Three-dimensional porosity

The final demonstration of the developed methodology is to determine the three-dimensional porosity distribution of a porous media sample obtained from the subsurface. A cylindrically shaped rock sample was prepared, and is labeled MAG. The sample has a 2.54-cm diameter and is 3.90 cm in length. A bulk porosity of 0.284 was determined gravimetrically, with 5.61 g of brine solution being imbibed. The reference sample contained 0.217 g of water. The field of view was 10.0 cm x 3.0 cm x 3.0 cm, of which lengths are divided into 128x8x8. This yields voxel sizes of 0.078 cm x 0.375 cm x 0.375 cm. 

The three-dimensional porosity image of MAG sample is shown in Fig. 9. The porosity image is displayed as a series of two-dimensional images, each of which represents a plane of voxels sliced perpendicularly to the other direction. In Fig. 9, axial limits of the sample are apparent. The middle slices have more columns of voxels which are inside the sample than the others, due to the cylindrical shape of the sample. The white spots above the sample are attributed to the signal corresponding to the fluid in the reference. The resolution is poor because the voxel... 

Slice 1 Slice2 Slice 3 Slice 4 Slice 5 Slice6 Slice 7 Slice 8 Fig. 9. Three-dimensional porosity image of a cylindrically shaped sample (MAG). 

To facilitate the ultrahigh three-dimensional porosity values necessary in these scaffolds (as noted above) and to provide the ability to easily manipulate pSi materials in a biological environment, pSi can be blended with known FDA-approved polymers such as poly(caprolactone) (PCL). 

Spunbonded fabrics are effective filters in that they are layered stmctures of relatively fine fibers, the three-dimensional stmcture of which creates a torturous path. Even relatively thin spunbonded fabrics (eg, 0.2—0.25 mm) present a significant challenge to the passage of soil fines and are suitable for use in some filtration appHcations. The porosity of geotextile fabrics is classified by means of several procedures such as flux (volume flow/area per time) and equivalent opening size (EOS), which is a measure of the apparent pore size of the openings in the fabric. The flux measures the porosity to Hquid water, and the EOS measures the porosity to soHd particles of a known diameter. Literature is available on limitations of particular styles of fabrics within an apphcation (63). 

Polymer-based, synthetic ion-exchangers known as resins are available commercially in gel type or truly porous forms. Gel-type resins are not porous in the usual sense of the word, since their structure depends upon swelhng in the solvent in which they are immersed. Removal of the solvent usually results in a collapse of the three-dimensional structure, and no significant surface area or pore diameter can be defined by the ordinaiy techniques available for truly porous materials. In their swollen state, gel-type resins approximate a true molecular-scale solution. Thus, we can identify an internal porosity p only in terms of the equilibrium uptake of water or other liquid. When crosslinked polymers are used as the support matrix, the internal porosity so defined varies in inverse proportion to the degree of crosslinkiug, with swelhng and therefore porosity typically being more... 

Internal diffusion ofreactants. This step depends on the porosity of the catalyst and the size and shape of the catalyst particles, and occurs together with the surface reaction. The active catalyst component is usually highly dispersed within the three-dimensional porous support. The reactant molecules have to diffuse through the network of pores toward the active sites. The activation energy for pore diffusion li2 may represent a substantial share of the activation energy of the chemical reaction itself. 

The pore size of the membrane could also be controlled independently of the porosity by altering the size of the salt particles (Fig. 5a). Membranes with high surface area/volume ratios were produced and the ratio was dependent on both salt weight fraction and particle size (Fig. 5b). In addition, the crystallinity of PLLA membranes can be tailored to that desired for each application. These characteristics are all desirable properties of a scaffold for organ regeneration. The major disadvantage of this technique is that it can only be used to produce thin wafers or membranes (up to 2 mm in thickness). A three-dimensional scaffold cannot be directly constructed. This problem may be circumvented however, by membrane lamination. 

The regeneration of specific tissues aided by synthetic materials has been shown to be dependent on the porosity and pore size of the supporting three-dimensional structure. A large surface area favors cell attachment and growth, whereas a large pore volume is required to accommodate and subsequently deliver a cell mass sufficient... 

The ground mixture is heated to about 750 °C under reducing conditions, normally in a batch process. This can be done in directly fired kilns with the blend in lidded crucibles of controlled porosity, or muffle kilns. The heating medium can be solid fuel, oil, or gas. The sodium carbonate reacts with the sulfur and reducing agent at 300 °C to form sodium polysulfide. At higher temperatures the clay lattice reforms into a three-dimensional framework, which at 700 °C is transformed to the sodalite structure, with entrapped sodium and polysulfide ions. 

We believe that the high surface area and porosity of the carbon provides a three-dimensional matrix over which the sample molecules are dispersed and from which ions can be emitted for extended periods of time. For example, 2 g of a PAC on carbon... 

Besides specific surface area, silicas are also characterised by their porosity. Most of the silica s are made out of dense spherical amorphous particles linked together in a three dimensional network, this crosslinked network building up the porosity of the silica. Where the reactivity of diborane towards the silica surface has been profoundly investigated, little attention has been paid to the effect of those reactions on the pore structure. However different methods are developed to define the porosity and physisorption measurements to characterise the porosity parameters are well established. Adsorption isotherms give the specific surface area using the BET model, while the analysis desorption hysteresis yields the pore size distribution. 

Estimation of three-dimensional properties. Images obtained from computer generated random structures and from drug delivery devices were analyzed for porosity, extent of orientation, and distribution of particle size. In addition, the images from the drug delivery device were examined for individual drug particle shape. 

Figure 2.8 illustrates the SAS concept as well as the method used for its determination. SASs are essentially computed by generating a three-dimensional, graphical representation of the dendrimer and computationally rolling probes (p) of various radii (r) over the surface. Intuitively, as well as physically, the larger the probe radius the less chance for contact the probe has within the internal void region of the dendrimer. For probes with a small radius, and in particular at the limit r = 0 A, the total internal surface area can be determined. Typically, the solvent accessible surface area ( Msas) is plotted versus probe radius or diameter. Thus, a measure of dendritic porosity can be derived. 

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