Theory and Experimental Data

From Tolmin s theory and experimental data (e.g., Reichardtthe relationship between velocity profile and temperature profile in the jet cross-section can be expressed using an overall turbulent Prandtl number Pr = v /a, where Vf is a turbulent momentum exchange coefficient and a, is a turbulent heat exchange coefficient ... 

Kira Hagstrom and Alexander Zhivov. Design algorithm for room air distribution design using jet theory and experimental data on temperature and velocity distribution uniformity. Draft, Espoo 14.09, 1998. 

Bockris and Parry-Jones were the first to carry out experiments with a pendulum to measure the friction between a wetted substrate and the pivot upon which the pendulum swung. It should be noted that Rebinder and Wenstrom199 used such a device for an objective similar to that of Bockris and Parry-Jones, but they claimed that the characteristics of the pendulum oscillations reflected the hardness of the solid surface. The plastic breakdown determining this would be a function of v and this is a potential-dependent value.100, 01 More extensive determinations were made later by Bockris and Argade200 the theoretical treatment was given by Bockris and Sen.201 In the absence of adjustable parameters in the theory, a good agreement between theory and experimental data was assumed.201 The studies by Bockris and Parry-Jones indicated that the... 

We consider the problem of liquid and gas flow in micro-channels under the conditions of small Knudsen and Mach numbers that correspond to the continuum model. Data from the literature on pressure drop in micro-channels of circular, rectangular, triangular and trapezoidal cross-sections are analyzed, whereas the hydraulic diameter ranges from 1.01 to 4,010 pm. The Reynolds number at the transition from laminar to turbulent flow is considered. Attention is paid to a comparison between predictions of the conventional theory and experimental data, obtained during the last decade, as well as to a discussion of possible sources of unexpected effects which were revealed by a number of previous investigations. 

Fig. 4. Comparison between the theory and experimental data [53] for the turning moment coefficient.

The comparison between experimental and predicted intensity (Fig. 10.3) reveals deviations between theory and experimental data already at relatively low uniaxial deformation. A reasonable explanation is an increase of lattice distortions by local tensions which modify the envelope and thus the total intensity. Theoretical computation of mechanical anisotropy in a bcc-lattice supports the explanation [265],... 

Cramer III, R.D. (1977) Hydrophobic interaction and solvation energies Discrepancies between theory and experimental data. J. Am. Chem. Soc. 99, 5408-5412. 

It is not possible to say that a model is correct but a good fit between theory and experimental data is taken as confirming the likelihood of the model being the correct one. 

The theory of quanta has been a central preoccupation of the Solvay Conference since the first Solvay Conference on Physics, which took place in 1911. On that occasion, the fundamental discrepancies between classical theory and experimental data, which appeared at the beginning of the century, were discussed by major figures of modem science like Marie Curie, Albert Einstein, Max Planck, Henri Poincare, and many others. 

Comparisons with collision theory and experimental data... 

Electron transfer reactions and spectroscopic charge-transfer transitions have been extensively studied, and it has been shown that both processes can be described with a similar theoretical formalism. The activation energy of the thermal process and the transition energy of the optical process are each determined by two factors one due to the difference in electron affinity of the donor and acceptor sites, and the other arising from the fact that the electronically excited state is a nonequilibrium state with respect to atomic motion (P ranck Condon principle). Theories of electron transfer have been concerned with predicting the magnitude of the Franck-Condon barrier but, in the field of thermal electron transfer kinetics, direct comparisons between theory and experimental data have been possible only to a limited extent. One difficulty is that in kinetic studies it is generally difficult to separate the electron transfer process from the complex formation... 

Formation and stability studies of black foam films can be summarised as follows 1) surface forces in black foam films direct measurement of disjoining pressure isotherm DLVO- and non-DLVO-forces 2) thin foam film/black foam film transition establishing the conditions for the stability of both types of black films and CBF/NBF transition 3) formation of black foam films in relation to the state of the adsorption layers at the solution/air interface 4) stability of bilayer films (NBF) theory and experimental data. 

The points in Fig. 24 represent the experimental values of A for a ladder poly-dichlorophenylsfloxane and cellulose carbanilate For both polymers the experimental data are in agreement with theoretical Curve 4 corresponding to the value of d/A = 0.5 for a kinetically flexible chain polymer. This qualitatively demonstrates that the hydrodynamic properties of the molecules of these two polymers at low X differ from those of an infinitely thin worm-like model. However, to obtain quantitative agreement between theory and experimental data according to Curve 4 in Fig. 24, A/d should be equal to 2 — a reasonable value for many flexible-chain polymers not realistic for such r d-chain polymers as ladder polysiloxanes or cellulose ethers and esters. 

Only a smaU number of researchers have attempted to interpret the experiments data on the Kerr effect from the standpoint of theories based on a rotational isomer medianism of chain flexibility and tensor additivity of the polarizability of chain bonds > These attempts did not yield good agreement between theory and experimental data. This may result from both the unreliability of the data and the inadequacy of some suggestions used in the theory (additivity of optical properties of vSence bonds, character of the internal field etc.). 

For polymers, x is usually defined on a per monomer basis or on the basis of a reference volume of order one monomer in size. However, x is usually not computed from formulas for van der Waals interactions, but is adjusted to obtain the best agreement between the Flory-Huggins theory and experimental data on the scattering or phase behavior of mixtures (Balsara 1996). In this fitting process, inaccuracies and ambiguities in the lattice model, as well as in the mean-field approximations used to obtain Eq. (2-28), are papered over, and contributions to the free energy from sources other than simple van der Waals interactions get lumped into the x parameter. The temperature dependences of x for polymeric mixtures are often fit to... 

The metlrod requires suitable intennolecularpotentialenergy functionsZY(r) and solution of tire equations of statistical mechanics for the assemblies of molecules. As mentioned in Sec. 16.1, potential energy functions are as yet primarily empirical. Except for the simplest molecules, U r) caimot be predicted by ab initkr calculations, because of still-inadequate computer speed. Therefore, semi-empirical functions based on quantum-mechanical theory and experimental data are employed. 

Murphy, W.M. 1988. Dislocations and feldspar dissolution Theory and experimental data. Chem. Geology 70 163. 

Table 2.1. Comparison of theory and experimental data of various cellulose derivative solutions. (From Flory, 1978.)...

Disagreement between classical network theory and experimental data occurs. The entanglement effect was thought to be responsible for the deviation. According to the classical network theory, the stress-strain relationship should follow Equation 2.139. The plot of the reduced force, ct /(A2 — 1/A), against the reciprocal strain, 1/A, should be constant, i.e., unity. But experiments show that the reduced force is a function of the extension ratio A. Figure 2.33 shows the typical experimental data of PDMS... 

With the above corrections, the presence of waves can easily explain the noted 15-20 percent discrepancy between the Nusselt theory and experimental data. 

Manufacturers of flares usually provide estimates of flare radiation based on proprietary models. These models are commonly semiempirical in nature in that they use a combination of theory and experimental data. The purpose of this section is to discuss, in general, why and how semiempirical modeling is used to estimate flare radiation and why accurate experimental data is crucial for these models. 

Calculations show that the model of a non-equilibrium surface layer is an alternative to kinetic-controlled adsorption models. On the basis of the purely diffusion-controlled adsorption mechanism the proper consideration of a non-equilibrium diffusion layer leads to a satisfactory agreement between theory and experimental data for various studied systems, systematically demonstrated for the short-chain alcohols [132], The non-equilibrium model is applicable in the concentration range from 10 to 10 mol/cm at different values of the Langmuir constant at- For l < 10 mol/cm a consideration of non-equilibrium layer effects is not necessary. For ai > 10 mol/cm and large surfactant concentration the Ay values calculated from the proposed theory do not compensate the discrepancy to the experimental data so that other mechanisms have to be taken into account. An empirical formula also proposed in [132] for the estimation of the non-equilibrium surface layer thickness leads to a better agreement with experimental data, however this expression restricts the validity of the non-equilibrium surface layer model as alternative to non-diffusional adsorption kinetics. 

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