Diffusion coefficients liquid

Concentration of solute in mobile phase Cm Diffusion coefficient, liquid film Dt... 

Various parameters such as adsorption and desorption isotherms, diffusion coefficients, liquid/gas, gas/solid and liquid/solid equilibrium distribution coefficients, as well as mass transfer coefficients and many other physicochemical property values have to be used in the models proposed for supercritical fluid extractions. These parameter values are either obtained from existing correlations, or from independent data sources using parameter estimation. However, in those cases where the above stated means are not sufficient to estimate the values of all parameters used in the model, the researcher(s) may be forced to use the model and the associated data to evaluate best fit or optimal values for the missing parameters. The fact is that, the number of reliable correlation s and methods for the SFE are still quite scarce. 

There is also a traffic between the surface region and the adjacent layers of liquid. For most liquids, diffusion coefficients at room temperature are on the order of 10 cm /sec, and the diffusion coefficient is related to the time r for a net displacement jc by an equation due to Einstein ... 

It was commented that surface viscosities seem to correspond to anomalously high bulk liquid viscosities. Discuss whether the same comment applies to surface diffusion coefficients. 

The state of an adsorbate is often described as mobile or localized, usually in connection with adsorption models and analyses of adsorption entropies (see Section XVII-3C). A more direct criterion is, in analogy to that of the fluidity of a bulk phase, the degree of mobility as reflected by the surface diffusion coefficient. This may be estimated from the dielectric relaxation time Resing [115] gives values of the diffusion coefficient for adsorbed water ranging from near bulk liquids values (lO cm /sec) to as low as 10 cm /sec. 

Table 4. Diffusion Coefficients for Dilute Solutions of Gases in Liquids at 20°C ...

Cg = the concentration of the saturated solution in contact with the particles, D = a diffusion coefficient (approximated by the Hquid-phase diffusivity), M = the mass of solute transferred in time t, and S = the effective thickness of the liquid film surrounding the particles. For a batch process where the total volume H of solution is assumed to remain constant, dM = V dc and... 

Umesi, N. O., Coirelating Diffusion Coefficients in Dilute Liquid Mixtures, M.S. Thesis, Penn State University, University Park, PA, 1980. van Velzen, D., R. L. Cardozo, and H. Langenkamp, Ind. Eng. Chem. Fun-dam., 11 (1972) 20. 

Experiment diffusion coefficients are scarce and not highly accurate, especially in the liquid phase, leading to prediction methods with marginal accuracy. However, use of the v ues predicted are generally suit le for engineering calculations. At concentrations above about 10 mole percent, predicted values should be used with caution. Diffu-sivities in liquids are lO -lO times lower than those in gases. 

In the special case that A and B are similar in molecular weight, polarity, and so on, the self-diffusion coefficients of pure A and B will be approximately equal to the mutual diffusivity, D g. Second, when A and B are the less mobile and more mobile components, respectively, their self-diffusion coefficients can be used as rough lower and upper bounds of the mutual diffusion coefficient. That is, < D g < Dg g. Third, it is a common means for evaluating diffusion for gases at high pressure. Self-diffusion in liquids has been studied by many [Easteal AIChE]. 30, 641 (1984), Ertl and Dullien, AIChE J. 19, 1215 (1973), and Vadovic and Colver, AIChE J. 18, 1264 (1972)]. 

Many more correlations are available for diffusion coefficients in the liquid phase than for the gas phase. Most, however, are restiicied to binary diffusion at infinite dilution D°s of lo self-diffusivity D -. This reflects the much greater complexity of liquids on a molecular level. For example, gas-phase diffusion exhibits neghgible composition effects and deviations from thermodynamic ideahty. Conversely, liquid-phase diffusion almost always involves volumetiic and thermodynamic effects due to composition variations. For concentrations greater than a few mole percent of A and B, corrections are needed to obtain the true diffusivity. Furthermore, there are many conditions that do not fit any of the correlations presented here. Thus, careful consideration is needed to produce a reasonable estimate. Again, if diffusivity data are available at the conditions of interest, then they are strongly preferred over the predictions of any correlations. 

With regard to the liqiiid-phase mass-transfer coefficient, Whitney and Vivian found that the effect of temperature upon coiild be explained entirely by variations in the liquid-phase viscosity and diffusion coefficient with temperature. Similarly, the oxygen-desorption data of Sherwood and Holloway [Trans. Am. Jnst. Chem. Eng., 36, 39 (1940)] show that the influence of temperature upon Hl can be explained by the effects of temperature upon the liquid-phase viscosity and diffusion coefficients. 

It is important to recognize that the effects of temperature on the liquid-phase diffusion coefficients and viscosities can be veiy large and therefore must be carefully accounted for when using /cl or data. For liquids the mass-transfer coefficient /cl is correlated in terms of design variables by relations of the form... 

D( = diffusion coefficient of solute in liquid g = gravity-acceleration constant h = length of wetted wall kf = mass-transfer coefficient, liquid phase r = mass rate of flow of hqnid. f = viscosity of liquid = density of hqnid... 

Higher diffusion coefficients and lower viscosities compared with liquids. Rapid diffusion of GO2 through condensed phases, e.g. polymers. 

To illustrate, consider the hmiting case in which the feed stream and the two liquid takeoff streams of Fig. 22-45 are each zero, thus resulting in batch operation. At steady state the rate of adsorbed carty-up will equal the rate of downward dispersion, or afV = DAdC/dh. Here a is the surface area of a bubble,/is the frequency of bubble formation. D is the dispersion (effective diffusion) coefficient based on the column cross-sectional area A, and C is the concentration at height h within the column. 

Table 10.1 Self diffusion coefficients of some liquid metals expressed by an Arrhenius equation...

In connection with the earlier consideration of diffusion in liquids using tire Stokes-Einstein equation, it can be concluded that the temperature dependence of the diffusion coefficient on the temperature should be T(exp(—Qvis/RT)) according to this equation, if the activation energy for viscous flow is included. 

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