Asian Research Thesis Index

Abstract

This dissertation presents solutions of general rate models (GRMs) of non-reactive and reactive liquid chromatography with a focus on evaluating the eﬀect of ﬁnite rates for the adsorption and desorption steps, typically considered to be in equilibrium. Such slow rates of adsorption-desorption steps inﬂuence the column eﬃciency and elution shapes. The model equations are partial diﬀerential equations accounting for convection, dispersion, mass transfer resistances, and/or reaction kinetics coupled with algebraic and ordinary diﬀerential equations for describing adsorption-desorption on the stationary phase. Mostly in liquid chromatography operations, the injected sample is diluted or of small volume, justifying the use of linear models for process simulation. In this study, the Laplace trans formation is applied for deriving analytical solutions of the linear model equations. To get back solutions in the original time domain, numerical Laplace inversion formula is applied. Analytical solutions are further used for deriving the Laplace domain expressions of the ﬁrst four temporal moments. In some applications, mixture samples are concentrated and have large volumes, necessitating the use of nonlinear models which are not solvable analyt ically. A high resolution ﬁnite volume scheme is applied for the numerical approximation of nonlinear GRM considering core-shell particles. Several test problems are considered to compute inﬂuences of the rate constants for adsorption and desorption, axial dispersion, intraparticle diﬀusion resistance, ﬁlm mass transfer resistance, core-radius fraction and in let boundary conditions on the elution proﬁles. The developed analytical and numerical solutions are helpful tools to predict dynamic behaviors inside the column and to evalu ate the inﬂuence of model parameters on the elution proﬁles, in particular the eﬀects of ﬁnite rates of the intrinsic adsorption and desorption steps. They provide useful tools for sensitivity analysis, process optimization and for parameters estimation from experiments.

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