Adsorption Isotherms and Their Determination

The underlying equilibrium-dispersion model, for which the mass balance for solute / in a A component mixture and a volume element is given in equation (21-2), has been very often successfully applied to quantify chromatographic processes under overloaded conditions. 

In this equation, c is the concentration in the fluid phase and q is the quantity in the solid phase. The column porosity e (expressed as phase ratio f = (1 -e)/e) defines the fraction of the fluid phase in the column. Furthermore, u stands for the linear velocity and t and x are the time and space coordinates, respectively. All contributions leading to band-broadening are lumped in a simplifying manner into an apparent dispersion coefficient, D p. In equation (21-2), it is assumed that the two phases are constantly in equilibrium expressed by the adsorption isotherms. Due to the nonlinear character of the isotherm equations, the solution of equation (21-2) requires the use of numeri- 

The concentrations of component i in the liquid and in the solid phases, C and Qi, respectively, are related through the adsorption isotherms [equation (21-3)]. 

To model the adsorption equilibrium, a suitable isotherm equation has to be chosen. For mixtures, the model equations are usually coupled to take into 

For enantiomeric separations, the modified competitive Langmuir equation (21-8) was found to represent several sets of experimental data satisfactorily [47]. This equation considers noncompetitive and competitive adsorption at different types of adsorption sites. Other useful equations are described and reported in the literature [48,49]. 

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