Electro-osmotic flow and hydrodynamic dispersion in a channel with surface heterogeneities

Abstract

Theoretical studies are presented in this thesis on the hydrodynamic dispersion due to electro-osmotic flow (EOF) through a parallel-plate or circular channel under the combined effects of wall heterogeneities, including surface topography, hydrodynamic slip, and zeta potential. These wall properties, which are periodically varied along the channel, are called wall patterns in general. The electric potential field and the velocity field of the EOF are determined by solving the linearized Poisson-Boltzmann (P-B) equation and the Stokes equation, respectively, subject to the spatially varying electrohydrodynamic boundary conditions caused by the wall patterns. In particular, for wall patterns with discrete step changes (in contrast with slowly varying and continuous ones), the solutions are expressed by Fourier series that satisfy the mixed-type boundary conditions. The effective expression for the dispersion is derived using the theory of homogenization by introducing multiple-scale variables and expansions. The effective dispersion coefficient is determined either by purely analytical analysis or numerical methods combined with analytical deduction, depending on the complexity of the problem formulation.

This thesis consists of two parts. In the first part, the aggregate effect on the flow due to non-uniformly distributed wall properties is studied in two problems. The first problem considers the combined effects of wall corrugations and slippage modulation on pressure-driven cross (transverse) flow through a thin parallel-plate channel in terms of the hydrodynamic effective slip length and flow enhancement. The second problem considers the combined effects of charge distribution and slippage modulation on both longitudinal and transverse EOF through a channel with the same geometry in terms of the electroosmosis (EO) mobility and flow morphology. It is shown that the interaction between different wall patterns due to surface heterogeneity can play a significant role in determining the flow velocity as well as the local convection pattern, both quantitatively and qualitatively.

In the second part, hydrodynamic dispersion due to EOF under the aggregate effect of surface heterogeneities in wall potential and hydrodynamic slippage is studied also in two problems. The first problem considers a limiting case where certain geometric and dynamic requirements are satisfied so that the theory of lubrication approximation can be applied to simplify the analysis, for which analytical solutions are obtained for the flow as well as the dispersion. The second problem is for a similar but more general case without using the lubrication approximation, in which the velocity of the flow, the dispersion coefficient and the plate height for the mass transfer are numerically determined after the mathematical formulation of the problem. It is remarkable that the introduction of hydrodynamic slippage can dramatically change the dispersion arising from EOF in various aspects, especially when both the slippage and electric potential are non-uniformly distributed on the channel wall.