TITLE:
Concentration Wave for a Class of Reaction Chromatography System with Pulse Injections
AUTHORS:
Jing Zhang, Maofei Shao, Tao Pan
KEYWORDS:
Reaction Chromatography Model, Hyperbolic Partial Differential Equations, Initial-Boundary Problem, Stability Analysis
JOURNAL NAME:
American Journal of Computational Mathematics,
Vol.6 No.3,
September
6,
2016
ABSTRACT: By using
fluid dynamics theory with the effects of adsorption and reaction, the
chromatography model with a reaction A → B
was established as a system of two hyperbolic partial differential equations
(PDE’s). In some practical situations, the reaction chromatography model was
simplified a semi-coupled system of two linear hyperbolic PDE’s. In which, the
reactant concentration wave model was the initial-boundary value problem of a
self-closed hyperbolic PDE, while the resultant concentration wave model was
the initial-boundary value problem of hyperbolic PDE coupling reactant
concentration. The general explicit expressions for the concentration wave of
the reactants and resultants were derived by Laplace transform. The δ-pulse
and wide pulse injections were taken as the examples to discuss detailedly, and
then the stability analysis between the resultant solutions of the two modes of
pulse injection was further discussed. It was significant for further analysis
of chromatography, optimizing chromatographic separation, determining the
physical and chemical characters.