Electroosmotic Flow and Dispersion in Microfluidic Separation Systems

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Motivated by applications to microfluidic separation systems like Capillary Electrophoresis (CE) and Capillary Electrochromatography (CEC), the research described in this dissertation analyzes through numerical and asymptotic methods the effect of variation in the wall zeta potential (or surface charge) on the electroosmotic flow field in a microchannel and the effect of inhomogeneities in the flow field and wall interactions on the dispersion (spreading) of a solute undergoing separation in a microchannel. The electroosmotic flow field is solved numerically in a rectangular microchannel with several representative zeta potential distributions on the wall. When the axial scale of variation of zeta potential is larger than the microchannel width, the numerical results show good agreement with an asymptotic analysis based on lubrication theory. In the opposite limit, when the axial scale of variation in zeta potential is smaller than the microchannel width, the numerical results indicate that a parallel plate approximation of the rectangular geometry serves as an adequate model. The transport of a solute in a straight microchannel of arbitrary cross-section in presence of an adsorption-desorption process on the wall is studied. An asymptotic approach valid in the long time limit is developed that leads to the formulation of a one-dimensional partial differential equation for the cross-sectionally averaged solute concentration. Integration of this equation is much less expensive computationally compared to the numerical solution of the full three-dimensional problem. Further, the asymptotically reduced model allows us to calculate the three-dimensional concentration field in the microchannel algebraically, once the axial distribution of the cross-sectionally averaged concentration has been calculated. In the limit when adsorption and desorption are at least as fast as the cross-diffusion, useful analytical expressions applicable to dispersion calculations in CEC and a wide variety of chromatographic separations are obtained from this model. The asymptotic analysis is also extended to handle axial variations in the flow field and the cross-sectional shape. Several test problems are solved in a rectangular microchannel through asymptotic reduction as well as through complete numerical solution in three dimensions. The results from the threedimensional numerical solution are found to be in good agreement with the results from the asymptotically reduced model.

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  • 06/26/2018
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