Simplified theoretical models

Gal-Or and Resnick (Gl) have developed a simplified theoretical model for the calculation of mass-transfer rates for a sparingly soluble gas in an agtitated gas-liquid contactor. The model is based on the average gas residencetime, and its use requires, among other things, knowledge of bubble diameter. In a related study (G2) a photographic technique for the determination of bubble flow patterns and of the relative velocity between bubbles and liquid is described. 

The second factor on the right-hand side of Eq. (5.1) is called the combinatorial factor. It is the partition sum of the equivalent ensemble of molecules that interact only through steric restraints. The combinatorial factor takes into account all size and shape effects of the molecules. There is no exact expression for Zc but, by fitting the simplified theoretical models to thermodynamic data of... 

Some of the gaps in the database can be filled by routine (but tedious and time-consuming) calculations using simplified theoretical models (e.g., BGG-model for electron-impact excitation and ionization of H2(NA v) states, the more involved impact-parameter method for excitation, etc.) For some of above listed processes (such as those mentioned under (d) and (e)), however, it is necessary to develop appropriate theoretical models for description of their dynamics. 

Kinetics The capacity and efficiency of biofilter operation is a function of active surface area, filter void space, target removal efficiency, gas species, gas concentration, and gas flow rate. A simplified theoretical model described by S.P.P. Ottengraf et al. is schematically represented by in Fig. 25-18. The mass balance made around the liquid-phase biolayer can be described as follows ... 

Another prediction of Vorkenstein s theory is that crystallite size influences semiconductor electronics. Figure 4.16 shows the bending of energy levels at the surface, the so-called Debye length. Since catalytic crystallites are much smaller than this dimension, the phenomenon is not found in these materials." Catalysts may be treated as two-dimensional semiconductors, a fact that greatly simplifies theoretical models. 

In both experimental and theoretical work, the principal uncertainty is often not in the raw data collected, but in their interpretation. Experimental measurements are frequently interpreted and adjusted on the basis of simplified theoretical models. 

Simplified theoretical model without consideration of the actual number of intemeurons)... 

Finally, it was shown that rapid granular flow simulations (RGFS) into which the effect of binder viscosity and surface tension are introduced, readily predict the outcome of granulation. These simulations support the simplified theoretical models of granule growth by coa-lescenee and granule deformation and breakup and... 

A review of the literature reveals that previous finite-element analyses of adhesive joints were either based on simplified theoretical models or the analyses themselves did not exploit the full potential of the finite-element method. Also, several investigations involving finite-element analyses of the same adhesive joint have reported apparent contradictory conclusions about the variations of stresses in the joint.(24,36) while the computer program VISTA looks promising (see Table 1), its nonlinear viscoelastic capability is limited to Knauss and Emri.(28) Recently, Reddy and Roy(E2) (see also References 37 and 38) developed a computer program, called NOVA, based on the updated Lagrangian formulation of the kinematics of deformation of a two-dimensional continuum and Schapery s(26) nonlinear viscoelastic model. The free-volume model of Knauss and Emri(28) can be obtained as a degenerate model from Schapery s model. 

Local-field corrections should be used with caution, bearing in mind that they depend on simplified theoretical models and cannot be measured directly. 

In Figure 5.13, fit against the concentration in the feed solution, Cq, is schematically plotted according to the simplified theoretical model discussed. 

---