Isotherm parameters

Etaulsifier Oiaracteristics. Tlie values for CHC , adsorption isotherm parameters and micellar specific surface for sodium lauryl sulitoate as previously reported ( ) have heen usea... 

Table 1. Adsorption isotherm parameters of CPA and 2,4-D with different pH (298 K).

Table 3.1 Protonation isotherm parameters of different oxides...

For the simulation of SMB-separations efficient software packages,based on the Triangle-Theory, are commercially available. The number of columns, the column dimensions, the theoretical number of plates in the columns, the feed concentration, the bi-Langmuir adsorption isotherm parameters and the number of cycles need to be defined by the user. Then the separation is simulated and values for the flow rate ratios, the flow rates, the switching time and the quality of the separation, purity and yield, are calculated. Based on these values an actual separation can be performed. However, some optimization/further development is usually necessary, since the simulations are based on an ideal model and the derived parameters and results therefore can only be taken as indications for the test runs. 

Isotherm plots of TOC data for only Bottom Ash Solid waste and isotherm equations for the different solid phases are shown in Fig. 12, and the isotherm parameters determined from statistical regression analyses with their coefficients are given in Table 4. 

Gritti, F. and Guiochon, G, Effect of the mohUe phase composition on the isotherm parameters and the high concentration band prohles in reversed-phase liquid... 

An overloaded profile is calculated by integrating Equation 10.8 and using the initial guesses for the isotherm parameters. 

The isotherm parameters are changed to minimize the squares of the differences between calculated and experimental profiles. 

Equilibrium Results. Table V shows all of the isotherm parameters computed for the sorption of methanol on the acetylated and unaltered coals. These values are on a moisture-free basis. 

The inclusion of the non-linear isotherm effect requires that the isotherm parameters be known in order to calculate the rate curves. Thus, for each system analyzed, both rate and equilibrium data were required. 

This equation reduces to the linear isotherm at low concentrations, to the Freundlich isotherm at high concentrations, and to the Langmuir isotherm when 0=1. However, the equation cannot be linearized for easy estimation of isotherm parameters. 

Kim H, Kaczmarski K, Guiochon G (2006) Isotherm parameters and intraparticle mass transfer kinetics on molecularly imprinted polymers in acetonitrile/buffer mobile phases. Chem Eng Sci 61(16) 5249-5267... 

In supercritical adsorption processes the crucial problem encountered is that, summing up to fluid phase solute concentration, the adsorption equilibria is influenced by the system temperature and by the supercritical fluid density. So, the variation of the parameters in isotherm models as a function of both temperature and density limits the applicability of the equations when they are used for fitting experimental data. To date, due partly to insufficient data, the density and temperature dependence of the isotherm parameters has not been established. 

It is general, in the literature, ion-exchange (and adsorption) processes are evaluated by a linearized isotherm. The number of active sites and the K isotherm parameter characteristic of the sorption affinities are determined from the slope and the intercept of the plot. When the isotherm is not linear, a heterogeneous surface is supposed. The isotherms are divided into linear portions, and different Q and K values are determined for the linear portions. However, for competitive processes, including competitive adsorption and ion exchange is not correct because the so-called intercept is a complex quantity containing the concentration of the competing substance. 

The transformation of the equilibrium (or selectivity) constants and the ion-exchange isotherms can easily be made only for homovalent ion exchange because the ion-exchange isotherms usually do not take into consideration the heterovalent character of the ion exchange. This causes additional serious problems in the evaluation of isotherm parameters. It is shown for the exchange of monovalent and divalent cations that... 

By this method, the ion-exchange isotherms and selectivity coefficients can precisely be determined in a wide surface concentration range, which allows the construction of the ion-exchange isotherm and selectivity function, and the integration of the selectivity function (Chapter 1, Section 1.3.4.2.1, Equation 1.81). An example of a cation-exchange isotherm and isotherm parameters is shown in Figure 2.2 for the cation exchange of cobalt ions and calcium-montmorillonite. 

The results of the cobalt and calcium ion exchange on montmorillonite shows that the ion-exchange isotherm equation (Chapter 1, Equation 1.94) can be applied well in this case, the estimated isotherm parameters (t, and K/K have real physical meaning and their values can be confirmed by independent experimental procedures. 

The Estimated Isotherm Parameters of Zinc lon/Calcium Montmorillonite Interfacial Reactions (pH 5.8)... 

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