Agglomeration model

The product granules are also assumed to be spherical and of uniform radius gr the envelope volume Vg and external surface area Sg of a single granule are given by equafions 5.19. and 5.20 respecfively. 

The ratio of total binder volume to total particle volume in the bed is denoted by y. If all granules are uniform fhis quantity must equal the binder volume to particle volume ratio for each granule. By defini-fion, the volume of parficles per granule is aVg and fhe volume of binder per granule isfWg less fhe deficiency of binder at the granule surface, AS sn Therefore y is given by 

if p (=l/g), the ratio of initial particle diameter to granule diameter, is introduced then equation 5.23 becomes 

This equation defines the relationship between the quantity of binder fed info the fluidized bed and the mean diameter of the product granules. A plot of y against P should give a straight line of gradient -3 k s and an intercept, at = 0, equal to kf. 

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It calculates one-dimensional heat conduction through walls and structure no solid or liquid ciMiibustion models are available. The energy and mass for burning solids or liquids must be input. It has no agglomeration model nor ability to represent log-normal particle-size distribution. 

Gloaguen F, Convert P, Gamhurzev S, Velev OA, Srinivasan S. 1998. An evaluation of the macro-homogeneous and agglomerate model for oxygen reduction in PEMFCs. 

The equations used in these models are primarily those described above. Mainly, the diffusion equation with reaction is used (e.g., eq 56). For the flooded-agglomerate models, diffusion across the electrolyte film is included, along with the use of equilibrium for the dissolved gas concentration in the electrolyte. These models were able to match the experimental findings such as the doubling of the Tafel slope due to mass-transport limitations. The equations are amenable to analytic solution mainly because of the assumption of first-order reaction with Tafel kinetics, which means that eq 13 and not eq 15 must be used for the kinetic expression. The different equations and limiting cases are described in the literature models as well as elsewhere. 

If external mass-transfer limitations can be neglected, then the surface concentration in eq 58 (via eq 13) can be set equal to the bulk concentration, which is assumed uniform throughout the catalyst layer in the simple agglomerate models. Otherwise, the surface concentration is unknown and must be... 

This equation is the governing equation for the agglomerate models for the cathode, and without external mass-transfer limitations, it results in eq 58. For the anode, a similar analysis can be done. 

The rest of the comparisons were done for the cathode. The results all showed that the agglomerate model fits the data better than the porous-electrode model. However, it should be noted that the porous-electrode model used was usually a thin-film model and so was not very robust. Furthermore, the agglomerate model has more parameters that can be used to fit experimental data. Finally, some of the agglomerate models compared were actually embedded models that account for both length scales, and therefore, they normally agree better with the experimental data. 

A comparison of the two models with experimental data is given in Figure 12. In the figure, simulations were run with a simple agglomerate model and a... 

The other approach is more complicated and requires a deeper knowledge of the agglomerate structure or yields more fitting parameters. In this approach, the porous-electrode equations are used, but now the effectiveness factor and the agglomerate model equations are incorporated. Hence, eq 64 is used to get the transfer current in each volume element. The gas composition and the overpotential... 

Figure 5.8 Agglomeration model view of the granule surface.

In the system considered it is assumed that there is no variation in the rate constant locally in the structure. For electrochemical systems this is equivalent to assuming a constant potential in the structure and is an approach used in plane or agglomerate models of electrocatalysts. 

The membrane electrode assembly (MEA), which consists of three components (two gas diffusion electrodes with a proton exchange membrane in between), is the most important component of the PEMFC. The MEA exerts the largest influence on the performance of a fuel cell, and the properties of each of its parts in turn play significant roles in that performance. Although all the components in the MEA are important, the gas diffusion electrode attracts more attention because of its complexity and functions. In AC impedance spectra, the proton exchange membrane usually exhibits resistance characteristics the features of these spectra reflect the properties of the gas diffusion electrode. In order to better understand the behaviour of a gas diffusion electrode, we introduce the thin-film/flooded agglomerate model, which has been successfully applied by many researchers to... 

The characteristics of a gas diffusion electrode can also be illustrated by the thin-film/flooded agglomerate model. Paganin et al. [4] summarized the parameters that often appear in the impedance spectra of H2/02 and H2/air fuel cells ... 

Springer TE, Raistrick ID (1989) Electrical impedance of a pore wall for the flooded-agglomerate model of porous gas-dilFusion electrodes. J Electrochem Soc 136 1594-603... 

If the growth of the synthesized spherical gel is governed by Ihe agglomeration model, it is expected that the silica gels have high specific surface area, because the spherical gels are composed of primary nanogels. 

Prins-Jansen, J.A. Hemmes, K. de Wit, J.H.W. An extensive treatment of the agglomerate model for porous electrodes in molten carbonate fuel cells—I. Qualitative analysis of the steady-state model. Electrochim. Acta 1997, 42 (23-24), 3585-3600. 

For cylindrical-shaped soot agglomerates, Mackowski et al. [190] presented more detailed expressions for both absorption and scattering efficiency factors, and showed that the expressions were reliable from the visible wavelength range up to 5 pm. They also applied a hybrid sphere/cylinder-shaped soot agglomerate model to interpret the experimental results obtained for the hydrocarbon flames, and showed that a larger fraction of soot agglomerates behave like cylinders [190,191]. 

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