Boundary value problems in electrophoresis, with applications to separations and colloid science

Persistent Link:
http://hdl.handle.net/10150/280277
Title:
Boundary value problems in electrophoresis, with applications to separations and colloid science
Author:
Erker, Joseph A.
Issue Date:
2003
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
The topic of this thesis is investigation of models applied to different aspects of separations and colloid science. Many tools are used for solving the models, which are manifested as boundary value problems. The problems are to determine the equilibrium electrostatics of a fluid droplet, the electrokinetics of such, the (nonuniform) temperature profile of an electrophoresis capillary due to Joule heating, and the temperature at the wall of the capillary. In the fluid drop model, special attention given to a drop that, in addition to the surrounding fluid, supports electrolytes. Matched asymptotic expansions based on thin double layers are applied to the equilibrium electrostatics problem. Attention is given to how conditions on the interface of the drop, such as discontinuity of equilibrium potential and the presence of surface excesses of solutes, affect the electrokinetics. A perturbation scheme is used to formulate a problem for the electrophoretic mobility of a droplet. An approximate solution for the mobility of a drop is derived, based on small interfacial potentials. The formula encompasses those of several past theoretical studies. A regular perturbation is used to determine heating effects in capillary electrophoresis, based on a small power input to the system. The resulting expression for temperature in the capillary is then used implicitly to determine the temperature at the wall of the capillary. Some of the results are compared with experimental data. For the drop electrophoresis problem, the electrophoretic mobility formula is compared with measured mobility of oil drops and drops in aqueous two-phase systems. In the study of heating in capillary electrophoresis, the implicit expression is used to make reasonable estimates of the wall temperature based on published operating conditions. Accuracy of all analytic estimates of the problems are tested against numerical solutions, taken to be exact. In all cases, the analytic approximations are satisfactorily accurate under appropriate conditions.
Type:
text; Dissertation-Reproduction (electronic)
Keywords:
Mathematics.; Chemistry, Analytical.
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Graduate College; Applied Mathematics
Degree Grantor:
University of Arizona
Advisor:
Baygents, James C.

Full metadata record

DC FieldValue Language
dc.language.isoen_USen_US
dc.titleBoundary value problems in electrophoresis, with applications to separations and colloid scienceen_US
dc.creatorErker, Joseph A.en_US
dc.contributor.authorErker, Joseph A.en_US
dc.date.issued2003en_US
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.abstractThe topic of this thesis is investigation of models applied to different aspects of separations and colloid science. Many tools are used for solving the models, which are manifested as boundary value problems. The problems are to determine the equilibrium electrostatics of a fluid droplet, the electrokinetics of such, the (nonuniform) temperature profile of an electrophoresis capillary due to Joule heating, and the temperature at the wall of the capillary. In the fluid drop model, special attention given to a drop that, in addition to the surrounding fluid, supports electrolytes. Matched asymptotic expansions based on thin double layers are applied to the equilibrium electrostatics problem. Attention is given to how conditions on the interface of the drop, such as discontinuity of equilibrium potential and the presence of surface excesses of solutes, affect the electrokinetics. A perturbation scheme is used to formulate a problem for the electrophoretic mobility of a droplet. An approximate solution for the mobility of a drop is derived, based on small interfacial potentials. The formula encompasses those of several past theoretical studies. A regular perturbation is used to determine heating effects in capillary electrophoresis, based on a small power input to the system. The resulting expression for temperature in the capillary is then used implicitly to determine the temperature at the wall of the capillary. Some of the results are compared with experimental data. For the drop electrophoresis problem, the electrophoretic mobility formula is compared with measured mobility of oil drops and drops in aqueous two-phase systems. In the study of heating in capillary electrophoresis, the implicit expression is used to make reasonable estimates of the wall temperature based on published operating conditions. Accuracy of all analytic estimates of the problems are tested against numerical solutions, taken to be exact. In all cases, the analytic approximations are satisfactorily accurate under appropriate conditions.en_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
dc.subjectMathematics.en_US
dc.subjectChemistry, Analytical.en_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.disciplineApplied Mathematicsen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorBaygents, James C.en_US
dc.identifier.proquest3089942en_US
dc.identifier.bibrecord.b44420614en_US
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