Critical particle diameter for

Figure 14.7 Plot of saturation ratio or supersaturation as a function of critical particle diameter for soluble nuclei of 10-1B and 10-16 g.

If we assume that all particles with an equilibrium orbit radius greater than or equal to the cyclone body radius will be collected, then substituting r = R in Equation (9.19) we derive the expression below for the critical particle diameter for separation, Xan. ... 

The far left-hand curve of Figure 9.2 shows S to be always positive, so that there is no solution for the stability limit, S = 0 this represents a system that always fluidizes homogeneously. Increasing the particle diameter tends to shift the curve downwards the particle diameter dp which causes the curve to just touch the e-axis (second curve from the left) fixes a point on the homogeneous-transitional boundary of the stability map, as shown in Figure 9.1 the full boundary is obtained by finding this critical particle diameter for a range of values of particle density. 

In Figure 13 the relation between the intrinsic coercivity and the particle diameter dis given. The figure is based on a described model (35). The maximum is found around the critical particle diameter. In general the particle diameter and size is not very well defined. For the multidomain particles (d > ) the is smaller than the intrinsic anisotropy field of the particle. Nucleation effects cause a decrease in as the increases. This behavior is... 

Example Determine the dimensions of a simple settling chamber required to remove 50 ft size particles under the following conditions Gas capacity, q = 2400 mVhr Particle density, Pp = 2400 kg/m Gas temperature, t = 20 °C Gas density, p = 1.2 kg/m Gas viscosity, ft = 1.8x 10 N-s/m. The solution is as follows. The settling regime for the particles must be determined first. Hence, the critical particle diameter is computed first ... 

The question these correlations ask is why does the entrainment rate decrease for smaller particles for some systems whereas in other systems, the entrainment rate correlates with the particle terminal velocity or particle drag. Baeyens infers that particles may be clnstering due to an interparticle adhesion force that becomes dominant at some critical particle diameter. However, no evidence of particle clnsters was reported. Baeyens assnmption was based on fitting their data. Therefore, the role of particle clnstering on entrainment rates was difficult to establish from first principles. 

The above table is true for all fluids, and particles provided the critical particle diameter is not exceeded. The maximum particle diameters for which the four settling laws apply may be predicted with the formulas at the right side of Fig. 2. Also note that the particle velocity is determined by the Reynolds Num-... 

Capacity and efficiency depend on the inlet velocity and the dimensions of the vessel. Correlated studies have been made chiefly for the design of Figure 18.9 with a rectangular inlet whose width is D/4 (one-fourth of the vessel diameter) and whose height is 2-3 times the width. A key concept is a critical particle diameter which is the one that is removed to the extent of 50%. The corresponding % removal of other droplet sizes is correlated by Figure 18.11. The... 

The critical particle diameter and the final particle size for copolymerization with macromonomer were re-written by Guyot et al. as shown ... 

Figure 14.3 Saturation ratio for water as a function of critical particle diameter, single ion, atmospheric pressure, T = 273°C.

Fig. 11. Effect of density difference at various liquid viscosities on particle Reynolds number evaluation at lower critical particle diameter, (a) Solid-liquid fluidized beds [a = 3.0, Cv = f(s), pi = 1000 kg/m ]. (b) Gas-solid fluidized beds [a = 3.0, Cy = /(e), po = 1 kg/m ]. (c) Unified stability map of particle Reynolds number vs density difference for different values of transition hold-up solid-liquid fluidized beds [a = 3.0, Cy = f(s), p-l = 1 mPas, pi = 1000 kg/m ].

When a fast chemical reaction or a rapid quench leads to the formation of a high density of condensable molecules, panicle formation may take place either by homogeneous nucleation, an activated process, or by molecular "coagulation a process in which nearly all collisions are successful. What determines which of these processes controls In principle, this problem can be analyzed by solving the GDE for the discrete distribution discussed in the previous section. An approximate criterion proposed by Ulrich (1971) for determining whether nucleation or coagulation is the dominant process is based on the critical particle diameter d that appears in the theory of homogeneous nucleation (Chapter 9)... 

El-Shobokshy and Ismail [1981] noted that there was a critical particle size in deposition in relation to thermophoresis and inertial impaction. Deposition was a minimum at the critical particle size For particle diameters < the mechanism of deposition was largely due to thermophoresis above d the deposition was associated with inertia. 

Filtering is a method for the separation of materials. Materials with a particle diameter larger than the pores of the filter are collected as a filter cake, particles, which are smaller than the pores, can pass through the filter. With a fine filter one expects a transmission curve in the shape of a step function. For particles, which are smaller than the pore size, the transmission is 1 for particles, which are larger than the pore size, the transmission is zero, cf. Fig. 20.2. We will refer the diameter of particles that are in the range of the pore size of the filter the critical particle diameter, or consequently also as the critical pore size in the reverse view. 

Two characteristics are used to define cyclone performance. They are the critical particle diameter (particle size that is completely removed from the air stream) and the cut size (the particle diameter for which 50% collection efficiency is achieved). A typical example of theoretically and experimentally obtained efficiency curves is shown in Figure 9.24. It is evident from this diagram that particles above 15 pm are removed with high efficiency in the cyclone. The pressure drop across the cyclone unit ranges between 700 and 2000 Pa. 

The equilibrium vapor pressure of boron at the synthesis temperature of 2300 K is about 0.1 Pa, r 1 pm, andZ) 10 m s we obtain the flow of the order of 2 X 10 kg (m s) , which converted to the diameter of the evaporated particle in 1 s of the process provides a value of 1 pm. The critical particle diameter of boron at which the stationary combustion mode can be implemented is 0.1 pm. The typical combustion rates for the B-N2 system is l-5 mms thus, the characteristic times of the crystal growth processes are on the order of 1 -10 s. Thus, it is obvious that 0.1 pm B particle can be easily evaporated through the considered above mechanism. 

The same trend was also observed for fluidized beds with binary particle mixtures—alines in a coarse particle fluidized bed— by Ma and Kato (1998). The reason for this effect is probably the formation of particle agglomerates in the case of very fine particles for which adhesion forces are large compared to the gravitational forces. Baeyens et al. (1992) suggest based on their measurements a correlation for the critical particle diameter at which the inflection occurs ... 

For the system find the critical particle diameter. Also, if the separation is done with a no. 2 disk centrifuge (50 disks at a 45° angle), what is the rate of throughput ... 

The models agree well in terms of critical particle diameter or cut size. The grade-efficiency curve of Mothes-Loffier is obviously much flatter than that of Barth. We refer to our discussion above, where we state that Barth s index of 6.4 in Eq. (5.2.2) is in the high end of the range, and best suited for smooth, well-designed cyclones. In our experience the index for many older units of poorer design often lies between 2 and 4, which gives a slope much more in line with the model of Mothes and Lofiier. 

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