Diffusion theoretical model

Reilly P D and Skinner J L 1995 Spectral diffusion of individual pentacene molecules in p-terphenyl crystal theoretical model and analysis of experimental data J. Phys. Chem 102 1540-52... 

Combustion chemistry in diffusion flames is not as simple as is assumed in most theoretical models. Evidence obtained by adsorption and emission spectroscopy (37) and by sampling (38) shows that hydrocarbon fuels undergo appreciable pyrolysis in the fuel jet before oxidation occurs. Eurther evidence for the existence of pyrolysis is provided by sampling of diffusion flames (39). In general, the preflame pyrolysis reactions may not be very important in terms of the gross features of the flame, particularly flame height, but they may account for the formation of carbon while the presence of OH radicals may provide a path for NO formation, particularly on the oxidant side of the flame (39). 

Figure 6 Apparent elastic incoherent structure factor A q(Q) for ( ) denatured and ( ) native phosphoglycerate kinase. The solid line represents the fit of a theoretical model in which a fraction of the hydrogens of the protein execute only vihrational motion (this fraction is given by the dotted line) and the rest undergo diffusion in a sphere. For more details see Ref. 25.

It would appear that the effects of impurities at the grain boundary must be either (a) to increase the diffusion rates or (b) to influence the microstructure and increase the number of short-circuit paths. However, theoretical modelling of the grain boundary structure by Duffy and Tasker and... 

Glaser and Litt (G4) have proposed, in an extension of the above study, a model for gas-liquid flow through a b d of porous particles. The bed is assumed to consist of two basic structures which influence the fluid flow patterns (1) Void channels external to the packing, with which are associated dead-ended pockets that can hold stagnant pools of liquid and (2) pore channels and pockets, i.e., continuous and dead-ended pockets in the interior of the particles. On this basis, a theoretical model of liquid-phase dispersion in mixed-phase flow is developed. The model uses three bed parameters for the description of axial dispersion (1) Dispersion due to the mixing of streams from various channels of different residence times (2) dispersion from axial diffusion in the void channels and (3) dispersion from diffusion into the pores. The model is not applicable to turbulent flow nor to such low flow rates that molecular diffusion is comparable to Taylor diffusion. The latter region is unlikely to be of practical interest. The model predicts that the reciprocal Peclet number should be directly proportional to nominal liquid velocity, a prediction that has been confirmed by a few determinations of residence-time distribution for a wax desulfurization pilot reactor of 1-in. diameter packed with 10-14 mesh particles. 

Tadaki and Maeda (Tl) examined the desorption of carbon dioxide from water in a bubble-column and analyzed the experimental results under the assumption that while the gas phase moves in piston flow, the liquid undergoes axial mixing that can be characterized by the diffusion model. (Shulman and Molstad, in contrast, assumed piston flow for both phases.) Only poor agreement was obtained between the theoretical model and the experimental... 

Calderbank et al. (C6) studied the Fischer-Tropsch reaction in slurry reactors of 2- and 10-in. diameters, at pressures of 11 and 22 atm, and at a temperature of 265°C. It was assumed that the liquid-film diffusion of hydrogen from the gas-liquid interface is a rate-determining step, whereas the mass transfer of hydrogen from the bulk liquid to the catalyst was believed to be rapid because of the high ratio between catalyst exterior surface area and bubble surface area. The experimental data were not in complete agreement with a theoretical model based on these assumptions. 

Figure 10. Theoretical model for the electrical double layer at an electrode with a polycrystalline surface, (a) Model of independent diffuse layers [Eq. (S3)], and (b) model of common diffuse layer [Eq. (54)).

Theoretical models available in the literature consider the electron loss, the counter-ion diffusion, or the nucleation process as the rate-limiting steps they follow traditional electrochemical models and avoid any structural treatment of the electrode. Our approach relies on the electro-chemically stimulated conformational relaxation control of the process. Although these conformational movements179 are present at any moment of the oxidation process (as proved by the experimental determination of the volume change or the continuous movements of artificial muscles), in order to be able to quantify them, we need to isolate them from either the electrons transfers, the counter-ion diffusion, or the solvent interchange we need electrochemical experiments in which the kinetics are under conformational relaxation control. Once the electrochemistry of these structural effects is quantified, we can again include the other components of the electrochemical reaction to obtain a complete description of electrochemical oxidation. 

Roper, F.G., The prediction of laminar jet diffusion flame sizes Part I. theoretical model. Combust. Flame, 29, 219, 1977. 

Experimental non-ideality at pH extremes in isotachophoresis has been compared with theoretical models.56 The model was able to predict phenomena that are usually regarded as artifactual, including system peaks, diffuse... 

RW Korsmeyer, EW Meerwall, NA Peppas. Solute and penetrant diffusion in swellable polymers. II. Verification of theoretical models. J Polym Sci Polym Phys Ed 24 409-419, 1986. 

The vast majority of theoretical models are based on diffusion equations. The phenomenon of diffusion is intimately connected to the structure of the... 

Although the trajectory and convective diffusion techniques are conceptually simple, certain mechanisms, in particular, the exact role of the intermolecular force between the particle and the electrode remains an element of debate. Most of these problems arise because continuum models about short-range interactions break down at very short distances, where other factors, much less defined come into play. A complete understanding of the coelectrodeposition process requires a synergy between theoretical models and thorough experimental work. 

Some experiments outlined the frequency dependence of phonon scattering on surfaces [74]. Thus, Swartz made the hypothesis that a similar phenomenon could take place at the interface between solids and proposed the diffuse mismatch model [72]. The latter model represents the theoretic limit in which all phonons are heavily scattered at the interface, whereas the basic assumption in the acoustic mismatch model is that no scattering phenomenon takes place at the interface of the two materials. In the reality, phonons may be scattered at the interface with a clear reduction of the contact resistance value as calculated by the acoustic model. 

Bimolecular electron-transfer reactions in solutions frequently have rates limited by the diffusion of the donor and acceptor molecules, because one or both of the reactant species is usually at a low concentration relative to the solvent. To obtain a detailed mechanistic and kinetic understanding of electron-transfer reactions in solutions, chemists have devised ingenious schemes in which the two reactants, the donor and acceptor, are held in a fixed distance and orientation so that diffusion will not complicate the study of the intrinsic electron-transfer rates. Recent developments, however, have led to theoretical models in which the orientation and the distance are changeable (see Rubtsov et al. 1999). 

---