(165c) Local Equilibrium Theory for the Binary Chromatography of Species Subject to a Generalized Langmuir Isotherm: Wave Interactions

The generalized Langmuir isotherm model was recently developed to describe the competitive adsorption equilibria of a binary mixture [1]. This formalism captures the competitive effect of solutes that show either Langmuirian or anti-Langmuirian behaviour. This results in four isotherm types that show markedly different chromatographic behaviour. The equilibrium theory of chromatography has been developed in a previous work to study Riemann problems (saturation, elution and the chromatographic cycle) that are of practical relevance [1].

This work focuses on the development of the equilibrium theory to account for wave interactions, and is divided into two parts. In the first part, the theory of wave interactions is developed based on the method of characteristics. It is shown that the rules developed for competitive Langmuir isotherms can be extended to describe possible wave interactions in the case of the generalized Langmuir isotherm [2]. The second part of the study deals with the development of the chromatographic cycle for binary pulse injections, a problem of considerable practical importance. The general case of short pulses in which the waves from the adsorption and desorption front interact within the column is considered. The solution of this problem results in a set of algebraic equations that describe the movement of the solutes in the column. The solution of the problem is unique to the type of adsorption isotherm considered owing to the different sequences in which wave interactions occur in the column. Finally the elution profiles for the four isotherm types obtained from the equilibrium theory are shown to be fully consistent with those obtained through numerical simulations.

References

[1] Mazzotti, M. Local equilibrium theory for the binary chromatography of species subject to a generalized Langmuir isotherm. Ind. Eng. Chem. Res. 2006, 45, 5332.

[2] Rhee, H.-K; Aris, R.; Amundson, N. R. First-order partial differential equations; Prentice-Hall: Englewood Cliffs, NJ, 1989; Vol II.

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