Velocity sinking

FIGURE lO.iS Anafyti cal and line sink velocity contours for a flanged slot. 

Fig. 2.9 Seasonal mean sinking velocity in the euphotic zone [m/d] in the season from June to August (JJA), and in the season from December to February (DJF).

Figure 23.2 Removal of suspended particles (described by the solid-to-water phase ratio rsw) with uniform sinking velocity vs. (a) No mixing constant particle flux Fs = rsw vs until upper horizon reaches the bottom after time t = h /vs (b) homogeneously mixed system exponential decrease of rsw (c) change of mean particle flux across level z0 for the case of heterogeneous distribution of particles and a spatially variable vertical velocity component.

In conclusion, the first-order particle removal model, Eq. 23-16, is a reasonable approximation to describe the influence of suspended particles on sorbed chemical species. However, the sinking velocity is not necessarily identical with the Stokes law velocity, but rather is an empirical parameter which may strongly depend on lake currents and biological processes and may vary over short time periods. 

Bloesch, J., and M. Sturm, Settling flux and sinking velocities of particulate phosphorus (PP) and particulate organic carbon (POC) in Lake Zug, Switzerland . In Sediments and Water Interactions, P. G. Sly, Ed., Springer, New York, 1986, pp. 481-490. 

As illustrated in Fig. 5.2, the classic Jeffery-Hamel flow concerns two-dimensional radial flow in a wedge-shaped region between flat inclined walls. The flow may be directed radially outward (as illustrated) or radially inward. The flow is assumed to originate in a line source or terminate in a line sink. Velocity at the solid walls obeys a no-slip condition. In practice, there must be an entry region where the flow adjusts from the line source to the channel-confined flow with no-slip walls. The Jeffery-Hamel analysis applies to the channel after this initial adjustment is accomplished. 

Fig. 5.4 shows the effect of the dynamic viscosity /z upon Although the state of flow in the tank is turbulent, the viscosity of the medium is important, because it affects the sinking velocity of the particle swarm iVss. The particle Reynolds number Rep formulated with Wss and dp ties in the laminar to transition ranges. 

Measurements at = 0.25 and 0.95 have additionally shown that the stirrer speed required to realize this distribution quality initially increases with

constant from = 0.15-0.20. This also demonstrates the relevance of the sinking velocity iVss in the swarm, which decreases with increasing... 

On the basis of the analogy between no.9 and dp (Fig. 5.5), on the one hand, and the sinking velocity of the particle swarm Wss and dp, on the other, the sinking velocity of the swarm u>gs was later incorporated into the relevance list. This consciously took account of the fact, that this property of the particle swarm is calculated from the sinking velocity Wg of a single particle in a liquid at rest and thus strictly speaking only applies to a liquid at rest. 

It is currently usual to see the volume fraction y>, of the solids as a parameter in the suspension, since this and not the mass fraction affects the sinking velocity in the swarm. 

The particle sinking velocity in the swarm iVss is a kinematic quantity, which can be calculated according to different recommendations. 

Since at the fluidization point the superficial velocity v and the sinking velocity of the particle in the swarm iVjs are equal to one another, v can be replaced by Wjs in the above equations. 

The following expression for die sinking velocity iVs of a single particle follows from equation (5.12) ... 

According to [497] the sinking velocities in a turbulent field are up to a half smaller than those in the liquid at rest, thus the calculation of the minimum stirrer speed for suspension is on the safe side [567]. 

From what has been said above, it should be borne in mind that the sinking velocity of a single particle w, which has been mostly calculated for monodisperse... 

Kipke cited, as a possible reason for this discrepancy the fact, that the iVss, which applies for liquids at rest, is tacitly used in the calculations of [112 and 114]. When, however, the turbulence field is determining for the sinking velocity and this changes in the macro-range by /z, then it can be imagined that for particles with particular dimensions relative to the micro- and macro-scales no generally valid scale-up criterion for all boundary conditions is to be expected [277]. 

The study carried out by Geisler et al. [152], which considered the dimensioning of the specific stirrer power per unit mass of the suspension e = FlpV, indicated the paramount importance of the D/dp parameter. In industrially-sized tanks (D/dp > 500) this quantity consists of two sum terms from an Ejs, which is required for maintaining that vertical flow rate n>t, which is equal to the terminal sinking velocity of the particle swarm Wss, and from the term edre, which covers the frictional losses of the flow upon reversal of the flow direction ... 

After the 1-s criterion was recognized as a poorly sensitive measuring quantity for the so-called critical stirrer speed and was replaced by the layer height criterion h = 0.9, the sinking velocity of the swarm iVss was incorporated into the relevance list, which was derived from the analogy to suspension processes in fluidized beds for which physical calculation formulae exist. Conscious account was taken of the fact that this only applies to non-stirred liquids [114]. In addition, in view of physical insight, the mass fraction of solids was replaced by the volume fraction of solids... 

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