Random nonuniformities

If fasks are nonuniform, randomization of fasks before disfribution may improve load balance... 

Jin X, Wang NHL, Tarjus G and Talbot J 1993 Irreversible adsorption on nonuniform surfaoes the random site model J. Phys. Chem. 97 4256-8... 

Heterogeneity, nonuniformity and anisotropy are based on the probability density distribution of permeability of random macroscopic elemental volumes selected from the medium, where the permeability is expressed by the one-dimensional form of Darcy s law. 

Catalytic reactors can roughly be classified as random and structured reactors. In random reactors, catalyst particles are located in a chaotic way in the reaction zone, no matter how carefully they are packed. It is not surprising that this results in a nonuniform fiow over the cross-section of the reaction zone, leading to a nonuniform access of reactants to the outer catalyst surface and, as a consequence, undesired concentration and temperature profiles. Not surprisingly, this leads, in general, to lower yield and selectivity. In structured reactors, the catalyst is of a well-defined spatial structure, which can be designed in more detail. The hydrodynamics can be simplified to essentially laminar, well-behaved uniform fiow, enabling full access of reactants to the catalytic surface at a low pressure drop. 

Despite extensive efforts toward covalent immobilization on the solid phase, surface adsorption is still the most widely used method for immobilization. Most adsorptions are carried out by empirically adjusting conditions to avoid or minimize immunoreactivity loses. Other factors that may affect the success of immobilization include (1) limited surface area availability, (2) nonuniform distributions of the immune complexes on the solid phase (3) the nature of random absorption of the immunoreactive species on the solid surface. 

In general, pores swell nonuniformly. As a simplification, fhe random network was assumed to consist of fwo types of pores. In fhis fwo-stafe model, nonswollen or "dry" pores (referred to later as "red" pores) permit only a small residual conductance due to tightly bound surface water, which solvates the charged surface groups. Swollen or "wet" pores (referred to later as "blue" pores) contain extra water in the bulk, allowing them to promote the high bulk-like conductance. Water uptake by the membrane corresponds to the swelling of wef pores and to the increase of their relative fraction. 

Under equilibrium conditions in a stressed b.c.c. Fe crystal, interstitial C atoms are generally unequally distributed among the three types of sites identified in Fig. 8.86. This occurs because the C atoms in sites 1, 2, and 3 in Fig. 8.86 expand the crystal preferentially along the x, y, and 2 directions, respectively. These directions are oriented differently in the stress field, and the C atoms in the various types of sites therefore have different interaction energies with the stress field. In the absence of applied stress, this effect does not exist and all sites are populated equally. In Exercise 8.22 it was shown that when the stress on an equilibrated specimen is suddenly released, the relaxation time for the nonuniformly distributed C atoms to achieve a random distribution, t, is t = 2/(3r), where T is the total jump frequency of a C atom in the unstressed crystal. 

On each of these, random and structured reactors behave quite differently. In terms of costs and catalyst loading, random packed-bed reactors usually are most favorable. So why would one use structured reactors As will become clear, in many of the concerns listed, structured reactors are to be preferred. Precision in catalytic processes is the basis for process improvement. It does not make sense to develop the best possible catalyst and to use it in an unsatisfactory reactor. Both the catalyst and the reactor should be close to perfect. Random packed beds do not fulfill this requirement. They are not homogeneous, because maldistributions always occur at the reactor wall these are unavoidable, originating form the looser packing there. These maldistributions lead to nonuniform flow and concentration profiles, and even hot spots can arise (1). A similar analysis holds for slurry reactors. For instance, in a mechanically stirred tank reactor the mixing intensity is highly non-uniform and conditions exist where only a relatively small annulus around the tip of the stirrer is an effective reaction space. 

In actual applications, the gas flow in a gravity settler is often nonuniform and turbulent the particles are polydispersed and the flow is beyond the Stokes regime. In this case, the particle settling behavior and hence the collection efficiency can be described by using the basic equations introduced in Chapter 5, which need to be solved numerically. One common approach is to use the Eulerian method to represent the gas flow and the Lagrangian method to characterize the particle trajectories. The random variations in the gas velocity due to turbulent fluctuations and the initial entering locations and sizes of the particles can be accounted for by using the Monte Carlo simulation. Examples of this approach were provided by Theodore and Buonicore (1976). 

FIGURE 5.14 The force on a magnetic dipole in a nonuniform field depends on the orientation. Thus a beam of randomly oriented dipoles should fan out in a wide range of directions. 

We have noted before that by texture, we mean composition nonuniformity reflected in patches, stripes, and streaks. Thus, by texture, we mean composition nonuniformity that has some unique pattern that can be recognized by visual perception. Thus, a blind random sampling of concentration at various points, though it may reveal the existence of compositional nonuniformity and may even suggest the intensity of this nonuniformity, will reveal nothing about the character of the texture. 

Nevertheless, as a mass deacidification process, it does have some limitations. The process requires a manual, item-by-item preselection procedure to remove books with plasticized covers, and books printed with unstable inks, to avoid color and ink transfer problems. Books with colored illustration (using unstable inks) can also cause problems. Testing has shown that some plastics used on modern paperback books react adversely. The finish might crack and flake. Examination of randomly selected books treated with the Wei T o solution has shown nonuniform deacidification. 

So far we have concentrated on the behavior of particles in translational motion. If the particles are sufficiently small, they will experience an agitation from random molecular bombardment in the gas, which will create a thermal motion analogous to the surrounding gas molecules. The agitation and migration of small colloidal particles has been known since the work of Robert Brown in the early nineteenth century. This thermal motion is likened to the diffusion of gas molecules in a nonuniform gas. The applicability of Fick s equations for the diffusion of particles in a fluid has been accepted widely after the work of Einstein and others in the early 1900s. The rate of diffusion depends on the gradient in particle concentration and the particle diffusivity. The latter is a basic parameter directly... 

The question raised as to the role (or behavior) of phospholipids in a biological setting centers on whether there is general uniformity of species or whether there is a random setting. There is both good news and bad news. There are certain examples of uniformity of phospholipids in various cells and there are easily an equal number of examples of nonuniformity. A brief discussion of this subject follows. 

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