Diffusion Coefficients in Liquids at Infinite

The gas-phase diffusion coefficients are calculated using the equation given in Ref. [40]. The liquid-phase diffusion coefficients of components at infinite dilution in... 

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. 

This equation is simply Pick s first law of diffusion. Note that Ui — 0, but Ui is nonzero. Furthermore, for this binary system of solute i in a liquid s, the ideal solution binary diffusion coefficient D (valid at infinite dilution) is... 

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. 

In liquids, predictive methods for diffusivity are typically semiempirical, relating the diffusivity of a solute at infinite dilution to the solvent viscosity, the molar volumes of the components, and sometimes other quantities [15]. For finite concentrations, the manner in which the diffusion coefficients pass from one infinite-dilution limit to the other is sometimes complex, and the models that exist [15] typically have a parameter that must be fitted to data. 

A wastewater stream of 0.038 m3/s, containing 10 ppm (by weight) of benzene, is to be stripped with air in a packed column operating at 298 K and 2 atm to reduce the benzene concentration to 0.005 ppm. The packing specified is 50-mm plastic Pall rings. The airflow rate to be used is five times the minimum. Henry s law constant for benzene in water at this temperature is 0.6 kPa-m3/mol (Davis and Cornwell, 1998). Calculate the tower diameter if the gas-pressure drop is not to exceed 500 Pa/m of packed height. Estimate the corresponding mass-transfer coefficients. The diffusivity of benzene vapor in air at 298 K and 1 atm is 0.096 cm2/s the diffusivity of liquid benzene in water at infinite dilution at 298 K is 1.02 x 10 5 cm2/s (Cussler, 1997). 

In these equations, I is the distance from the edge of the plate in the flow direction, v is relative velocity between the electrode and the liquid at infinite distance from the electrode surface, v is kinematic viscosity and D the diffusion coefficient. 

However, for most cases involving gases and even low sorbing vapors or liquids, swelling of the polymer and non-Fickian complications are minimal. In these situations, solutions to equation 1, unconfused by bulk flow, provide an adequate description of the process and allow estimation of the mutual diffusion coefficient. In such cases with a constant diffusion coefficient, standard solutions of equation 1 for Mt, the amount of material sorbed (or desorbed) at time t relative to Moo, the amount of material sorbed (or desorbed) at infinite time, can be used for this estimation of the mutual diffusion coefficient. If the initial and final concentrations in the sample of thickness f are uniform and the external penetrant activity is held constant, two mathematically equivalent solutions to equation 1 are given (5) ... 

Table 3.7B Diffusion coefficients at infinite dilation in nonaqueous liquids (Cussler, 1997)...

Table A16 Experimental diffusion coefficient of water in organic liquids at 20-25 °C at infinite dilution...

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