Two-particle model

Kalyuzhnyi, S., A. Veeken, and B. Hamelers (2000), Two-particle model of anaerobic solid state fermentation, Water Set Tech., 41(3), 43-50. 

Figure 3. Two particle models used to calculate the theoretical scattered intensity. (A) = the discoid (B) = the closed lamella (o) water molecule ( ) s oxyethylene chain ...

The conversion in the reactor decreases with larger particles. The effect is greater for the two-particle model and occurs at smaller particle sizes. The reason for this is that for two particles the CO2 have to diffuse out of the catalyst particle, through the bulk phase, and into the sorbent and this becomes... 

It is our opinion that these results provide a powerful impetus towards the further development of the egg model (already developed in its main features by Stepanov and Shliomis [80]) for the purpose of gaining a simple analytic formula for the effective relaxation time (analogous to Eqs. (8.1) and (8.5)). This approach, as it is essentially based on a two particle model, allows one to take account of the Interdependence of the Neel and Debye relaxation mechanisms and simultaneously eliminates the undesirable features of the present theory which is based on the two extremes of a frozen liquid matrix [17] and a frozen magnetic moment [16]. 

Figure 4.2. Two-particle model for initial stage sintering (a) without shrinkage and (b) with shrinkage.

In the two-particle model of initial stage sintering, the neck growth is expressed as xldf = F T)d "t (Eq. (4.28)), where x is the neck radius and a the particle radius. The equation is, in general, acceptable for (x/u) < 0.2. With increasing values of (x/a) above 0.2, would the exponent n become smaller or larger Explain. 

Explain why the shrinkage equation derived from a two-particle model cannot be applicable to the prediction of the shrinkage of a real powder compact with a particle size distribution. 

Figure 16.2. Kingery s two-particle model of liquid phase sintering.

For a two-particle model with a constant volume fraction of liquid, explain the variation of the compressive pressure between the particles with particle size. 

Figure 8.2 Two-particle model made of glass spheres (3 mm diameter) sintered at 1000°C. (x and a represent the radius of the neck and the sphere, respectively.). (From Ref. 66.)...

The presented continuous analysis methods, both the multibody system and the two-particle model, have been compared to the piecewise analysis method. For the piecewise analysis, the impulse-momentum equations used at the time of impact are of canonical... 

For the piecewise analysis of this multibody system, a coefficient of restitution of 0.83 was used [19]. Two continuous analyses were then performed. In one, the contact force model with hysterisis damping, equation (10) was directly used in the multibody system equations ot motion. These equations were numerically integrated forward in time over the period of contact. In the second, the analysis was performed for the two-particle model. Summary of the results are shown in Table 1. 

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