Diffusion coefficients in liquid and

The sorption coefficient (K) in Equation (2.84) is the term linking the concentration of a component in the fluid phase with its concentration in the membrane polymer phase. Because sorption is an equilibrium term, conventional thermodynamics can be used to calculate solubilities of gases in polymers to within a factor of two or three. However, diffusion coefficients (D) are kinetic terms that reflect the effect of the surrounding environment on the molecular motion of permeating components. Calculation of diffusion coefficients in liquids and gases is possible, but calculation of diffusion coefficients in polymers is much more difficult. In the long term, the best hope for accurate predictions of diffusion in polymers is the molecular dynamics calculations described in an earlier section. However, this technique is still under development and is currently limited to calculations of the diffusion of small gas molecules in amorphous polymers the... 

In relation 8.6 - rA is the reaction rate in kmol/(kg catalyst s), pc density of solid catalyst, R particle radius, I ) i diffusion coefficient in liquid and CAs reactant concentration at the catalyst surface. If CWp 1 there are no diffusion limitations, but if CWP 1 the catalyst effectiveness is severely affected. 

One should note the large difference between diffusion coefficients in liquids and gases. 

Values of diffusion coefficients are frequently needed in many separation calculations. Readers should refer to Reid et al. (1987) and Cussler (1997) for diffusion coefficients in liquids and gases. For immediate use, the following correlations may be used. 

Ternary diffusion coefficients in liquids and solids cannot be found from binary values, but only from experiments. When experiments are not available, which is usually the case, one can make estimates by assuming that the Onsager phenomenological coefficients are a diagonal matrix that is. 

Othmer, D.F. and M.S. Thakar (1953), Correlating diffusion coefficients in liquids, Industrial and... 

Frank in dogs. The most likely explanation is that the model does not account for chemical reactions of ozone in the mucus and epithelial tissue. Another problem is that the nose is believed to behave more like a scrubbing tower with fresh liquid at each level, inasmuch as the blood supply is not continuous for the entire length of the nose, as assumed in the model. Neglecting the surface area, volume, flow, and thickness of the mucus layer in the nose will probably also give erroneous results for soluble gases with a small diffusion coefficient in mucus and for singlebreath inhalations of a low concentration of any gas. 

When one or more of the chemical reactions is sufficiently slow in comparison with the rate of diffusion to and away from the interface of the various species taking part in an extraction reaction, such that diffusion can be considered instantaneous, the solvent extraction kinetics occur in a kinetic regime. In this case, the extraction rate can be entirely described in terms of chemical reactions. This situation may occur either when the system is very efficiently stirred and when one or more of the chemical reactions proceeds slowly, or when the chemical reactions are moderately fast, but the diffusion coefficients of the transported species are very high and the thickness of the two diffusion films is close to zero. In practice the latter situation never occurs, as diffusion coefficients in liquids generally do not exceed 10 cm s, and the depth of the diffusion films apparently is never less than 10 cm. 

The molecular diffusion coefficients in liquid phase were estimated from the correlations Wilke and Chang (9) for organic solutions and Hayduk and Minhas (10) for aqueous solutions, respectively. The solvent viscosities needed in the correlations were obtained from the empirical equation based on the experimental data,... 

Although there are a lot of data in the literature regarding diffusion coefficients in liquids or then calculation from molecular properties (Appendix I, Section 1.2), it is not the case for diffusion coefficients in solids, where the phenomena appearing are more complex. In solids, the molecule may be forced to follow a longer and tortuous path due to the blocking of the cross-sectional area, and thus the diffusion is somehow impaired. Several models have been developed to take into consideration this effect in the estimation of diffusion coefficients, leading, however, to a variety of results. 

A number of useful empirical and semiempirical relations have been proposed for predicting diffusion coefficients in liquids a rather complete summary of these has been given by Treybal (T6, pp. 102 et seg.). Most of these are valid only for nonionic systems at very low concentrations. 

So far, we have treated the diffusion coefficients which appeared above as parameters which would necessarily need to be determined by experiment. As a result of 150 years of effort, the experimental measurements of these coefficients are now extensive. Their general characteristics are shown in Table I (Cussler, 1997). In general, diffusion coefficients in gases and liquids can be accurately estimated, but those in solids and polymers can not. In gases, estimates based on kinetic theory are accurate to around 8%. In liquids, estimates based on the assumption that each solute is a sphere moving in a solvent continuum are accurate to around 20%, but can be supplemented by extensive data and empiricisms (Reid et al., 1997). 

Because of the low diffusion coefficients in liquids, the particle size for packed columns in LC needs to be very small (see section 7.2.1). For the same reason, all external volumes and diameters need to be minimized. This may easily be understood if we express the standard deviation in volume units (ctv) in the parameters that represent the dimensions of the column ... 

In general, diffusion coefficients in gases can be often be predicted accurately. Predictions of diffusion coefficients in liquids are also possible using the Stokes-Einstein equation or its empirical parallels. On the contrary in solids and polymers, models allow coefficients to be correlated but predictions are rarely possible. 

Othmer, D. F., and M. S. Thakar, Correlating Diffusion Coefficients in Liquids, Industrial and Engineering... 

Therefore, if the observed peak is allowed to have a volume 10% greater than the column peak volume, the extra-column peak volume should be one-half (ca. 46%) of the column peak volume. Table 1 lists column peak volumes and maximum extra-column peak volumes for various types of columns for LC because the largest contribution from this extra-column volume should be considered in liquid phase separations, the diffusion coefficients in liquids are very small. 

The diffusion coefficient in a gas is proportional to -jP, the constant of proportionality being a rather slowly increasing function of temperature. The estimation of the diffusion coefficient in liquids is discussed briefly by Sherwood and Satterfield it is proportional to r// , where /z. is the viscosity. At atmospheric pressure and ordinary temperatures, the order of magnitude of D for a gas is 0.1-1 cm-/sec and for liquids it is smaller by a factor of about 10. ... 

Although these two expressions have the same form, the coefficients are different. In particular, the solubility constant varies much more between various gas solutes than does the diffusion coefficient D. This implies that polymer membranes tend to be much more selective in separation various gas species than porous membranes. Unfortunately, diffusion coefficients in solids and liquids are much smaller than for gases so this increase in selectivity is often traded off with lower permeation rates. 

Diffusion coefficients in binary liquid mixtures are of the order 10 m /s. Unlike the diffusion coefficients in ideal gas mixtures, those for liquid mixtures can be strong functions of concentration. We defer illustration of this fact until Chapter 4 where we also consider models for the correlation and prediction of binary diffusion coefficients in gases and liquids. 

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. 

By judicious choice of the membrane liquid, complexation agent and support, immobilized liquid membranes (ILM) can have both high selectivity and high permeant fluxes. Liquid membranes have the additional advantage that diffusion coefficients in liquids are several orders of magnitude larger than in polymeric membranes. Previously reported ILM research in the literature includes purification and recovery processes in both gas and liquid phases ( ). This variety of applications creates different requirements for supports for ILMs. This paper discusses criteria which influence selection of ILM support materials. 

Diffusion coefficients in liquid phases depend on concentration and are valid for dilute solutions, that is, solute concentrations no greater than 10%. Also, the lower the solute concentration, the more accurate the calculated coefficients. For a binary mixture of solute A in solvent B, the diffusion coefficient can be represented as D gfor concentrations of A up to 5 or 10 mole percent [20]. A number of correlations have been proposed for predicting D°gin dilute liquid solutions [21,22,23]. Here, the Wilke-Chang method is employed for estimating D°g. This can be expressed as ... 

The rate at which this condition is approached depends on many parameters, like diffusion coefficients in feed and membrane phases, partition coefficients, or membrane thickness. We can have two situations membrane-controlled pertraction, when the diffusion of the transported compound through the liquid membrane is the limiting step, and feed-controlled pertraction, when the diffusion through the feed phase to the feed-membrane interface is the limiting step [27]. 

Diffusion coefficients in liquids are of die order of 10"a frVs (10 m2/s) unless (he solution is highly viscous or the solute has a very high molecular weight. Table 2.3-3 presents a few exparimenial diffusion coefficients for liquids at room temperature in dilute solution. Ertl and Dulllen. Johnson and Babb.2 and Himmdblau21 provide extensive tabulations of diffusion coefficients in liquids. It is probably safe to say (hat most of the reported exparimenial diffusivities were computed based on Fick s Second Law without consideration of whether or not (he system was thermodynamically ideal. Since the binary diffusion coefficient in liquids may vary strongly with composition, tabulations and predictive equations usually deal with the diffiisivity of A at infinite dilution in B, Z> , and the diffusiviiy of B at infinite dilution in A, D a. Separate consideration is then given to the variation of tha diffusiviiy with composition. 

Note that Np in the figure and in equation (5-45) is defined on the basis of superficial velocity, thus Npe = dfv p/n. Owing to the small values of the molecular diffusion coefficient in liquids, the Schmidt number is not an important contributor to Np in... 

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