3.3: Estimating gaseous diffusion coefficients

A number of empirical or semiempirical correlations for estimating gaseous diffusion coefficients have also been developed. These include the method of Wilke and Lee (1955), which is based on Eq. 4.1.3 with C = 0.02199 - 0.00507 (Mi + ... 

In the characterization of porous membranes by liquid or gaseous permeation methods, the interpretation of data by the hyperbolic model can be of interest even if the parabolic model is accepted to yield excellent results for the estimation of the diffusion coefficients in most experiments. This type of model is currently applied for the time-lag method, which is mostly used to estimate the diffusion coefficients of dense polymer membranes in this case, the porosity definition can be compared to an equivalent free volume of the polymer [4.88, 4.89]. 

Magniiitde of gaseous diffusion coefficients. For the purpose of estimating gas diffusion effects, Table II shows some numerical values of gaseous diffusion coefficients. 

For process engineering calculations it is almost inevitable that experimental values of D or f), even if available in the literature, will not cover the entire range of temperature, pressure, and concentration that is of interest in any particular application. It is, therefore, important that we be able to predict these coefficients from fundamental physical and chemical data, such as molecular weights, critical properties, and so on. Estimation of gaseous diffusion coefficients at low pressures is the subject of Section 4.1.1, the correlation and prediction of binary diffusion coefficients in liquid mixtures is covered in Sections 4.1.3-4.1.5. We do not intend to provide a comprehensive review of prediction methods since such are available elsewhere (Reid et al., 1987 Ertl et al., 1974 Danner and Daubert, 1983) rather, it is our purpose to present a selection of methods that may be useful in engineering calculations. 

Estimate the gaseous diffusion coefficient for methanol diffusing through water vapor at 25°C and... 

Equation (2.3-15) is a dimensional equation with Oab in m2/s, Tin K, and p in atm. This equation mast moke use of the diffusion volumes that are tabulated for simple molecules and computed from atomic volnmas for more complex molecules. Table 2.3-4 provides some of these values. In summaty, it may. be said diet gaseous diffusion coefficients at low or modest pressures can be readily estimated from either Eq. (2.3-14) or (2.3-15) if exparimental data ate not available. 

This chapter suggests methods of estimating the diffusion coefficients, the viscosity and the thermal conductivity of pure substances and gaseous mixtures. 

For a rough estimation of diffusion coefficients in gaseous systems, the well-known Stokes-Einstein equation is a help even for high pressures. 

Estimate the gaseous phase diffusion coefficient for the following systems, at 1 atmosphere and the temperatures given ... 

The Knudsen diffusion coefficient Dk corresponds to the movement of gaseous solutes in small pores and can be estimated by using the following equation (Perry and Green, 1999) ... 

Dispersion Models Based on Inert Pollutants. Atmospheric spreading of inert gaseous contaminant that is not absorbed at the ground has been described by the various Gaussian plume formulas. Many of the equations for concentration estimates originated with the work of Sutton (3). Subsequent applications of the formulas for point and line sources state the Gaussian plume as an assumption, but it has been rigorously shown to be an approximate solution to the transport equation with a constant diffusion coefficient and with certain boundary conditions (4). These restrictive conditions occur only for certain special situations in the atmosphere thus, these approximate solutions must be applied carefully. 

This model does not take into account transport of liquid water in the backing layer and in the channel. If a small amount of liquid water partially fills voids of the backing layer, it simply reduces the effective diffusion coefficient of gaseous transport Di,. The level of flooding can be estimated from this model by comparing the diffusion coefficient which results from fitting of the experimental curves to the binary diffusion coefficients corrected for porosity-tortuosity. 

Various diffusion and thermal diffusion processes were used in World War II to separate gaseous molecules from uPg molecules. Calculate the mutual diffusion coefficient of these substances at 60°C and 1.000 atm. Calculate the self-diffusion coefficient of at this temperature and pressure. Make a reasonable estimate of the effective hard-sphere diameter of UFs and see Problem 10.26 for the necessary equation. 

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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