Diffusion in binary systems in a critical state

Diffusion in concentrated, non-ideal liquid solutions may take place not only through motion of single molecules but also through movement of groups of molecules, or "clusters." Analyzing this cluster diffusion leads to predictions that the diffusion coefficient can vary with the square root of the usual activity corrections to diffusion. These predictions seem consistent with experiments, particularly in highly non-ideal solutions. SCOPEThe purpose of this article is to describe diffusion in concentrated liquid solutions. Such solutions are frequently highly non-ideal. The diffusion coefficient D in liquids is often estimated from the equation a In a1 a In x1

“…The second explanation of the results in Figure 1 assumes that Fick's law fails in this region (Anisimov and Perelman 1966). This failure means that…”

Section: (2)mentioning

confidence: 93%

Cluster diffusion in liquids

Cussler

1980

“…Claersson and Sundelof (1957) and Haase and Siry (1968) experimentally demonstrated that the diffusion coefficient rapidly declines toward zero as the consolute point is approached. Attempts have been made to explain this phenomenon on thermodynamic grounds (Turner, 1975a,b) and by postulating the failure of Fick's law near the consolute point (Anisimov and Perelman, 1968). Cussler (1980) explained this behavior by assuming that concentration fluctuations, including both single molecules and clusters of molecules, dominate behavior near the consolute point.…”

Section: Introductionmentioning

confidence: 98%

The diffusivity of potassium chloride and sodium chloride in concentrated, saturated, and supersaturated aqueous solutions

Chang

Myerson

1985

The diffusion coefficients of potassium chloride and sodium chloride were measured in concentrated, saturated, and supersaturated solutions at 25°C employing Gouy interferometry. The results indicate a maximum in the diffusivity vs. concentration curve near saturation followed by a rapid decline in diffusivity toward zero with increasing concentration in the supersaturated region. This behavior supports the idea that the diffusion coefficient approaches zero at the spinodal concentration. The data were successfully correlated by modifying an empirical activity coefficient equation (Robinson and Stokes, 1955) to account for molecular cluster effects and employing the calculated activity coefficients along with a predictive equation for diffusivity in electrolytes (Robinson and Stokes, 1955 SCOPEThe study of diffusion coefficients in supersaturated solutions is of fundamental importance in understanding the mechanisms of diffusion and of crystal growth from solution. Virtually no data of this kind exist, however, resulting in the use of values obtained through the extrapolation of undersaturated diffusivity data into the supersaturated range. Sorell and Myerson (1982) demonstrated that diffusion coefficients obtained through extrapolation could be seriously in error. They measured the diffusivity of urea in supersaturated aqueous solutions and compared the results with those obtained through extrapolation of existing data. The experimental results showed a very rapid decline in the diffusion coefficient with increasing concentration in the supersaturated region. Differences of up to several hundred percent between the experimental and extrapolated data were reported. The purpose of this study is to: (1) experimentally measure diffusion coefficients in the electrolyte systems potassium chloride-water and sodium chloride-water at concentrations in the supersaturated region; (2) correlate the diffusion data through modification of existing relations for concentrationdependent diffusion in electrolytes; and (3) determine whether the rapid decline in diffusivity with increasing concentration in the supersaturated region observed in the urea-water system is observed in other systems. CONCLUSIONS AND SIGNIFICANCEThe diffusion coefficients of potassium chloride in water at 25°C were measured at concentrations ranging from 0.7-4.23 M. Experimental results in the undersaturated region were consistent to within f 3 % of those of Costing (1950). Results show a maximum in the diffusivity vs. concentration curve near saturation (4.09 M) followed by a rapid decline in the diffusivity with increasing concentration in the supersaturated region,The diffusion coefficients of sodium chloride in water at 25°C were measured at concentrations ranging from 0.1-5.46 M. Experimental results in the supersaturated region were consistent to within f 3 % of those reported by Rand and Miller (1979). A maximum in diffusivity in the region of saturation followed by a rapid drop of diffusivity with increasing concentration was also observed.It is ...

Diffusivity of urea in concentrated, saturated and supersaturated solutions

Sorell

Myerson

1982

Diffusivity of Urea in Concentrated, Saturated and Supersaturated SolutionsA relatively simple and extremely versatile optical method of obtaining diffusion coefficient data known as Gouy interferometry was employed to measure diffusion coefficients in undersaturated and supersaturated aqueous urea solutions at 25°C. The use of laser light as a monochromatic light source in the interferometer greatly simplified the procedure for obtaining diffusivity data from the interferometer. A novel design of a real image camera was employed to record the interferometric data. Values obtained from the interferometric data for low concentration (0-4 molar) aqueous urea solutions were within f 5 % of literature values.The diffusion coefficient was found to decrease linearly with increasing concentration up to the saturation point of the aqueous urea solutions, and to decrease drastically with increasing concentration in the supersaturated region. This behavior is similar to that observed in liquid-liquid systems near the consolute point (Cussler, 1980). It is speculated that this phenomenon is a result of molecular aggregation of the urea molecules in supersaturated aqueous solutions. Very little experimental data have previously been obtained in the supersaturated region due to crystallization problems. Supersaturated diffusion coefficient data are important in the study and design of crystallization processes.The solid-solute-liquid solvent binary systems urea-water and sucrose-water were modeled as a saturated solution solute-liquid solvent system in order to test various concentration dependent diffusion relationships. Two of these relationships, the Vignes and Leffler-Cullinan equations, showed improved correlation with experimentally determined diffusivity data for aqueous urea and aqueous sucrose solutions at undersaturated conditions. The measurement of diffusion coefficients in supersaturated solutions is of fundamental importance in further understanding the mechanism of diffusion. In particular, diffusion data in the supersaturated range are necessary for the rational design of crystallization processes. Virtually no data of this kind exists, however, resulting in the use of values obtained through the extrapolation of lower concentration data to the supersaturated region. Diffusion coefficients obtained through this extrapolation could be seriously in error as a result of molecular aggregation postulated to occur in supersaturated solutions. In L S Sorell is presently at the Teraco Research Laboratory Beacon N Y Correspondence concerning this paper should be sent to A S Myerson 0001-1541-82 5455-0772-52 00 (EI The American Institute of Chemical Engineers 1982 addition, the prediction of diffusion coefficients in concentrated solid solute-liquid solvent systems are limited by the fact that many of the widely used equations employed in the prediction of concentration dependent diffusion coefficients were designed for use with liquid-liquid systems. The purpose of this study is as follows: (1) the experimental measure...