On the theory of multicomponent chromatography

Abstract

A theoretical study of multicomponent chromatography is here presented in which the system is considered to be one-dimensional, isothermal, locally at equilibrium and to have negligible diffusion effects. The discussion starts with constant initial and entry conditions and goes on to stepwise constant data with an arbitrary number of discontinuities. The Langmuir adsorption isotherm is perfectly fitted to the exposition of the mathematical theory of quasilinear equations for it leads to explicit forms for the Riemann invariants and characteristic parameters. This paper develops the theory of simple waves and of shock waves on an independent basis and illustrates this theory by the construction of solutions and the analysis of the interaction of waves. It is shown incidentally that the entropy change across a shock is consistent with the second law of thermodynamics. The separation of solutes is discussed and brief consideration is given to the problems associated with non-uniform geometry and non-isothermal adsorption.