Diffusion experimental results

Table 1. Oxygen diffusion experimental results for La1 ySryMn03 8...

The interaction of turbulent flow containing regions of high strain rate and high shear rate with polymer molecules can involve both individual molecules and polymer structures. The results of this interaction lead to suppressions of the small scale motions and to production of some large scale motions that do not contribute to turbulent diffusion. Experimental results are interpreted in terms of the interaction of molecules near the wall and movement of the polymeric large scale structures in the center of pipe flows. 

To permit a comparison of the cell diffusion experimental results with scaling predictions of the protein partitioning behavior, the partition coefficients were correlated... 

Thus his experiments were the first to indicate the surprising result that relation (6,1) remains valid even in conditions where bulk diffusion resistance is completely dominant. Accordingly (6.1), perhaps the most important single experimental result on diffusion in porous media, will be referred to as Graham s relation. 

It follows from this discussion that all of the transport properties can be derived in principle from the simple kinetic dreoty of gases, and their interrelationship tlu ough k and c leads one to expect that they are all characterized by a relatively small temperature coefficient. The simple theory suggests tlrat this should be a dependence on 7 /, but because of intermolecular forces, the experimental results usually indicate a larger temperature dependence even up to for the case of molecular inter-diffusion. The Anhenius equation which would involve an enthalpy of activation does not apply because no activated state is involved in the transport processes. If, however, the temperature dependence of these processes is fitted to such an expression as an algebraic approximation, tlren an activation enthalpy of a few kilojoules is observed. It will thus be found that when tire kinetics of a gas-solid or liquid reaction depends upon the transport properties of the gas phase, the apparent activation entlralpy will be a few kilojoules only (less than 50 kJ). 

Pore diffusion limitation was studied on a very porous catalyst at the operating conditions of a commercial reactor. The aim of the experiments was to measure the effective diffiisivity in the porous catalyst and the mass transfer coefficient at operating conditions. Few experimental results were published before 1970, but some important mathematical analyses had already been presented. Publications of Clements and Schnelle (1963) and Turner (1967) gave some advice. 

Among the commonly used criteria is the air distribution performance index (ADPI), defined as the percentage of ItKadons where a combination of air temperature and air velocity meets comfort requirements. This criterion is based on experimental results of air diffuser performance for specifically tested room configurations. Data on the ADPI are available only for sedentary activity. 

Fig. 7 gives an example of such a comparison between a number of different polymer simulations and an experiment. The data contain a variety of Monte Carlo simulations employing different models, molecular dynamics simulations, as well as experimental results for polyethylene. Within the error bars this universal analysis of the diffusion constant is independent of the chemical species, be they simple computer models or real chemical materials. Thus, on this level, the simplified models are the most suitable models for investigating polymer materials. (For polymers with side branches or more complicated monomers, the situation is not that clear cut.) It also shows that the so-called entanglement length or entanglement molecular mass Mg is the universal scaling variable which allows one to compare different polymeric melts in order to interpret their viscoelastic behavior. 

Table 4-1 lists some rate constants for acid-base reactions. A very simple yet powerful generalization can be made For normal acids, proton transfer in the thermodynamically favored direction is diffusion controlled. Normal acids are predominantly oxygen and nitrogen acids carbon acids do not fit this pattern. The thermodynamicEilly favored direction is that in which the conventionally written equilibrium constant is greater than unity this is readily established from the pK of the conjugate acid. Approximate values of rate constants in both directions can thus be estimated by assuming a typical diffusion-limited value in the favored direction (most reasonably by inspection of experimental results for closely related... 

It should be pointed out that Eq. (10) can correctly represent experimental results (cited papers recorded reasonable agreement between theory and experiment) only when diffusion of gas from bubble to bubble can be ignored. When the bubble is small, surface Laplace pressure PL P, and coalescence of bubbles occurs in such a way as to make the volume of the resul tant bubble greater than the sum of the original bubble volumes [27]. 

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... 

Kishinev ski/23 has developed a model for mass transfer across an interface in which molecular diffusion is assumed to play no part. In this, fresh material is continuously brought to the interface as a result of turbulence within the fluid and, after exposure to the second phase, the fluid element attains equilibrium with it and then becomes mixed again with the bulk of the phase. The model thus presupposes surface renewal without penetration by diffusion and therefore the effect of diffusivity should not be important. No reliable experimental results are available to test the theory adequately. 

Figure 40. Plot of the fluctuation-diffusion current J vs. iwr.91 id is the slope of the fluctuation-diffusion current given by Eq. (115). Solid and dotted lines correspond to the theoretical and experimental results, respectively. (NiCljJ = 0.1 mol nT3. [NsCl] = 7 mol m 3. V = 0.1 V, T= 300 K. (Reprinted from M. Asanuma and R. Aogaki, Nonequilibrium fluctuation theory on pitting dissolution, n. Determination of surface coverage of nickel passive film, J. Chem. Phys. 106, 9938, 1997, Fig. 8. Copyright 1997, American Institute of Physics.)...

Equations 4.31 and 4.32 also suggest another important fact regarding NEMCA on noble metal surfaces The rate limiting step for the backspillover of ions from the solid electrolyte over the entire gas exposed catalyst surface is not their surface diffusion, in which case the surfacediffusivity Ds would appear in Eq. 4.32, but rather their creation at the three-phase-boundaries (tpb). Since the surface diffusion length, L, in typical NEMCA catalyst-electrode film is of the order of 2 pm and the observed NEMCA time constants x are typically of the order of 1000 s, this suggests surface diffusivity values, Ds, of at least L2/t, i.e. of at least 4 10 11 cm2/s. Such values are reasonable, in view of the surface science literature for O on Pt(l 11).1314 For example this is exactly the value computed for the surface diffusivity of O on Pt(lll) and Pt(100) at 400°C from the experimental results of Lewis and Gomer14 which they described by the equation ... 

Computer simulations therefore have several inter-related objectives. In the long term one would hope that molecular level simulations of structure and bonding in liquid crystal systems would become sufficiently predictive so as to remove the need for costly and time-consuming synthesis of many compounds in order to optimise certain properties. In this way, predictive simulations would become a routine tool in the design of new materials. Predictive, in this sense, refers to calculations without reference to experimental results. Such calculations are said to be from first principles or ab initio. As a step toward this goal, simulations of properties at the molecular level can be used to parametrise interaction potentials for use in the study of phase behaviour and condensed phase properties such as elastic constants, viscosities, molecular diffusion and reorientational motion with maximum specificity to real systems. Another role of ab initio computer simulation lies in its interaction... 

Diffusivities. Our results for the dlffuslvltles of both systems are summarized In Table I. The pore average transverse dlffuslvlty for the bulk fluid at equilibrium agrees very well with experimental and simulation values for the dlffuslvlty of Argon at the same density and temperature (18.12.5). 

Torkelson and coworkers [274,275] have developed kinetic models to describe the formation of gels in free-radical pol5nnerization. They have incorporated diffusion limitations into the kinetic coefficient for radical termination and have compared their simulations to experimental results on methyl methacrylate polymerization. A basic kinetic model with initiation, propagation, and termination steps, including the diffusion hmitations, was found to describe the gelation effect, or time for gel formation, of several samples sets of experimental data. 

Archie [23] examined electrical resistivity of various sand formations having pore spaces filled with saline solutions of different salt concentrations. Based upon his own experimental results, he obtained a simple relationship for the conductivity of beds of sand (assuming the sand itself is nonconductive) containing saline solution in terms of the porosity. In terms of diffusion coefficients his expression is... 

Perrin model and the Johansson and Elvingston model fall above the experimental data. Also shown in this figure is the prediction from the Stokes-Einstein-Smoluchowski expression, whereby the Stokes-Einstein expression is modified with the inclusion of the Ein-stein-Smoluchowski expression for the effect of solute on viscosity. Penke et al. [290] found that the Mackie-Meares equation fit the water diffusion data however, upon consideration of water interactions with the polymer gel, through measurements of longitudinal relaxation, adsorption interactions incorporated within the volume averaging theory also well described the experimental results. The volume averaging theory had the advantage that it could describe the effect of Bis on the relaxation within the same framework as the description of the diffusion coefficient. 

Johansson, L Skantze, U Lofroth, J-E, Diffusion and Interaction in Gels and Solutions. 2. Experimental Results on the Obstruction Effect, Macromolecules 24, 6019, 1991. 

Sodium diffusion coefficients in glass cullets calculated from fitting Eq. (10) with the profiles of sodium were 2.9 - 3.9><10 m /s at 823K (see Fig. 1). Comparison of experimental results with predicted results for Na neutralized with HCl at 823K was fairly consistent and indicated that Dns calculated would well represent the neutralization kinetics. 

The experimental results imply that the main reaction (eq. 1) is an equilibrium reaction and first order in nitrogen monoxide and iron chelate. The equilibrium constants at various temperatures were determined by modeling the experimental NO absorption profile using the penetration theory for mass transfer. Parameter estimation using well established numerical methods (Newton-Raphson) allowed detrxmination of the equilibrium constant (Fig. 1) as well as the ratio of the diffusion coefficients of Fe"(EDTA) andNO[3]. 

Experimental results are consistent with this relation, but inaccuracies in sedimentation constants preclude precise evaluation of the empirical exponent. Similarly, the diffusion constant at infinite dilution, given by... 

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