Citation
Ammons, Richard Lewis Martin (1992) Mathematical control theory for liquid chromatography. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechTHESIS:09082011113722649
Abstract
A more comprehensive mathematical theory for liquid chromatography is set forth, incorporating dynamical models for mixed solvents and solutes, and new mathematical models for adsorption, including adsorbent and exchange processes. The equations for solvent and solute are shown to possess unique solutions, using socalled energy methods. The solvent modulation of local velocity is found theoretically, as is solvent control of solute adsorption, diffusivity, and dispersion. The theory for solvent control of solute adsorption is found to be very accurate against experiment, and offers a useful method of treating normal phase, reversed phase, ion exchange, and ion pair liquid chromatography in a unified mathematical framework, under the name catalyzed adsorption. The longrecognised problem of solvent localization is modelled, and the model shown to be consistent with experiment. Another classical problem, solvent demixing, is explained in terms of the nonlinear multicomponent solvent model, wherein solvent gradients steepen according to the adsorption and shock formation. Perturbation theory, based on a small packing number d_p/L « 1 (where d_p is substrate particle diameter, L is column length), is applied to the solventcontrolled pulsed solute dynamical equations. When moment techniques are used in conjunction with perturbation theory, very useful and simplified system control equations are obtained. These control equations are used in some model problems to discuss HETP (Height Equivalent to a Theoretical Plate) variations with Peclet number, with relative solvent concentration, and between solutes. Finally, numerical methods for the solvent and solute equations are discussed.
Item Type:  Thesis (Dissertation (Ph.D.)) 

Subject Keywords:  Applied Mathematics 
Degree Grantor:  California Institute of Technology 
Division:  Engineering and Applied Science 
Major Option:  Applied And Computational Mathematics 
Thesis Availability:  Restricted to Caltech community only 
Research Advisor(s): 

Thesis Committee: 

Defense Date:  2 October 1990 
Record Number:  CaltechTHESIS:09082011113722649 
Persistent URL:  http://resolver.caltech.edu/CaltechTHESIS:09082011113722649 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  6655 
Collection:  CaltechTHESIS 
Deposited By:  Dan Anguka 
Deposited On:  08 Sep 2011 21:56 
Last Modified:  26 Dec 2012 04:38 
Thesis Files
PDF
 Final Version
Restricted to Caltech community only See Usage Policy. 21Mb 
Repository Staff Only: item control page