Comparison of Model Predictions with Experiment

The approach described in Sections 8.2.3 and 8.2.4.5.3 was used to construct quasi-2D (Q2D) analytical and semi-analytical models of PEFC [246, 247] and DMFC [248, 249], The Q2D model of a PEFC [246] takes into account water management effects, losses due to oxygen transport through the GDL, and the effect of oxygen stoichiometry. The model is fast and thus suitable for fitting however, the systematic comparison of model predictions with experiment has yet not been performed. Q2D approaches have been employed to construct a model of PEFC performance degradation [250], to explain the instabilities of PEFC operation [251, 252] and to rationalize the effect of CO2 bubbles in the anode channel on DMFC performance [253, 254],... 

Onr discussion of the free energy driving forces will mostly follow the discussions ontlined in Venables et al. [5] and in Markov [3], The extension of the atomistic approach to the organics will come from Verlaak et al. [15]. The elements of the rate equation will follow Venables et al. [5]. Dynamic scaling will then follow as an extension to the rate equations coupled with some assumptions about the island size distributions [23]. For deposition beyond the first layer the comparison of model predictions with experiment will follow Cohen et al. [29]. The height-height correlation description will follow Krim and Palasantzas [30]. 

The immobihzed papain system has been subjected to much theoretical analysis using diffusion-reaction and partial differential equation models that take into account the pH-sensitivity of papain s activity [55-58]. The models predict a sharp pH front that moves back and forth across the membrane. Comparison of model predictions with experiment has been disappointing, however [58]. The models predict much sharper oscillations than are attained in the experiments. 

Fig. 2 Comparison of model prediction with experimental data on radius of SUwet L-77 drop in the spreading and de-oiling experiments. The dotted line represents Eq. 3 with...

The model and the results presented here illustrate the physicochemical processes involved in char gasification with simultaneous sulfur capture. In particular, they demonstrate that diffusion limitations in the gasification reactions enable the conversion of CaO to CaS within the char even though CaS formation is not feasible at bulk gas conditions. Furthermore, this first version of the model correctly predicts the trends observed experimentally. Future effort in this area will focus on quantitative comparisons of model predictions with results from carefully designed gasification experiments. 

For the dissociation dynamics of diatom on rigid surface, the TD treatment is discussed using models ranging from the crude 3D flat-surface model to the exact 6D model with full inclusion of the surface corrugation effect. The H2/Cu system is used as an benchmark system and the theoretical results obtained from several model calculations are presented for H2 and HD dissociation on Cu(lll) surface. Interesting dynamical effect, such as the steric effect in molecular-surface reaction, is discussed and comparison of theoretical predictions with experiment is also made. 

An excellent comprehensive survey on the fundamentals of different types of model for RD processes has recently been given by Taylor and Krishna [1]. In that paper the focus is on modeling concepts, we focus here on the application of such models, especially the comparison of model predictions with experimental data and the bacdcground of the complexity of the model and the effort needed for its parameterization. We do account for the fact that the results of any sucdi comparison win depend on the cdiosen example, but emphasize that comparison with experimental data, especially in predictions, is the final test for any modeling strategy. Unfortunately, there is only a very limited amount of data on RD experiments available in the open hterature for sucdi comparisons. 

We now show that equations analogous to Eq. (34) follow for the enthalpy and entropy of mixing, AHM and ASM, but that, in contrast to the chemical potentials, the partial molar enthalpies and entropies for the components differ from those for the species. Finally we show that the equation for the constant pressure relative heat capacity is of a slightly more complicated form than Eq. (34). Equation (34) and its analogs for and ASM are necessary for comparison of model predicted quantities with experiment. From basic thermodynamic equations we have... 

Recently, the stiff-chain polyelectrolytes termed PPP-1 (Schemel) and PPP-2 (Scheme2) have been the subject of a number of investigations that are reviewed in this chapter. The central question to be discussed here is the correlation of the counterions with the highly charged macroion. These correlations can be detected directly by experiments that probe the activity of the counterions and their spatial distribution around the macroion. Due to the cylindrical symmetry and the well-defined conformation these polyelectrolytes present the most simple system for which the correlation of the counterions to the macroion can be treated by analytical approaches. As a consequence, a comparison of theoretical predictions with experimental results obtained in solution will provide a stringent test of our current model of polyelectrolytes. Moreover, the results obtained on PPP-1 and PPP-2 allow a refined discussion of the concept of counterion condensation introduced more than thirty years ago by Manning and Oosawa [22, 23]. In particular, we can compare the predictions of the Poisson-Boltzmann mean-field theory applied to the cylindrical cell model and the results of Molecular dynamics (MD) simulations of the cell model obtained within the restricted primitive model (RPM) of electrolytes very accurately with experimental data. This allows an estimate when and in which frame this simple theory is applicable, and in which directions the theory needs to be improved. 

Figure 16. Comparison of model predictions and experimental data for MEO of EG by Ag(II) in the electrochemical batch reactor. The cell was maintained at 40% i (673 mA and 33°C). Square ( ) and triangular (A) symbols represent data obtained during experiments with Nafion 117 cation-exchange membrane and Vycor microporous glass, respectively.

The following comparison of the predictions of this model with experiment has not been hitherto presented (no earlier test, e.g. in refs [1,48,77,78], took into account all of the effects of compartmentalization, coagulation, and the full models for entry and exit including aqueous-phase kinetics, although all of the cited references included some of these). The present test involves a comparison between model predictions and experiment for styrene emulsion polymenzation at 50 °C with Aerosol MA (the trade name of the dihexyl ester of sodium sulfo-succinic acid, Cytec) as surfactant. For this system, Os = 45 [79], the cmc... 

In Spite of the existence of numerous experimental and theoretical investigations, a number of principal problems related to micro-fluid hydrodynamics are not well-studied. There are contradictory data on the drag in micro-channels, transition from laminar to turbulent flow, etc. That leads to difficulties in understanding the essence of this phenomenon and is a basis for questionable discoveries of special microeffects (Duncan and Peterson 1994 Ho and Tai 1998 Plam 2000 Herwig 2000 Herwig and Hausner 2003 Gad-el-Hak 2003). The latter were revealed by comparison of experimental data with predictions of a conventional theory based on the Navier-Stokes equations. The discrepancy between these data was interpreted as a display of new effects of flow in micro-channels. It should be noted that actual conditions of several experiments were often not identical to conditions that were used in the theoretical models. For this reason, the analysis of sources of disparity between the theory and experiment is of significance. 

Comparisons of the data with predictions based on the theory of Brinkman (45) and Debye and Bueche (79) or on the model experiments of Kuhn and Kuhn (153) lead to very similar conclusions. 

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