Size-independent constants

Assuming that the particle size dependent rate constant Kl for bubble-induced attrition can—in analogy to the other sources—be written as the product of a particle size independent constant Cb and the surface mean diameter of the bed material d, ... 

The derivation of equations 13.34 and 13.35 has been carried out assuming that u0 is constant and independent of the flowrates, up to and including the flooding-point. This in turn assumes that the droplet size is constant and that no coalescence occurs as the hold-up increases. Whilst this assumption is essentially valid in properly designed spray towers, this is certainly not the case with packed towers. Equations 13.34 and 13.35 cannot therefore be used to predict the flooding-point in packed towers and a more empirical procedure must be adopted. 

Pipe sizes are based on the approximate diameter and are reported as nominal pipe sizes. Although the wall thickness varies depending on the schedule number, the outside diameter of any pipe having a given nominal size is constant and independent of the schedule number. This permits the use of standard fittings and threading tools on pipes of different schedule numbers. A table showing outside diameters, inside diameters, and other dimensions for pipes of different diameters and schedule numbers is presented in the Appendix. 

AB. Rising small bubbles of gas in liquid, continuous phase. C derbank and Moo-Young correlation Nsk = = 2 + 0.31(ATcr) W, dy < 0.25 cm Njsa = = Raleigh number IIlDl [E] Use with arithmetic concentration difference. Valid for single bubbles or swarms. Independent of agitation as long as bubble size is constant. Recommended by [136]. Note that Na, = Ncr fsc- [47] [66] p. 451 [88] p. 119 [152] p. 156 [136]... 

Crystal growth is a description of the linear velocity of a growing face, that is, the linear velocity perpendicular to that face. Growth velocity, in the classical view, is considered to be constant (size independent), according to the classical McCabe AL Law (McCabe 1929). 

From Eqs. (41) and (43) one infers the same hnite size scaling of ST and t, in accord with Fisher s analysis [193]. From this analysis, one concludes that bT/t = constant, being size-independent. Indeed, this relation is reasonably well obeyed (within a numerical factor of 3 over the range Rq = 14-400 A) for the quantum simulations for small clusters, for porous gold, and for the membrane polymer (Table V). However, a marked (one order of magnitude) deviahon from this relation is exhibited for " He conhned in vicor glass (Table V), which may be attributed to constrained randomness effects [203, 204] and which calls for further scrutiny. 

The absorption spectra of spherical particles of colloidal dimensions can be calculated by Mie theory from a wavelength dependence of optical constants of the particles relative to the surrounding medium [7]. Spherical particles that do not interact with each other exhibit a single resonance as long as r T is valid, where r and A are the particle size and wavelength of the incident light, respectively. In this size regime the surface plasmon frequency is essentially size independent. Colloidal metallic particles produced by laser ablation have dimensions typically on the... 

As discussed earlier, the analytical solutions for the CSD for a batch or semibatch crystallizer are difficult to obtain unless both the initial condition for the CSD and appropriate kinetic models for nucleation and growth are known. An example of such an analytical solution—simple yet not overly restrictive—was given by Nyvlt (1991). It is assumed that the process, in which both external seeding and nucleation take place, occurs at constant supersaturation (G = constant, Bq = constant) in an ideally mixed crystallizer. An additional assumption of size-independent growth allows one to rewrite the time-dependent moments, Eqs. (10.12)-(I0.15), in terms of the physical properties such as the total number (A), length (L), surface area A), and mass of... 

Regarding the average lifetime of ortho-positronium to.ps for the unaged epoxy film on Au substrate in Fig. 29.2, Tq-ps is constant within the experimental scatter for positron implantation depths above approx. 20 nm. This reflects constant free-volume void sizes, independent of the sample depth. A shallow maximum around 150 nm and a decrease in x. p above 400 nm are not significant. On the other hand, for very low depths up to 20 nm, a significant increase in To-Ps is observed. This can be interpreted as the effect of a surface region in the order of less than 20 nm wide where the sizes of the free-volume voids increase [19]. However, a diffusion of ortho-positronium to the epoxy surface and into vacuum or an impediment of the positronium formation due to a reduced... 

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