Dead flux

A typical grade efficiency curve for the product classification step is given in Figure 4. A value of nearly 100 percent is attained at large sizes, whereas normally a value equal to or larger than the so-called dead flux is attained at small sizes. This is caused by the diluted discharge of the coarse fraction. It represents the minimum amount of residual fines in the product after one separation stage. 

Grade efficiency curve (a) without taking into account dead flux effect, and (b) taking into account dead flux effect. 

Table 10.2 presents the particle size distributions for the overflow and underflow through the hydrocyclone. Therefore, Equation 10.28 would be the appropriate to derive the grade efficiency. Since the separation was carried out in a hydrocyclone, and this type of device normally presents a dead flux effect previously described. Equation 10.29 should be used to derive the reduced grade efficiency. Carrying out the proper computations using the tabulated data and the equations mentioned. Table 10.3 is obtained. 

The total flux plot depends not only on the settling characteristics of the solids, but also on the selected underflow concentration because total flux includes the transport flux, or dead flux, contributed by movement of particles downward as underflow is withdrawn. The plot can be made independent of Cu by subtracting the transport flux contribution from G and plotting the resultant settling flux G, as done in Figure 10.23b. A line drawn tangentially... 

Owing to the effect of the suspension concentration that has an influence in the dead flux effect, sufficiently discussed in previous sections, the concentration as a fraction C and the imderflow-to-throughput ratio Rf are... 

Note that the S-shaped grade efficiency curves do not necessarily start from the origin—in applications with a considerable underflow to throughput ratio (by volume) R, the grade efficiency curves tend to the value G x) = / f as X —> 0. This is a result of the splitting of the flow, or dead flux that carries even the finest solids into the underflow in proportion to the volumetric split of the feed. Section 3.4 discusses possible modifications to the efficiency definitions which account for the volumetric split and illustrate only the net separation effect. Such reduced efficiencies are widely used for hydrocyclones and nozzle-type disc centrifuges where large diluted underflows occur. 

Rf = UIQ is the underflow-to-throughput ratio (by volume) which is the minimum efficiency due to dead flux. 

The effect of flow splitting (or dead flux ) in applications with appreciable and dilute underflow, as is common with some separators, is to modify the shape of the grade efficiency curve to make it appear as if the performance of the separator were better than it actually is. As shown in Figure 3.15, the curve does not start from the origin (as it should for inertial separation) but has an intercept, the value of which is usually equal to the underflow-to-throughput ratio Rf. This is because the very fine particles simply follow the flow and are split between the underflow and the overflow in the same ratio as the fluid. The R ratio is defined as the fraction of the volumetric feed rate which turns up in the underflow, i.e. the underflow rate, divided by the feed rate. 

In order to be able to optimize the system, we have to know how the flow ratio affects the separation of the solids. In the case of hydrocyclones, the effect of the ratio is two-fold increasing Rf leads to improvements to separation efficiency through the contribution of dead flux and a further improvement is caused by the reduction in the crowding of the underflow orifice. Both of the effects can be described analytically for certain hydrocyclone geometries and the above-mentioned optimization is therefore possible, using the entropy index as a general criterion for the optimization. 

The effect of dead flux on total efficiency is eliminated in the same way as for grade efficiency (egn.1), i.e. 

Since the void fraction distribution is independently measurable, the only remaining adjustable parameters are the A, so when surface diffusion is negligible equations (8.23) provide a completely predictive flux model. Unfortunately the assumption that (a) is independent of a is unlikely to be realistic, since the proportion of dead end pores will usually increase rapidly with decreasing pore radius. 

In Germany and Japan, pulverized quicklime is used in making self-fluxing sinters, partially replacing limestone. Granular dead-burned dolomite is stiU used to protect the refractory lining of open-hearth and electric furnaces, but not the basic oxygen furnace. Refractory time has declined with the... 

Fluxes are linear functions of reservoir contents. Reservoir size and the residence time of the carbon in the reservoir are the parameters used in the functions. Between the ocean and the atmosphere and within the ocean, fluxes rates are calculated theoretically using size of the reservoir, surface area of contact between reservoirs, concentration of CO2, partial pressures of CO2, temperature, and solubility as factors. The flux of carbon into the vegetation reservoir is a function of the size of the carbon pool and a fertilization effect of increased CO2 concentration in the atmosphere. Flux from vegetation into the atmosphere is a function of respiration rates estimated by Whittaker and Likens (79) and the decomposition of short-lived organic matter which was assumed to be half of the gross assimilation or equal to the amount transferred to dead organic matter. Carbon in organic matter that decomposes slowly is transferred... 

The transfer of P from land to terrestrial biota (F23) represents the sum of terrestrial biological productivity. There is no significant gaseous form of P, nor is there a major transfer of living organisms between the freshwater-terrestrial system and the oceans. The terrestrial biota system is, therefore, essentially a closed system where the flux of P to the biota (p23) is balanced by the return of P to the land from the biota (F32) due to the decay of dead organic materials. 

To determine the expressions for the optimised counting times, we write the expressions (10) and (11) in terms of count-rates and times (count rates are constant quantities for each Bragg reflection). We assume that the incident neutron flux is constant during a flipping ratio measurement, and that no dead-time correction is needed. In these conditions, we have the relations ... 

The other output from watershed and slope landscapes positions is related to the surface and subsurface runoff of trace metals. The ecosystems of waterlogged glacial valleys, geochemically subordinate to the above mentioned landscape, can receive with surface runoff an additional amount of various chemical species. This results in 3 1-fold increase of plant productivity in comparison with elevated landscapes and in corresponding increase of all biogeochemical fluxes of elements, which are shown in Table 6. For instance, the accumulation of trace metals in dead peat organic matter of waterlogged valley was assessed as the follows Fe, n x 101 kg/ha, Mn, 1-2 kg/ha, Zn, 0.1-0.3 kg/ha, Cu, Pb, Ni, n x 10-2 kg/ha. 

Dead time considerations in the alpha particle detection limit the count rate, and hence limit the neutron flux that can be used with this approach. This means that large scan times will probably be required with most implementations of this approach. 

As stated in Chapter 9, cross-flow filtration (CFF) provides a higher efficiency than dead-end filtration, as some of particles retained on the membrane surface are swept off by the liquid flowing parallel to the surface. As shown by a solid line in Figure 14.6 [3], filtrate flux decreases with time from the start of filtration due to an accumulation of filtered particles on the membrane surface, as in the case of dead-end filtration. The flux then reaches an almost constant value, where... 

Ischemia may be major with absence of blood flux over the entire ocular surface, making it look like dead eye (Fig. 7.5). 

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