Stefan correction factor

Fig. 1.49 Stefan correction factor = from film theory...

The factor is known as the Stefan correction factor , [1.28]. In order to calculate the mass transferred using film theory, the mass transfer coefficient (3 has to be found. In cases where convection is negligible the mass transferred is calculated from equation (1.181), whilst where convection is significant the mass transferred is given by (1.183). 

Conversely, the correct approach to formulate the diffusion of a single component in a zeolite membrane is to use the MaxweU-Stefan (M-S) framework for diffusion in a nonideal binary fluid mixture made up of species 1 and 2 where 1 and 2 stands for the gas and the zeohtic material, respectively. In the M-S theory it is recognized that to effect relative motions between the species 1 and 2 in a fluid mixture, a force must be exerted on each species. This driving force is the chemical potential gradient, determined at constant temperature and pressure conditions [68]. The M-S diffiisivity depends on coverage and fugacity, and, therefore, is referred to as the corrected diffiisivity because the coefficient is corrected by a thermodynamic correction factor, which can be determined from the sorption isotherm. 

Do is generally referred to as the corrected or Maxwell-Stefan diffusivity, and r is called the thermodynamic correction factor, which corrects for the nonlinearity between the pressure and the concentration of the adsorbate. Often, the corrected diffusivity is used in experimental studies where the transport diffusion is measured. Although Do can still depend on the concentration, in systems near the saturation limit or in the low concentration (Henry s law) regime this dependence has been experimentally shown to be quite small, and the use of the corrected diffusivity helps in directly comparing experimental results under different conditions [3]. 

The ternary diffusion coefficient strongly depends on the solution concentration. In order to calculate accurate mass transfer coefficients, experimental data of diffusion coefficients at the interest concentrations and temperatures are necessary. However, data are not available at concentrations and temperature used at the present study, it was assumed that the ternary diffusion coefficients were equal to the binary diffusion coefficients. The binary diffusion coefficients of the KDP-water pairs and the urea-water pairs were taken from literature (Mullin and Amatavivadhana, 1967 Cussler, 1997). The values were transformed into the Maxwell-Stefan diffiisivities using the thermodynamic correction factor. 

In fact, X is a correction parameter for the Pick diffusion coefficient. This correction has a similar effect on the apparent diffusivity as the correction given in Eq. (14). When X is less then 1, the diffusivity increases with occupancy. This correction can also be applied to the Maxwell-Stefan diffusivity, which results in an even larger effect of concentration on the flux. The concentration dependence of the flux in the Maxwell-Stefan equations depends largely on the adsorption isotherm chosen, since this isotherm determines the thermodynamic factor. For Langmuir adsorption the concentration dependence of the flux increases in the following order using different models ... 

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