Comparison of experimental

A ll ide variety of thermodynamic properties can be calculated from compufer simulations a Comparison of experimental and calculated values for such properties is an important way in which the accuracy of the simulation and the underlying energy model can be quantified. Simulation methods also enable predictions to be made of the thermodynamic properties of V.stems for which there is no experimental data, or for which experimental data is difficult or impossible to obtain. Simulations can also provide structural information about the... 

There must be ongoing comparison of experimental results and modelistic predictions. Experiment and theory feed each other. 

FIG. 13-18 Comparison of experimental K-value data and SRK correlation. [Henley and Seader, Equilibrium-Stage Separation Operations in Chemical Engineering, Wiley, New York, 1981 data of Yarhorough, J. Chem. Eng. Data, 17,129(1972).]... 

A comparison of experimental data for carbon dioxide absorption obtained oy Hatta anci Katori (op. cit.), Grimley [Trans. Inst. Chem. Eng., 23, 228 (1945)], and Vyazov [Zh. Tekh. Fiz. (U.S.S.R.), 10, 1519 (1940)] and for absorption or oxygen and hydrogen by Hodgson (S. M. thesis, Massachusetts Institute of Technology, 1949), Henley (B.S. thesis. University of Delaware, 1949), Miller (B.S. thesis. University of Delaware, 1949), and Richards (B.S. thesis. University of Delaware, 1950) was made by Shei wood and Pigford (Absorption and Extraction, McGraw-Hill, New York, 1952) and is indicated in Fig. 14-78. 

Fig. 28. A comparison of experimental and predicted tensile failure probabilities for four graphites with widely different textures AGX, H-451, IG-110 and AXF-5Q.

Table 1. Comparison of experimentally observed electronic shell closings with model calculations ...

The contiguity factor, Cj is actually a so-called fudge factor used to make sense out of the comparison of experimental dataTwitlirtheore-tical predictions. This correlation factor is useful only when the data fall between the theoretical bounds. The concept of a contiguity factor, i.e.. 

One of the most important concepts in pharmacology is the comparison of experimental data to models, notably to... 

In this equation, AH is not known, but Eucken (as quoted by von Stackelberg48) suggested, AH = 0, and comparison of experimental and calculated heats of hydrate formation30 certainly supports a low value of AH. The variation of the composition of a gas hydrate along the three-phase line ice-hydrate-gas will therefore be small. (The variation along the three-phase line hydrate-aqueous liquid-gas is larger, cf. Section III.C.(l).)... 

Fig. 1. Comparison of experimental and theoretical values of Mc at free-radical copolymerization of AAm with MBAA as a crosslinking agent CT — total concentration of monomers, C — that of MBAA C = 10 wt% (/), CT = 6.7 g dl-1 (2). From Baselga et al. [18]...

Figure 7.8 Comparison of experimental ln7 for 1 1, 2 1, and 2 2 electrolytes. The symbols indicate the experimental results, with representing HC1 (z+ = 1, z = — 1) representing SrC ( + = 2, r = — 1) and A representing ZnS04 (z+ = 2, z = -2). The lines are the Debye-Huckel predictions, with the solid line giving the prediction for (z+ = 1, z = -1) the dashed line for (z+ = 2, r = -1) and the dashed-dotted line for (z+= 2, z =-2). In (a), In 7- calculated from the limiting law [equation (7.45)] is shown graphed against I 2. In (b). In 7- calculated from the extended form [equation (7.43)] is shown graphed against 7m2.

Although Hammett convincingly explained the nitrosation of aliphatic amines and the diazotization of aniline under the conditions employed by Schmid and others, one unsatisfactory point remained namely the second-order kinetic equation obtained by Hantzsch and the workers who followed him for diazotization in a more weakly acidic medium. Comparison of experimental details shows that at concentrations of free mineral acid below 0.05 m the reaction is apparently second-order, but it becomes third-order at higher concentrations of acid. 

Sn + Pb is a two-phase eutectic system in which fine crystals of Pb with a linear parameter of 0.01 to 0.02 fim are localized along the grain boundaries of large Sn crystals (3 to4//m). A comparison of experimental... 

Metal/molten salt interfaces have been studied mainly by electrocapillary833-838 and differential capacitance839-841 methods. Sometimes the estance method has been used.842 Electrocapillary and impedance measurements in molten salts are complicated by nonideal polarizability of metals, as well as wetting of the glass capillary by liquid metals. The capacitance data for liquid and solid electrodes in contact with molten salt show a well-defined minimum in C,E curves and usually have a symmetrical parabolic form.8 10,839-841 Sometimes inflections or steps associated with adsorption processes arise, whose nature, however, is unclear.8,10 A minimum in the C,E curve lies at potentials close to the electrocapillary maximum, but some difference is observed, which is associated with errors in comparing reference electrode (usually Pb/2.5% PbCl2 + LiCl + KC1)840 potential values used in different studies.8,10 It should be noted that any comparison of experimental data in aqueous electrolytes and in molten salts is somewhat questionable. 

The recipe (5.58) is even more sensitive to the high-frequency dependence of kjj than similar criterion (5.53), which was used before averaging over kinetic energy of collisions E. It is a much better test for validity of microscopic rate constant calculation than the line width s j-dependence, which was checked in Fig. 5.6. Comparison of experimental and theoretical data on ZR for the Ar-N2 system presented in [191] is shown in Fig. 5.7. The maximum value Zr = 22 corresponding to point 3 at 300 K is determined from the rate constants obtained in [220],... 

Fig. 5.7. Comparison of experimental data from [191] (1), [221] (2), [220] (3) and ultrasonic point [216] (4) with SCS calculation [191] (solid line) and classical trajectories calculations from [222] (dotted line), [223] (broken line) and [216] (4 ).

Fig. 3. Comparison of experimental values (solid curves) and predicted values (dashed lines) of a a for Fe-Co, Co-Ni, and Ni-Cu alloys. The short vertical lines indicate change in crystal structure.

Table 4. Comparison of experimental values (see text) with calculated data for Eqs. (3)-(5) (in kJ mol-1)...

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. 

This chapter has the following structure in Sect. 3.2 the common characteristics of experiments are discussed. Conditions that are needed for proper comparison of experimental and theoretical results are formulated in Sect. 3.3. In Sect. 3.4 the data of flow of incompressible fluids in smooth and rough micro-channels are discussed. Section 3.5 deals with gas flows. The data on transition from laminar to turbulent flow are presented in Sect. 3.6. Effect of measurement accuracy is estimated in Sect. 3.7. A discussion on the flow in capillary tubes is given in Sect. 3.8. 

We begin the comparison of experimental data with predictions of the conventional theory for results related to flow of incompressible fluids in smooth micro-channels. For liquid flow in the channels with the hydraulic diameter ranging from 10 m to 10 m the Knudsen number is much smaller than unity. Under these conditions, one might expect a fairly good agreement between the theoretical and experimental results. On the other hand, the existence of discrepancy between those results can be treated as a display of specific features of flow, which were not accounted for by the conventional theory. Bearing in mind these circumstances, we consider such experiments, which were performed under conditions close to those used for the theoretical description of flows in circular, rectangular, and trapezoidal micro-channels. 

Thus, the comparison of experimental results to those obtained by conventional theory is correct when the experimental conditions were consistent with the theoretical ones. The experimental results corresponding to these requirements agree quite well with the theory ... 

TABLE VI. COMPARISON OF EXPERIMENTAL AND CALCULATED DEGREES OF POLYMERIZATION... 

Figure 8. Comparison of experimental and calculated weight fraction distributions for Run 2 ((0) Exp (---------) Micro- D (---) Micro (---) Seg)...

Extensive comparisons of experimental frequencies with HF, MP2 and DFT results have been reported [7-10]. Calculated harmonic vibrational frequencies generally overestimate the wavenumbers of the fundamental vibrations. Given the systematic nature of the errors, calculated raw frequencies are usually scaled uniformly by a scaling factor for comparison with the experimental data. 

Figure 29 shows a comparison of experimental results with calculation results obtained for cyclohexane. The discretization of film thickness is again observed as in the OMCTS results, and the interval is 0.5-0.6 nm, which is roughly the same as the molecular diameter of cyclohexane. 

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