Diffusion correlations for

Diffusivity correlations for gases are outlined in Table 5-10. Specific parameters for individual equations are defined in the specific text regarding each equation. References are given at the beginning of the Mass Transfer subsection. The errors reported for Eqs. (5-202) through (5-205) were compiled by Poling et al., who compared the predictions with 68 experimental values of D. Errors cited for Eqs. (5-206) to (5-212) were reported by the authors. 

Fig. 5.2. Diffusivity correlation for dilute solutions of nonelectrolytes. C. R. Wilke [Chem. Eng. Progress 46, 218 (1949). Reproduced with the permission of the American Institute of Chemical Engineers.]...

Condemarin, R. Scovazzo, P. (2009). Gas permeabilities, solubilities, diffusivities, and diffusivity correlations for ammonium-based room temperature ionic liquids with comparison to imidazolium and phosphonium RTIL data. Chem. Eng.., 147, 51-57, ISSN 1385-8947. 

Under conditions of limiting current, the system can be analyzed using the traditional convective-diffusion equations. For example, the correlation for flow between two flat plates is... 

Units employed in diffusivity correlations commonly followed the cgs system. Similarly, correlations for mass transfer correlations used the cgs or Enghsh system. In both cases, only the most recent correlations employ SI units. Since most correlations involve other properties and physical parameters, often with mixed units, they are repeated here as originally stated. Common conversion factors are listed in Table 1-4. 

Wilke-Chang This correlation for D°b is one of the most widely used, and it is an empirical modification of the Stokes-Einstein equation. It is not very accurate, however, for water as the solute. Otherwise, it apphes to diffusion of very dilute A in B. The average absolute error for 251 different systems is about 10 percent. ( )b is an association factor of solvent B that accounts for hydrogen bonding. 

TABLE 5-18 Correlations for Diffusivities of Dilute/ Binary Mixtures of Nonelectrolytes in Liquids... 

Hayduk-Laudie They presented a simple correlation for the infinite dilution diffusion coefficients of nonelectrolytes in water. It has about the same accuracy as the Wilke-Chang equation (about 5.9 percent). There is no explicit temperature dependence, but the 1.14 exponent on I compensates for the absence of T in the numerator. That exponent was misprinted (as 1.4) in the original article and has been reproduced elsewhere erroneously. 

Riazi-Whitson They presented a generahzed correlation in terms of viscosity and molar density that was apphcable to both gases and liqmds. The average absolute deviation for gases was only about 8 percent, while for liquids it was 15 percent. Their expression relies on the Chapman-Enskog correlation [Eq. (5-194)] for the low-pressure diffusivity and the Stiel-Thodos correlation for low-pressure viscosity ... 

Vigne.s empirically correlated mixture diffusivity data for 12 binary mixtures. Later Ertl et al. evaluated 122 binary systems, which showed an average absolute deviation of only 7 percent. None of the latter systems, however, was veiy nonideal. 

For bubble-cap plates, the eddy-diffusion correlation in the AlChE Bubble-Ti ay Design Manual should be used. 

PasquiU Atmo.spheric Diffusion, Van Nostrand, 1962) recast Eq, (26-60) in terms of the dispersion coefficients and developed a number of useful solutions based on either continuous (plume) or instantaneous (puff) releases, Gifford Nuclear Safety, vol, 2, no, 4, 1961, p, 47) developed a set of correlations for the dispersion coefficients based on available data (see Table 26-29 and Figs, 26-54 to 26-57), The resulting model has become known as the Pasquill-Gifford model. 

The diffusivity coefficient for a liquid-liquid system can be estimated from the Wilke correlation ... 

F = Function of the molecular volume of the solute. Correlations for this parameter are given in Figure 7 as a function of the parameter (j), which is an empirical constant that depends on the solvent characteristics. As points of reference for water, (j) = 1.0 for methanol, (j) = 0.82 and for benzene, (j) = 0.70. The two-film theory is convenient for describing gas-liquid mass transfer where the pollutant solute is considered to be continuously diffusing through the gas and liquid films. 

Dynamic information such as reorientational correlation functions and diffusion constants for the ions can readily be obtained. Collective properties such as viscosity can also be calculated in principle, but it is difficult to obtain accurate results in reasonable simulation times. Single-particle properties such as diffusion constants can be determined more easily from simulations. Figure 4.3-4 shows the mean square displacements of cations and anions in dimethylimidazolium chloride at 400 K. The rapid rise at short times is due to rattling of the ions in the cages of neighbors. The amplitude of this motion is about 0.5 A. After a few picoseconds the mean square displacement in all three directions is a linear function of time and the slope of this portion of the curve gives the diffusion constant. These diffusion constants are about a factor of 10 lower than those in normal molecular liquids at room temperature. 

Calderbank and Moo-Young (C5) have studied gas-liquid mass transfer in systems characterized by high viscosities and high diffusion coefficients, and have on the basis of data obtained in this and other studies developed correlations for the mass-transfer coefficients. 

At a close level of scrutiny, real systems behave differently than predicted by the axial dispersion model but the model is useful for many purposes. Values for Pe can be determined experimentally using transient experiments with nonreac-tive tracers. See Chapter 15. A correlation for D that combines experimental and theoretical results is shown in Figure 9.6. The dimensionless number, udt/D, depends on the Reynolds number and on molecular diffusivity as measured by the Schmidt number, Sc = but the dependence on Sc is weak for... 

In addition to chemical reactions, the isokinetic relationship can be applied to various physical processes accompanied by enthalpy change. Correlations of this kind were found between enthalpies and entropies of solution (20, 83-92), vaporization (86, 91), sublimation (93, 94), desorption (95), and diffusion (96, 97) and between the two parameters characterizing the temperature dependence of thermochromic transitions (98). A kind of isokinetic relationship was claimed even for enthalpy and entropy of pure substances when relative values referred to those at 298° K are used (99). Enthalpies and entropies of intermolecular interaction were correlated for solutions, pure liquids, and crystals (6). Quite generally, for any temperature-dependent physical quantity, the activation parameters can be computed in a formal way, and correlations between them have been observed for dielectric absorption (100) and resistance of semiconductors (101-105) or fluidity (40, 106). On the other hand, the isokinetic relationship seems to hold in reactions of widely different kinds, starting from elementary processes in the gas phase (107) and including recombination reactions in the solid phase (108), polymerization reactions (109), and inorganic complex formation (110-112), up to such biochemical reactions as denaturation of proteins (113) and even such biological processes as hemolysis of erythrocytes (114). 

Flayduk, W. and Minhas, B.S. (1982) Correlations for prediction of molecular diffusivities in liquids. Can.]. Chem. 

There are several correlations for estimating the film mass transfer coefficient, kf, in a batch system. In this work, we estimated kf from the initial concentration decay curve when the diffusion resistance does not prevail [3]. The value of kf obtained firom the initial concentration decay curve is given in Table 2. In this study, the pore diffusion coefficient. Dp, and surface diffusion coefficient, are estimated by pore diffusion model (PDM) and surface diffusion model (SDM) [4], The estimated values of kf. Dp, and A for the phenoxyacetic acids are listed in Table 2. 

Restricted diffusion, correlated motion of spins, or any deviation from a free behavior of the molecules will result in a propagator shape different from a Gaussian one. A wide range of studies have dealt with such problems during the last two decades and NMR has turned out to be the method of choice for quantifying restricted diffusion phenomena such as for liquids in porous materials or dynamics of entangled polymer molecules. 

Our approach is to use the two-dimensional relaxation and diffusion correlation experiments to further enhance the resolution of different components. It is important to note that the correlation experiment, e.g., the Ti-T2 experiment, is different from two experiments of and T2 separately. For instance, the separate Ti and T2 experiment, in general, cannot determine the T1(/T2 ratio for each component. On the contrary, a component with a particular Tj and T2 will appear as a peak in the 2D 7i-T2 and the Ti/T2 ratio can be obtained directly. For example, small molecules often exhibit rapid rotation and diffusion in a solution and Ti/T2 ratio tends to be close to 1. On the other hand, the rotational dynamics of larger molecules such as proteins can be significantly slow compared with the Larmor frequency and resulting in a Ti/T2 ratio significantly larger than 1. 

Diffusivity correlates linearly with the ratio of temperature and viscosity. Therefore the diffusivity can also be expected to correlate with relaxation time because the latter correlates with temperature and viscosity according to Eq. (3.6.1). Figure 3.6.3 illustrates the correlation between relaxation time and diffusivity with the gas/oil ratio as a parameter [13]. The correlation between diffusivity and relaxation time extends to hydrocarbon components in a mixture and there is a mapping between the distributions of diffusivity and relaxation time for crude oils [17]. 

Wilke, C. R. and Chang, P. (1955) AIChE Jl 1, 264. Correlation for diffusion coefficients in dilute solutions. 

Summary of experimental data Film boiling correlations have been quite successfully developed with ordinary liquids. Since the thermal properties of metal vapors are not markedly different from those of ordinary liquids, it can be expected that the accepted correlations are applicable to liquid metals with a possible change of proportionality constants. In addition, film boiling data for liquid metals generally show considerably higher heat transfer coefficients than is predicted by the available theoretical correlations for hc. Radiant heat contribution obviously contributes to some of the difference (Fig. 2.40). There is a third mode of heat transfer that does not exist with ordinary liquids, namely, heat transport by the combined process of chemical dimerization and mass diffusion (Eq. 2-162). 

The side-by-side diffusion cell has also been calibrated for drug delivery mass transport studies using polymeric membranes [12], The mass transport coefficient, D/h, was evaluated with diffusion data for benzoic acid in aqueous solutions of polyethylene glycol 400 at 37°C. By varying the polyethylene glycol 400 content incrementally from 0 to 40%, the kinematic viscosity of the diffusion medium, saturation solubility for benzoic acid, and diffusivity of benzoic acid could be varied. The resulting mass transport coefficients, D/h, were correlated with the Sherwood number (Sh), Reynolds number (Re), and Schmidt number (Sc) according to the relationships... 

Schutz s correlation for free convection at a sphere, Eq. (25) in Table VII, takes pure diffusion into account by means of the constant term Sh = 2. According to his measurements using local spot electrodes, the flow here is not laminar but already in transition to turbulence. 

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