Diffusion coefficients empirical formulas

The attractive feature of LADM Is that once the fluid structure Is known (e.g., by solution of the YBG equations given In the previous section or by a computer simulation) then theoretical or empirical formulas for the transport coefficients of homogeneous fluids can be used to predict flow and transport In Inhomogeneous fluid. For diffusion and Couette flow In planar pores LADM turns out to be a surprisingly good approximation, as will be shown In a later section. 

However, we must keep in mind the limitations of this approach, especially the transfer of consistent sets of dispersion parameters to the propagation of air pollution in the vicinity of a source. The Gaussian plume formula should be used only for those downwind distances for which the empirical diffusion coefficients have been determined by standard diffusion experiments. Because we are interested in emissions near ground level and immissions nearby the source, we use those diffusion parameters which are based on the classification of Klug /12/ and Turner /13/. The parameters are expressible as power functions,... 

The most well-known empirical formula for diffusion coefficients is that due to Gilliland (G3, S9), which is written in terms of the molecular volumes of the diffusion species and gives SDab proportional to TH. Since this temperature dependence has since been shown to be incorrect the Gilliland formula should not be used. Another empirical formula has been suggested by Arnold (Al). Recently Slattery (S10) has proposed the following relation on the basis of corresponding states arguments ... 

Several other empirical relations for diffusion coefficients have been suggested Olson and Walton (01) have devised a means for estimating diffusion coefficients of organic liquids in water solution from surface-tension measurements. Hill (H5) has proposed a method based on Andrade s theory of liquids which allows for the concentration dependence of the diffusion coefficient in a binary liquid mixture. The formula of Arnold (A2, T6, p. 102) does not seem generally useful inasmuch as it contains two constants ( abnormality factors ) characteristic of the solute and of the solvent. 

Pressure Dependencies Equation 3.95 predicts the binary diffusion coefficient to scale as p l, which is generally true except as the pressure approaches or exceeds the critical pressure. The Takahashi formula [392], which can be used to describe the high-pressure behavior, is discussed below. The Chapman-Enskog theory also predicts that Vji, increases with temperature as T3/2. However, it is often observed experimentally the temperature exponent is somewhat larger, say closer to 1.75 [332], An empirical expression for estimating T>jk is due to Wilke and Lee [433]. The Wilke-Lee formula is [332]... 

The thermal diffusion coefficients appearing in equations (18) and (19) in general may be positive or negative and depend on pressure, temperature, and concentrations. It is almost always found that the dimensionless ratio Dj J(pDij) is less than for all pairs of gaseous species i and), which implies that thermal diffusion usually is negligible in comparison with the ordinary concentration-gradient diffusion. The complicated expressions for the coefficients of thermal diffusion will therefore be omitted here the reader is referred to [5] and [9] for theoretical results and for useful empirical formulas. 

Due to its practical importance, the diffusion of water vapor in air has been the topic of several studies, and some empirical formulas have been developed for the diffusion coefficient DH,o-ai,- Marrero and Mason (1972) proposed this popular formula (Table 14-4) ... 

For either limiting case, ZJq/T and fcdiffusion-controlled reactions of electronically excited molecules (5) and for radical self-termination reactions (6), especially when high-molecular-weight alkanes or alcohols are employed as solvents. But even in such cases, rate constants for reactions considered to be diffusion-controlled mirror the behavior of empirical diffusion coefficients, which, if not known, can be calculated from available empirical or semiempirical formulas (6). 

G. Piringer published an empirical approximation formula for the determination of the diffusion coefficient as well (Piringer 1993). The formula reads ... 

The Stokes-Einstein formula for diffusion coefficients is limited to cases in which the solute is larger than the solvent. Predictions for liquids are not as accurate as for gases. The Wilke and Chang [16] correlation for diffusion in liquids is an empirical correlation and is given by... 

Estimate the diffusion coefficient of oxygen in nitrogen at 80°C and 2 atm using Chapman-Enskog s theoretical formula and by Fuller s empirical correlations. 

Another alternative form of effective mass diffusion coefficient for porous media that takes into account the effect of porosity and the tortuous morphology of the porous structure or the tortuous path is given by using the Bruggemann empirical correction formula (De La Rue and Tobias, 1959 Springer et al., 1991) as... 

Estimate the binary diffusion coefficient of methane in hydrogen at 200°C and 2 atm pressure using (a) Chapman-Enskog s theoretical formula, (b) Fuller s empirical correlations, and (c) Bird s correlation. 

The fact that the Brownian and quantum diffusions are indistinguishable by inteimined measurements perfomied in the configuration space (and this is just the equivalent of experimental techniques by means of which the periodic chemical reactions are investigated) justifies the direct comparison of empirical diffusion coefficients with the Furth s value Dg =h/2M. Assuming that the noise sources behind classical and quantum stochastic behavior are independent the obvious formula for diffusion coefficient may be written as D = DsDq /(Ds +... 

In addition to the theoretical and semiempirical methods for estimating molecular diffusivities in air, several empirical methods, based on regressions of measured diffusivities and other parameters, like molecular weight and molar volume, are available. These methods provide easily calculated estimates when the property data required to apply the more rigorous semiempirical methods are not available. Molecular weight is an excellent parameter for empirical correlations because it is easily determined from the chemical formula and is an important parameter in the theoretical model. Diffusion coefficients in air can be expected to have power-law dependence on molecular... 

Constant in the formula for D below, value 2.1 x 10 m /s. Diffusivity of water in membrane m /s. An empirical function of membrane temperature T and water content c [10]. Electro-osmotic drag coefficient, taken to be 1. 

Theoretical models exist that can be used to estimate diffusivities in gaseous and liquid media. Models of gaseous diffusion are based on the kinetic theory of gases and for ambient pressures are quite accurate, but for liquids theoretical approaches are less useful due to the need to account for intermolecular interactions between the diffusing species and bulk phase. The methods for estimating diffusivities in air and water are based on theoretical arguments, empirical functions based on measured data, or a combination of theoretical formulae with empirically determined correction factors and coefficients. 

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