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Solids spacing

Introducing the dimensionless variables x = t/L. and 9 = t/r, with = Lj/u = where is the solid space time in a section of a TMB unit, L. is the length of a TMB section, and is the number of columns per section in a SiWb unit, the model equations become ... [Pg.226]

Width assumes a great importance when one realizes that to maintain conductivity through the induced fracture it is nearly mandatory that the crack be filled with a solid spacing agent (called proppant) which will prevent the crack from closing completely after the hydraulic pressure on the well is released. [Pg.63]

It seems remarkable that solid figures can have equality and similarity without coincidence, since, in contrast, for figures in the plane or for systems of points on a line equality and similarity are always connected with coincidence. The reason for this may be that beyond the solid space of three dimensions there is no other, none of four dimensions. .. For the coincidence of two equal and similar systems in... [Pg.9]

In the case of the multifunctional porous catalysts, such as are familiar in hydrocarbon reactions, the situation is somewhat different from that in the model above. In the model above, the diffusion problem is confined to a volume of space where catalytic activities (the sources and sinks) occur only at its boundaries. In the present case a volume element of (porous solid) space is permeated by both diffusive resistance as well as distributed catalytic sources or sinks. [Pg.145]

The vertical or pendulum perforate basket (Fig. 8) is perhaps the most commonly used centrifuge. The perforated basket in its simplest form is lined with a cloth, wire mesh, or a bag that accumulates solids as the liquid passes through. When the solid space is filled, feeding is discontinued and the relevant portion of the batch cycle is continued. In smaller units, the bowl may simply spin down to a complete stop for manual removal of the cake or replacement of the bag. At higher G-levels or in larger diameter units, wire mesh or screen is added to support the filter media. Slowing the unit and plowing the solids out at low speed complete the batch cycle. Rinse can be isolated... [Pg.414]

Also, since (% pore space + % solid space) = 100... [Pg.51]

The disadvantage of this type of centrifuge is that it operates batch-wise, and when the solids spaces are filled with sohds, the centrifuge must be stopped and cleaned manually, although this process is helped by the fact that half of the baffles can be lifted out from the bowl when the bowl cover is removed. [Pg.463]

The specific surface area of a solid is one of the first things that must be determined if any detailed physical chemical interpretation of its behavior as an adsorbent is to be possible. Such a determination can be made through adsorption studies themselves, and this aspect is taken up in the next chapter there are a number of other methods, however, that are summarized in the following material. Space does not permit a full discussion, and, in particular, the methods that really amount to a particle or pore size determination, such as optical and electron microscopy, x-ray or neutron diffraction, and permeability studies are largely omitted. [Pg.572]

A variety of experimental data has been found to fit the Langmuir equation reasonably well. Data are generally plotted according to the linear form, Eq. XVn-9, to obtain the constants b and n from the best fitting straight line. The specific surface area, E, can then be obtained from Eq. XVII-10. A widely used practice is to take to be the molecular area of the adsorbate, estimated from liquid or solid adsorbate densities. On the other hand, the Langmuir model is cast around the concept of adsorption sites, whose spacing one would suppose to be characteristic of the adsorbent. See Section XVII-5B for an additional discussion of the problem. [Pg.615]

A still different approach to multilayer adsorption considers that there is a potential field at the surface of a solid into which adsorbate molecules fall. The adsorbed layer thus resembles the atmosphere of a planet—it is most compressed at the surface of the solid and decreases in density outward. The general idea is quite old, but was first formalized by Polanyi in about 1914—see Brunauer [34]. As illustrated in Fig. XVII-12, one can draw surfaces of equipo-tential that appear as lines in a cross-sectional view of the surface region. The space between each set of equipotential surfaces corresponds to a definite volume, and there will thus be a relationship between potential U and volume 0. [Pg.625]

The otiier type of noncrystalline solid was discovered in the 1980s in certain rapidly cooled alloy systems. D Shechtman and coworkers [15] observed electron diffraction patterns with sharp spots with fivefold rotational synnnetry, a syimnetry that had been, until that time, assumed to be impossible. It is easy to show that it is impossible to fill two- or tliree-dimensional space with identical objects that have rotational symmetries of orders other than two, tliree, four or six, and it had been assumed that the long-range periodicity necessary to produce a diffraction pattern with sharp spots could only exist in materials made by the stacking of identical unit cells. The materials that produced these diffraction patterns, but clearly could not be crystals, became known as quasicrystals. [Pg.1369]

Atom-surface interactions are intrinsically many-body problems which are known to have no analytical solutions. Due to the shorter de Broglie wavelengdi of an energetic ion than solid interatomic spacings, the energetic atom-surface interaction problem can be treated by classical mechanics. In the classical mechanical... [Pg.1808]

This method is smiple but experimentally more cumbersome than the volumetric method and involves the use of a vacuum microbalance or beam balance [22], The solid is suspended from one ann of a balance and its increase in weight when adsorption occurs is measured directly. The dead space calculation is thereby avoided entirely but a buoyancy correction is required to obtain accurate data. Nowadays this method is rarely used. [Pg.1877]

Figure C3.2.5. Strongest tunnelling patliways between surface histidines and tire iron atom in cytochrome c. Steps in patliways are denoted by solid lines (covalent bonds), dashed lines (hydrogen bonds), and tlirough-space contacts (dotted lines). Electron transfer distance to His 72 is 5 A shorter tlian in His 66, yet tire two rates are approximately... Figure C3.2.5. Strongest tunnelling patliways between surface histidines and tire iron atom in cytochrome c. Steps in patliways are denoted by solid lines (covalent bonds), dashed lines (hydrogen bonds), and tlirough-space contacts (dotted lines). Electron transfer distance to His 72 is 5 A shorter tlian in His 66, yet tire two rates are approximately...
For each combination of atoms i.j, k, and I, c is defined by Eq. (29), where X , y,. and Zj are the coordinates of atom j in Cartesian space defined in such a way that atom i is at position (0, 0, 0), atomj lies on the positive side of the x-axis, and atom k lies on the xy-plaiic and has a positive y-coordinate. On the right-hand side of Eq. (29), the numerator represents the volume of a rectangular prism with edges % , y ., and Zi, while the denominator is proportional to the surface of the same solid. If X . y ., or 2 has a very small absolute value, the set of four atoms is deviating only slightly from an achiral situation. This is reflected in c, which would then take a small absolute value the value of c is conformation-dependent because it is a function of the 3D atomic coordinates. [Pg.424]

Periodic boundary conditions can also be used to simulate solid state con dition s although TlyperChem has few specific tools to assist in setting up specific crystal symmetry space groups. The group operation s In vert, Reflect, and Rotate can, however, be used to set up a unit cell manually, provided it is rectangular. [Pg.201]


See other pages where Solids spacing is mentioned: [Pg.238]    [Pg.664]    [Pg.792]    [Pg.33]    [Pg.51]    [Pg.51]    [Pg.53]    [Pg.73]    [Pg.624]    [Pg.238]    [Pg.664]    [Pg.792]    [Pg.33]    [Pg.51]    [Pg.51]    [Pg.53]    [Pg.73]    [Pg.624]    [Pg.368]    [Pg.216]    [Pg.270]    [Pg.521]    [Pg.579]    [Pg.621]    [Pg.86]    [Pg.97]    [Pg.306]    [Pg.1098]    [Pg.1372]    [Pg.1436]    [Pg.1487]    [Pg.1562]    [Pg.1751]    [Pg.1806]    [Pg.1808]    [Pg.1914]    [Pg.1946]    [Pg.2265]    [Pg.2760]    [Pg.2771]    [Pg.2835]    [Pg.2842]    [Pg.67]   
See also in sourсe #XX -- [ Pg.258 ]




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