Compressibility, excess

In previous work, we have mainly used the DPM model to investigate the effects of the coefficient of normal restitution and the drag force on the formation of bubbles in fluidized beds (Hoomans et al., 1996 Li and Kuipers, 2003, 2005 Bokkers et al., 2004 Van der Floef et al., 2004), and not so much to obtain information on the constitutive relations that are used in the TFMs. In this section, however, we want to present some recent results from the DPM model on the excess compressibility of the solids phase, which is a key quantity in the constitutive equations as derived from the KTGF (see Section IV.D.). The excess compressibility y can be obtained from the simulation by use of the virial theorem (Allen and Tildesley, 1990). 

The conclusion is that the soft-sphere model can be used as an alternative for the hard-sphere model, as far as the calculation of the excess compressibility is concerned. 

Next, we consider a system of inelastic spheres (ISs). As can be seen from Eq. (81), the KTGF predicts that the excess compressibility yls of ISs is a linear function of the coefficient of normal restitution e,... 

In Fig. 21, the excess compressibility is shown as a function of the solid fraction for different coefficients of normal restitution e. These results are compared with the Eq. (54), where the excess compressibility yES is taken from either the Ma-Ahmadi correlation (Ma and Ahmadi, 1986) or the Carnahan-Starling correlation. As can be seen, the excess compressibility agrees well with both correlations for a solid fraction ss up to 0.55. For extremely dense systems, i.e., es>0.55, the Ma-Ahmadi correlation presents a much better estimate of the excess compressibility, which is also the case for purely elastic particles (see Fig. 23). 

Fig. 20. Excess compressibility yIS for a system of inelastic hard spheres, as function of the coefficient of normal restitution, for one solid fraction (as = 0.05). The excess compressibility has been normalized by the excess compressibility y is of the elastic hard spheres system. Other simulation parameters are as in Fig. 19.

Fig. 21. The excess compressibility from soft-sphere simulations, with random initial particle positions, for different coefficients of normal restitution e (a) e = 1.0 (top-right) (b) e = 0.95 (top-left) (c) e = 0.90 (bottom-right) (d) e = 0.80 (bottom-left). The simulation results (symbols) are compared with Eq. (54) based on the Ma-Ahmadi correlation (solid line) or the Camahan-Starling correlation (dashed line). The spring stiffness is set to k = 70,000.

Fig. 22. The effect of the cohesive force on the excess compressibility. The coefficient of normal restitution is e = 1.0, and granular temperature is T = 1.0. The Hamaker constant is A = 3.0 x 10-12 (circles) and 3.0 x 1CT10 (crosses).

Of the most common DL materials, carbon fiber papers are widely known for being mechanically weak because their microstructure is destroyed when excessive compression forces are applied to them (i.e., when compressing a fuel cell). This destruction of the materials affects the porosity, which has a... 

The fact that compounds with an 8,14 double bond (VIII) cannot be hydrogenated implies that the isomerization cannot proceed via a half-hydrogenated species, an essentially saturated structure. To avoid the excessive compression between the angular methyl groups at C-10 and C-13 which is enforced by the required geometry of the transition to the half-hydrogenated state (IX) the isomerization proceeds via an allylic intermediate (X) which permits the carbon atom at C-8 to retain its hybridization (Fig. 13). 

Other macroscopic properties that in principle can be measured are the excess density and the excess compressibility of the interfacial liquid. These excess quantities can be positive or negative and follow from a comparison of the corresponding quantities in systems with the liquid and solid separated. Alternatively, liquid behaviour in pores can be studied. An example of this kind has been given by Derjaguin ) who claims that water in narrow pores of silica gel or Aerosil does not exhibit the typical thermal expansion minimum at 4 C because of structural changes near the surface. Ldring and Findenegg ) studied surface excesses dilatometrically. 

Particularly attractive method for preparation of synthetic zeolite is recrystallization of natural aluminosilicates, such as kaolinite (halloysite), previously formed for elimination of plastic flow of highly thixotropic, pulverized zeolite. Some additional components of initial mixtures, such as texture modifiers (hard coal, lignite, cellulose, silica, aluminum oxide) are also introduced. They enrich the structure of zeolite adsorbent in transport pores and prevent an excessive compression of the clay material during the formation process. This results in an increase in product efficiency during the crystallization of zeolite phase. 

If ultra low temperatures down to -320°F (-196°C) are required, 9% nickel steel and austenitic stainless steels can be used. Nickel steels with their lower coefficients of thermal expansion may be preferred, since low temperature is likely to result in excessive compression of the CRM lining with the higher coefficient of expansion of austenitic stainless steels. 

Brick spalling is the condition wherein V4 to V2 in. of the brick face breaks away. This is not of concern if it occurs in a few brick in isolated locations since this would probably be a result of individual brick characteristics. However, if the condition occurs in a concentrated area involving a significant number of adjacent brick, there is cause for concern and a specialist should be contacted to analyze the problem. Spalling problems can be caused by thermal shock, excessive compression, receded mortar joints, exposed brick edges, or perhaps other factors. 

The eonditioning treatment can be overdone. If the wood is steamed for too long and the surfaee fibres re-adsorb too much water this will induce an excessive compression set in the surface fibres. At the end of drying, when the surface fibres return to the natural equilibrium moisture content they will want to shrink more than normal wood (because of the excessive compression set), thus producing tension at the surface and compression in the interior. The lumber has been reverse case hardened. This condition cannot be treated. 

---