Settling factor

Analytic results for cylinders comparable to those discussed for spheroids are not available. However, Heiss and Coull (H4) reported accurate experimental determinations for cylinders, spheroids, and rectangular parallelepipeds, and developed a general correlation for settling factors. In terms of the volume drag ratio,, their results may be written ... 

Veitch, F. R and Hidu, J., Gregarious settling in the American oyster Crassostrea virginica Gmelin. I. properties of a partially purified settling factor, Chesapeake Sci., 12, 173, 1971. 

This equation defines the characteristic speed, that is, the kinematic wave speed. Note that for s = constant the characteristic speed drldt= which is analogous to the wave speed in the gravity sedimentation problem except that here is not constant with distance. The analogy also holds with s — s p) if s d sp)/dp is defined as a hindered settling factor G(d>) (Eq. 5.4.18). 

We may conclude that the matter of optimal algorithms for integrating Newton s equations of motion is now nearly settled however, their optimal and prudent use [28] has not been fully exploited yet by most programs and may still give us an improvement by a factor 3 to 5. 

The particle can be assumed to be spherical, in which case M/N can be replaced by (4/3)ttR P2, and f by 671770R- In this case the radius can be evaluated from the sedimentation coefficient s = 2R (p2 - p)/9t7o. Then, working in reverse, we can evaluate M and f from R. These quantities are called, respectively, the mass, friction factor, and radius of an equivalent sphere, a hypothetical spherical particle which settles at the same rate as the actual molecule. 

Fig. 4. Terminal velocities in air of spherical particles of different densities settling at 21°C under the action of gravity. Numbers on curves represent tme (not bulk or apparent) specific gravity of particles relative to water at 4°C. Stokes-Cunningham correction factor is included for settling of fine particles.

Because mass flow bins have stable flow patterns that mimic the shape of the bin, permeabihty values can be used to calculate critical, steady-state discharge rates from mass flow hoppers. Permeabihty values can also be used to calculate the time required for fine powders to settle in bins and silos. In general, permeabihty is affected by particle size and shape, ie, permeabihty decreases as particle size decreases and the better the fit between individual particles, the lower the permeabihty moisture content, ie, as moisture content increases, many materials tend to agglomerate which increases permeabihty and temperature, ie, because the permeabihty factor, K, is inversely proportional to the viscosity of the air or gas in the void spaces, heating causes the gas to become more viscous, making the sohd less permeable. 

In equation 6, characterizes the settling behavior of the soHd particles or Hquid drops in the suspension, whereas the second part of the right-hand side refers to speed and size of the centrifuge and is expressed by the capacity factor Z g. For a bottle centrifuge, it takes the following form ... 

The foHowing factors are important in dump leaching (/) the role of bacteria (2) the appHcation of acid to prevent or delay precipitation of hydrated ferric sulfate (J) oxidation to remove excess iron from mine water in settling pools, as shown in equations 38 and 39 (4) optimization of dump configuration for good solution distribution and (5) avaHabHity of oxygen. 

Wall Effects When the diameter of a setthng particle is significant compared to the diameter of the container, the settling velocity is reduced. For rigid spherical particles settling with Re < 1, the correction given in Table 6-9 may be used. The factor k is multiplied by the settling velocity obtained from Stokes law to obtain the corrected set-... 

A feed stream to be clarified or thickened can exist at any state represented within this diagram. As it becomes concentrated owing to sedimentation, it may pass through all the regimes, and the settling rate in any one may be the size-determining factor for the required equipment. 

Shoiild the particles have a tendency to cohere slightly during sedimentation, each sampling time, representing a different nominal detention time in the clarifier, will produce different suspended-sohds concentrations at similar rates. These data can be plotted as sets of cui ves of concentration versus settling rate for each detention time by the means just described. Scale-up will be similar, except that detention time will be a factor, and both depth and area of the clarifier will influence the results. In most cases, more than one combination of diameter and depth will be capable of producing the same clarification result. 

Detention efficiency. Conversion from the ideal basin sized by detention-time procedures to an actual clarifier requires the inclusion of an efficiency factor to account for the effects of turbulence and nonuniform flow. Efficiencies vaiy greatly, being dependent not only on the relative dimensions of the clarifier and the means of feeding but also on the characteristics of the particles. The cui ve shown in Fig. 18-83 can be used to scale up laboratoiy data in sizing circular clarifiers. The static detention time determined from a test to produce a specific effluent sohds concentration is divided by the efficiency (expressed as a fraction) to determine the nominal detention time, which represents the volume of the clarifier above the settled pulp interface divided by the overflow rate. Different diameter-depth combinations are considered by using the corresponding efficiency factor. In most cases, area may be determined by factors other than the bulksettling rate, such as practical tank-depth limitations. 

The factors which may make CCD a preferred choice over other separation systems include the following rapidly settling solids, assisted by flocculation relatively high ratio of solids concentration between underflow and feed moderately high wash ratios allowable (2 to 4 times the volume of hquor in the thickened underflows) large quantity of sohds to be processed and the presence of fine-size sohds that are difficult to concentrate by other means. A technical feasibihty and economic study is desirable in order to make the optimum choice. 

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