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

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