall beneath the predicted values, indicating that the skeletal phase is not as stiff as conventional fused silica [31]. 

Determine the parameters in the equilibrium relationship of Eq. 1.4. Average pore radius is 50A, porosity is 0.62, and apparent density of support is 1,38 g/ml. 

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