International Journal of Bioinformatics and Biomedical Engineering
Articles Information
International Journal of Bioinformatics and Biomedical Engineering, Vol.1, No.3, Nov. 2015, Pub. Date: Nov. 12, 2015
Behavior of Concentration Wave for Chromatography System with a Reaction
Pages: 263-271 Views: 943 Downloads: 392
Authors
[01] Yun Han, Department of Optoelectronic Engineering, Jinan University, Guangzhou, P. R. China.
[02] Tao Pan, Department of Optoelectronic Engineering, Jinan University, Guangzhou, P. R. China.
[03] Jiemin Li, Department of Optoelectronic Engineering, Jinan University, Guangzhou, P. R. China;Department of Mathematics, Zhanjian Normal College, Zhanjiang, P. R. China.
Abstract
Based on fluid dynamics theory of the chromatographic process, combined with the effects of adsorption and reaction, the chromatography model with a reaction A→B was established by a system of two nonlinear hyperbolic partial differential equations (PDE). 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 explicit expressions for the concentration wave of the reactants and resultants were constructed by characteristic curve method in general situations. By taking pulse width injection taken as an example, the solution of concentration wave for reactant and resultant were derived detailedly, and then the shape of the outflow curves were further analyzed in a variety of situations. It was significant for further analysis between input and output of chromatography, optimizing chromatographic separation, determining the physical and chemical characters.
Keywords
Reaction Chromatography Model, Concentration Wave, Outflow Curve, Hyperbolic Partial Differential Equations, Characteristic Curve Method
References
[01] G. Guiochon, S. Ghodbane, S. Golshan-Shirazi, etc, Non-Linear Chromatography: Recent Theoretical and Experimental Results, Talanta. 36 (1989) 19-33.
[02] B. Lin, Guiding of the Chromatography Model Theory, Science Press, Beijing, 2004.
[03] B. Lin, F. Song, G. Guiochon, Analytical Solution of Ideal Nonlinear Model of Reaction Chromatography for a Reaction A→B and a Parabolic Isotherm, Journal of Chromatography A. 1003 (2003) 91-100.
[04] C. Bardos, A. Y. Leroux, and J. C. Nedelec, First Order Quasilinear Equations with Boundary Conditions, Comm. Part. Diff. Eqs. 4 (1979) 1017-1034.
[05] X. Wu, Adsorption Isotherm of No-linear Chromatography and Enzyme-Catalyzed Reaction Chromatography, Doctor Thesis, Dalian University of Technology, 2010.
[06] P. G. LeFloch and J. C. Nedelec, Explicit Formula for Weighted Scalar Nonlinear Conservation Laws, Trans Amer Math Soc. 308 (1988) 667-683.
[07] T. Pan, L. Lin, The Global Solution of the Scalar Nonconvex Conservation Laws with Boundary Condition, Journal of Partial Differential Equations. 8 (1995) 371-383.
[08] T. Pan, H. Liu, K. Nishihara, Asymptotic Stability of the Rarefaction Wave of a One Dimensional Model System for Compressible Viscous Gas with Boundary, Japan Journal Industrial Applied Mathematics. 16 (1999) 431-441.
[09] T. Pan, Q. Jiu, Asymptotic Behavior for Solution of the Scalar Viscous Conservation Laws in the Bounded Interval Corresponding to Rarefaction Waves, Progress in Natural Science. 9 (1999) 948-952.
[10] T. Pan, H. Liu, Asymptotic Behaviors of the Solution to an Initial-boundary Value Problem for Scalar Viscous Conservation Laws, Applied Mathematics Letters. 15 (2002) 727-734.
[11] T. Pan, H. Liu, K. Nishihara, Asymptotic Behavior of a One-Dimensional Compressible Viscous Gas with Free Boundary, SIAM Journal on Mathematical Analysis. 34 (2002) 273-291.
600 ATLANTIC AVE, BOSTON,
MA 02210, USA
+001-6179630233
AIS is an academia-oriented and non-commercial institute aiming at providing users with a way to quickly and easily get the academic and scientific information.
Copyright © 2014 - 2017 American Institute of Science except certain content provided by third parties.