Fundamental Basis of the Equilibrium Dispersive Model

The equilibrium-dispersive model had been discussed and studied in the literature long before the formulation of the ideal model. Bohart and Adams [2] derived the equation of the model as early as 1920, but it does not seem that they attempted any calculations based on this model. Wicke [3,4] derived the mass balance equation of the model in 1939 and discussed its application to gas chromatography on activated charcoal. In this chapter, we describe the equilibrium-dispersive model, its historical development, the inherent assumptions, the input parameters required, the methods used for the calculation of solutions, and their characteristic features. In addition, some approximate analytical solutions of the equilibrium-dispersive model are presented. 

The model of Lapidus and Amundson [5] is the focal point of study of linear and nonlinear chromatography. Since in chromatography we have two independent variables, z and t, and two dependent variables, the concentrations of the solute in the mobile and the stationary phases, C and Cg, respectively, two equations are required for the model to permit the calculation of C(x, t) and Cs x, t). The model of Lapidus and Amundson considers a set of two partial differential equations for a single component. The first equation is the mass balance equation (Eq. 2.2) 

The second equation of the model relates the two concentrations in Eq. 10.1. Lapidus and Amundson [5] chose a linear kinetic model 

Single-Component Profiles with the Equilibrium Dispersive Model 

It is convenient to separate these contributions to the column HETP and to distinguish the number of mixing stages, Noisp, the number of mass transfer stages, Nm, and the apparent number of theoretical plates. Nap = L/H. These various contributions are described by the following equations 

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