Haarhoff-Van der Linde solution

DatR,Q- It turns out that this procedure corrects the Houghton equation for its lack of mass conservation. In the Haarhoff-Van der Linde solution, mass is conserved. 

This new simplification is correct to the first order and conserves mass. This observation explains why the Haarhoff-Van der Linde equation conserves mass while the Houghton equation does not, even to the first order. In the next section we discuss the range of validity of these solutions. 

Profiles calculated with the equilibrium-dispersive model and the parabolic isotherm (1) or the Langmuir isotherm (3). 2, Houghton solution. The Haarhoff and Van der Linde solution is identified by squares. Reproduced with permission from S. Golshan-Shirazi and G. Guiochon,J. Chromatogr., 506 (1989) 495 (Figs. 17 and 18). 

The solution derived by Haarhoff and Van der Linde [14] gives a profile whose equation is very similar to the Houghton solution. It can be written in the same... 

Figure 10.2 Comparison between the band profiles derived from the Houghton equation, the Haarhoff and Van der Linde equation and the numerical solution of the equilibrium-dispersive model using the Rouchon procedure, (a) Influence of the isotherm model used.

If an isotherm can be reduced to the first two terms of a power expansion (i.e., to a parabolic isotherm), an approximate solution can be obtained by the method of Haarhoff and Van DER Linde [75] in the case of a single-component band. 

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