Critical particle

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 ... 

Critical Particle Diometer Above Which Law Will Nat Apply... 

Metal deposition can occur only if 77 is negative so the Gibbs energy of a cluster as a function of the particle number N first rises, reaches a maximum, and then decreases. This is illustrated in Fig. 10.4 for three different overpotentials. Notice how strongly the curve depends on the applied overpotential. AG reaches its maximum for a critical particle number of ... 

However, there is no exact quantitative method which makes it possible to calculate the critical particle size that will produce an optimum in hiding power in a colored pigment formulation. Although the basic theory behind this phenomenon has been treated extensively, it is still most advantageous for practical R D purposes to experimentally determine the particle size that affords a maximum in hiding power. A more approximate than quantitative rule has been established by H.H. Weber, which makes it possible to estimate the particle size that will afford a maximum in scattering ... 

This maximum in the entrainment flux observed by Wen and Tanaka is in some agreement with the work of Baeyens et al. [15]. Baeyens et al. worked with equilibrium fluidized catalytic cracking (FCC) catalyst powder with varying additions of fines. They found that below a critical particle size, entrainment rates leveled off and noted that this reflected the point where Van der Waals forces were in balance with gravitational forces. For their systems, this critical particle size was found to be approximated by the expression... 

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... 

Recall that this equation could be minimized with respect to particle radius to determine the critical particle size, r, as given by Eq. (3.35). This critical radius could then be used to determine the height of the free energy activation energy barrier, AG, as given by Eq. (3.36). A similar derivation can be performed for a cubic particle with edge length, a. 

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. 

It has been common practice to characterize initiation thresholds in terms of input pressure and in most of our subsequent discussion we will continue to use this criterion. As will be shown later, however, there is some merit to doing this in terms of a critical particle velocity u rather than pressure... 

The properties of immiscible polymers blends are strongly dependent on the morphology of the blend, with optimal mechanical properties only being obtained at a critical particle size for the dispersed phase. As the size of the dispersed phase is directly proportional to the interfacial tension between the components of the blend, there is much interest in interfacial tension modification. Copolymers, either preformed or formed in situ, can localize at the interface and effectively modify the interfacial tension of polymer blends. The incorporation of PDMS phases is desirable as a method to improve properties such as impact resistance, toughness, tensile strength, elongation at break, thermal stability and lubrication. 

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

As the particle size decreases, the ratio between the number of atoms at the surface to those in the bulk increases with a parallel decrease in the average coordination number for the metal atom, which is also expected to be a factor of electrocatalysis. It has been calculated for Pt that the minimum size of a crystallite (cluster) for all atoms to be on the surface is 4 nm, corresponding to a specific surface area of 280 m2g-1 [322] (note that this is larger than the critical particle size where absorption of H atoms disappears on Pd) [333]. It is also interesting that dispersed catalysts can in turn influence the electronic properties of the support so that an interesting combination of sites with varied properties can result [330]. At low catalyst loadings, spillover of intermediates is also possible. 

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]. 

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