Mass and Heat Balance Equations in Chromatography

The mass balance equation was derived and studied first by Wicke [3] and later and independently by Wilson [4] and DeVault [5], under different forms. In the derivation of this equation several assumptions are made. For the sake of clarity these assumptions will merely be stated in the text of Section 2.1.1. They are discussed separately in Section 2.1.2. As we show, their consequences are minor and do not limit significantly the range of validity of the system of mass balance equations finally derived. 

the column is assumed to be unidimensional. This means that it is radially homogeneous. All the column properties are constant in a given cross section and so are the concentrations of the individual components. Thus, the mass balance equations have two independent variables, the time t and the column length z. We shall consider two functions of these variables, the concentrations — C, in the mobile phase and Cg, in the stationary phase. 

The flux of solute that exits from the slice is 

the differential mass balance for the component i in the mobile phase is 

Assuming that u and Dij are constant along the column, and making Az tend toward 0, gives 

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