Binary mixtures process, dilution

One might expect that the partial-molal energy (rather than enthalpy) should appear in the expression for the energy flux by diffusional processes. This point is discussed briefly for dilute-gas binary mixtures by Chapman and Cowling (C3, p. 145ff.). 

Fast and satisfactory mass transfer calculations are necessary since we may have to repeat such calculations many times for a rate-based distillation column model or two-phase flow with mass transfer between the phases in the design and simulation process. The generalized matrix method may be used for multicomponent mass transfer calculations. The generalized matrix method utilizes the Maxwell-Stefan model with the linearized film model for diffusion flux, assuming a constant diffusion coefficient matrix and total concentration in the diffusion region. In an isotropic medium, Fick s law may describe the multicomponent molecular mass transfer at a specified temperature and pressure, assuming independent diffusion of the species in a fluid mixture. Such independent diffusion, however, is only an approximation in the following cases (i) diffusion of a dilute component in a solvent, (ii) diffusion of various components with identical diffusion properties, and (iii) diffusion in a binary mixture. 

A solution is t3q>lcally a system of more than one component. In actual cases, there are at least two substances that can adsorb. For a binary fluid mixture, including dilute solutions, adsorption of one type of molecule (say A) involves replacement of the other (B). Thus, adsorption from solution is essentially an exchange process. If one molecule of A replaces r molecules of B at the Interface, the adsorption equilibrium can be written as... 

A single-stage process is used to separate a binary mixture of ethyl alcohol (1) and cyclohexane (2) at 45°C. The following infinite dilution liquid activity coefficient data are given ... 

The coefficient of sell-diffusion does not appear to have an anomaly near the critical point. For the engineer, however, the mutual dift usion coefficient is the more important property. The binary dilfusion coefficient approaches zero at the mixture critical point ("critical slowing-down"). In dilute mixtures, however, the decrease of the binary dilfusion coefficient is not seen until the critical line is approached very closely. For many practical purposes, such as supercritical extraction and chromatography, the mixture is dilute, and it can be assumed that the coefficient of binary diffusion is intermediate between that in the vapor and that in the liquid. Since the diffusion coefficient decreases roughly inversely proportional to the density, dilfusion in supercritical solvents is much more rapid than in liquid solvents, thus increasing the speed of diffusion-controlled chemical processes. 

Pervaporation is a membrane separation process where the liquid feed mixture is in contact with the membrane in the upstream under atmospheric pressure and permeate is removed from the downstream as vapor by vacuum or a swept inert gas. Most of the research efforts of the pervaporation have concentrated on the separation of alcohol-water system [1-20] but the separation of acetic acid-water mixtures has received relatively little attention [21-34]. Acetic acid is an important basic chemical in the industry ranking among the top 20 organic intermediates. Because of the small differences in the volatility s of water and acetic acid in dilute aqueous solutions, azeotropic distillation is used instead of normal binary distillation so that the process is an energy intensive process. From this point of view, the pervaporation separation of acetic acid-water mixtures can be one of the alternate processes for saving energy. 

The activity coefficient of a component in a mixture is a function of the temperature and the concentration of that component in the mixture. When the concentration of the component proaches zero, its activity coefficient approaches the limiting activity coefficient of th component in the mixture, or the activity coefficient at infinite dilution, y . The limiting activity coefficient is useful for several reasons. It is a strictly dilute solution property and can be used dir tly in nation 1 to determine the equilibrium compositions of dilute mixtures. Thus, there is no reason to extrapolate uilibrium data at mid-range concentrations to infinite dilution, a process which may introduce enormous errors. Limiting activity coefficients can also be used to obtain parameters for excess Gibbs energy expressions and thus be used to predict phase behavior over the entire composition range. This technique has been shown to be quite accurate in prediction of vapor-liquid equilibrium of both binary and multicomponent mixtures (5). 

When water is the solute, values from Eq. (6.3-9) should be multiplied by a factor of 1/2,3 (Rl). Equation (6.3-9) predicts diffusivities with a mean deviation of 10-15% for aqueous solutions and about 25% in nonaqueous solutions. Outside the range 278-313 K, the equation should be used with caution. For water as the diffusing solute, an equation by Reddy and Doraiswamy is preferred (R2). Skelland (S5) summarizes the correlations available for binary systems. Geankoplis (G2) discusses and gives an equation to predict diffusion in a ternary system, where a dilute solute A is diffusing in a mixture of B and C solvents. This case is often approximated in industrial processes. 

Thermodynamic principles are relevant to separation processes that make use of the distribution of macromolecules between two phases. These two phases may form a partially miscible system. The diluted phase is called sol phase I, and the polymer-rich phase is the gel phase 11. The distribution coefficient depends on molar mass and on chemical composition. Figure 2 depicts the distribution functions in the sol and gel phases. Fractionation can be achieved in a single solvent by a change of temperature, but it is often more practical to vary the solvent quality by using a binary solvent mixture composed of a nonsolvent and a good solvent, usually miscible in all proportions. The solvent composition can be used to fine-tune the solvent quality at constant temperature. 

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