Upper size limit

Stokes equation is usually considered valid for Reynolds numbers less than 0.25 and the correction term is neglected. Combining equations (6.5) and (6.8) and applying the condition that Re 0.25 gives the upper size limit (upper critical diameter D ). 

The upper critical diameter can be increased by increasing the liquid viscosity alternatively a correction term may be applied. For routine applications the diameters obtained using Stokes equation at Re greater than 0.25 are accepted as correct. 

The following relationship is an empirical fit to experimental data for spherical particles, between drag coefficient and Reynolds number for Reynolds number between 0.01 and 1.0  

The resultant errors at Reynolds numbers of 0.25 and 1.0 are given in Table 6.2 where % error is defined as 100[(Z)-D5.,)/D]. 

Since C[ and Re are funetions of the two variables u and D, it is necessary to derive relationships that are functions of only one of these variables. C Re is a function of D only and Re/C is a function of u. For Reynolds Numbers less than 1.0, may be determined using equation (6.10) so that CpRe and Re/Cp can be calculated. 

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If exchangers are countercurrent devices, then the number of units equals the number of shells, providing indithdual shells do not exceed some practical upper size limit. If, however, equipment is used that is not completely countercurrent, as with the 1-2 shell and tube heat exchanger, then... 

Owing to the feed pan distance usually maintained on wet dmm cobbers, the wear encountered with coarser particles, and the feed velocities requited to move coarse particles, the recommended upper size limits for cobber separators is 10 mm in diameter. Individual ore characteristics requited to obtain Hberation determine the feed size in rougher and finisher feeds. For finishers, where all the nonmagnetics must be overflowed, a sufficiently fine size to accomplish the overflow must be obtained. Typical feed sizes for cobbers are from —841 fim (—20 mesh) to 10 mm for rougher, —420 fim (—35 mesh) to —297 fim (—48 mesh) and for finishers, —63 fim (—270 mesh) to —44 fim (—325 mesh). The magnetic content of the iton ores to be concentrated varies over fairly wide limits. Ores as low as 10 wt % Fe have been successfully treated, as have ores having up to 50 wt % or more Hon. 

The particle size deterrnined by sedimentation techniques is an equivalent spherical diameter, also known as the equivalent settling diameter, defined as the diameter of a sphere of the same density as the irregularly shaped particle that exhibits an identical free-fall velocity. Thus it is an appropriate diameter upon which to base particle behavior in other fluid-flow situations. Variations in the particle size distribution can occur for nonspherical particles (43,44). The upper size limit for sedimentation methods is estabHshed by the value of the particle Reynolds number, given by equation 11 ... 

So far, consideration has been limited to chemistry physical constraints such as heat transfer may also dictate the way in which reactions are performed. Oxidation reactions are highly exothermic and effectively there are only two types of reactor in which selective oxidation can be achieved on a practical scale multitubular fixed bed reactors with fused salt cooling on the outside of the tubes and fluid bed reactors. Each has its own characteristics and constraints. Multitubular reactors have an effective upper size limit and if a plant is required which is too large to allow the use of a single reactor, two reactors must be used in parallel. 

Colloid A form of matter that ranges in length from 0.001 to lOjxm. This is in between that of a solute and a solid. Some scientists recognize 100 pm as the upper size limit. 

Depending on the size, forged fittings are available with socket-weld (Fig. 10-129) or screwed ends in sizes 4 in and smaller however, 2 in is the upper size limit normally used. ASME B16.il gives minimum dimensions for Class 3000, 6000, and 9000 socket-weld fittings, and for Class 2000, 3000, and 6000 threaded fittings. The use of socket-weld and threaded fittings is restricted by the code. 

Bubble-size control was also critical. The intensity of scattering by nonresonant gas bubbles is proportional to the sixth power of the radius of the bubble. Hence, the larger the bubble, the better the scattering intensity. However, the acceptable upper size limit for in vivo administration is determined by the need for bubbles to cross capillary beds. Bubbles larger than 6-8 pm should be avoided as they are trapped in the lung capillaries. The current accepted sizes are in 1-7 pm, preferably around 3 pm, with as narrow a size distribution as possible. Bubble shell material needs to be biodegradable. Soft shells are generally preferable, as they minimally impede US backscatter. 

Two characteristics of the light from noctilucent clouds may be observed with no more than one s eyes and a polarizing filter its color and whether or not it is strongly polarized. This enabled Ludlum (1957) to estimate the size range of noctilucent cloud particles. Because of the observed strong polarization he set 0.16 jum as their upper size limit on the basis of the observed color—white, silvery, sometimes bluish, but not sufficiently so as to indicate very small particles—he set 0.008 jam as their lower size limit. From other than optical evidence he also concluded that the particles were not ice, but were more likely to be volcanic, meteoric, or interplanetary dust. 

The upper size limit of the larger sized population is 1000/x. This is based on review of the size/frequency data for close-in, early-time fallout collections. All reported size-frequency curves were dropping vertically between 800 and 1000/a. 

Various comparisons have been made (4, 27, 28, 61, 74, 89, 106, 111). For a particular task of fitting data, the recognition of an actual upper size limit leads to the modified logarithmic representation of Mugele and Evans (89). However, for pure mathematical ease the Rosin-Rammler distribution employed by Probert (98) is preferable from a vaporization point of view. 

The shape factor,fshape, is the ratio of the average volume of all particles with a maximum linear dimension equal to the applied mesh size of a sieve to that of the cubes which will just pass the same sieve. The value offshape can be assumed to be 0.5 for the most materials. The particle size distribution factor, fsize distribution> is the ratio of the upper size limit to the lower size limit. The composition factor, fcomposmon, is defined as ... 

Simple colloidal dispersions are two-phase systems, comprising a dispersed phase of small particles, droplets or bubbles, and a dispersion medium (or dispersing phase) surrounding them. Although the classical definition of colloidal species (droplets, bubbles, or particles) specifies sizes of between one nanometre and one micrometre, in dealing with practical applications the upper size limit is frequently extended to tens or even hundreds of micrometres. For example, the principles of colloid science can be usefully applied to emulsions whose droplets exceed the 1 tm size limit by several orders of magnitude. At the other extreme, the field of nano-... 

See Emulsion. The term is sometimes used to distinguish an emulsion from the microemulsion or micellar emulsion types. Thus a mini-emulsion would contain droplet sizes greater than 100 nm and less than 1000 nm, or some other specified upper-size limit. 

Use only high-grade nickel chrome wire employed by model builders to home-turn smalt springs. Generally, diameters of between. 015- and. 02G-inch are best, but if one has a less sensitive primer, more powerful batteries must be used with heavier wire. Anything over. 025-inch diameter will probably blow fuzes in a residential electrical system. This is definitely the upper size limit for bridge wires. 

The size of the polyplex is also crucial to its function. The threshold for first-pass elimination by the kidneys is approximately lOnm in diameter defining a rough lower size limit for nanoparticles (21). Upper size limits are more difficult to establish as they depend on a variety of factors that are variable within tumors including penetration of capillary endothelium, diffusion rates in tumor interstitium and intracellular spaces (22). Macromolecular complexes preferentially accumulate in tumors through the enhanced permeability and retention (EPR) effect (23). Ideally, a nanoparticle would be in a size window such that it could take advantage of the EPR effect. The size of the polyplex can be readily modified during complexation by altering the DNA to polymer ratio (24). 

Tencer J, Frick IM, Oquist BW, Aim P, Rippe B. Size-selectivity of the glomerular barrier to high molecular weight proteins upper size limitations of shunt pathways. Kidney Int 1998 53(3) 709—15. 

There is an upper size-limit of 35-40 kDa. However, this means that most protein domains can be studied using NMR spectroscopy. 

Forged fittings made by boring out solid forgings are available with socket-weld (Fig. 10-126) or with screwed ends in sizes through 4 in, but 2 in is the usual upper size limit for use. ANSI B16.il—1973 gives minimum dimensions for socket-weld 3000- and 6000-lb classes and... 

At high velocities, due to the onset of turbulence, the drag on the sphere increases above that predicted by Stokes equation and particles settle more slowly than the law predicts. However, settling velocities can be related to particle diameters by applying Newton s equation which is available as an empirical relationship between C, and Re. The upper size limit for Stokes equation is limited, due to the onset of turbulence, to Reynolds number smaller than 0.25. 

The upper size limit by gravity sedimentation is fixed by the unreliability of measurements taken in the first 30 s or so of the analysis and by the... 

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