Critical particle diameter

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. 

Dpmin = critical particle diameter p = gas viscosity B, = inlet duct width... 

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... 

These relations are used in Example 18.5 to find the size of a separator corresponding to a specified critical particle diameter, and to the reverse problem of finding the extent of removal of particles when the diameter of the vessel and the velocity are specified. 

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

Nevertheless, the microstructure cannot be directly correlated to the initial /1-content in the starting powder. The experimentally determined particle density in sintered samples indicates that only a part of the initial /I particles are able to grow [283]. The number of growing /1-particles depends on a critical particle diameter dcrit (Fig. 18). Particles below dcrit will dissolve in the oxide nitride liquid during phase transformation and reprecipitate on the overcritical /1-particles according to an anisotropic Ostwald ripening process [284, 292, 293]. 

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

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.

Fig. 7. Effect of liquid viscosity on lower critical particle diameter solid-liquid fluidized beds [a = 3.0, Cy = /(e), pl = 1000 kg/m ].

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 ].

Lower limit of critical particle diameter, m Upper limit of critical particle diameter, m Coefficient of dispersion, m /s Dimensionless coefficient of dispersion... 

Many theories have been proposed to predict the performance of a cyclone, although no fundamental relationship has been accepted. Attempts have been made to predict the critical particle diameter, (Dp) j,. 

This is the size of the smallest particle that is theoretically separated from the gas stream with 50 percent efficiency. The critical particle diameter is defined by [16]... 

The rate of condensation is proportional to the difference between the particle diameter and the critical particle diameter. 

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)... 

If the toughening effect is based mainly on the formation of crazes, the particle diameter, D, is of primary importance. Particles act as stress concentrators and directly initiate the crazes. There are critical particle diameters, which depend only on the ability of the matrix to form crazes (if all particles possess the same modulus, i.e., give the same stress concentration). The opti-... 

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. 

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