Electroosmotic flow of non-newtonian fluids in microchannels

Abstract

Most solid substances will acquire surface electric charges when brought into contact with a liquid electrolyte. A layer with unbalanced charges is consequently formed in the vicinity of the solid-liquid interface, known as the electric double layer (EDL). If an electric field is applied to the system, the free charges will move, thereby dragging the fluid into motion via viscous action, giving rise to the so-called electroosmotic (EO) flow. Electrokinetic pumping has been widely used in lab-on-a-chip microfluidic applications. Very often, microfluidic systems are used to handle complex materials like biological fluids and polymeric solutions, which cannot be simply regarded as Newtonian fluids. Motivated by the need for an in-depth understanding of non-Newtonian EO flow, the aim of this thesis is to theoretically investigate the characterization of hydrodynamics in such a flow on a microscale, in conjunction with some important aspects like surface heterogeneities, wall shape modulation, depletion layer and system rotation. The non-Newtonian rheological models of viscoplastic, Eyring and power-law fluids are chosen in this thesis. The key aspect of non-Newtonian fluids is the nonlinear constitutive relationship between shear stress and shear rate. In other words, the viscosity of a non-Newtonian fluid may depend on the flow conditions such as the applied stress, boundary geometry, and sometimes even on the time history of fluid motion. Such nonlinear rheology makes a problem of non-Newtonian fluid flow not amenable to analytical analysis in general. In the present study, analytical, semi-analytical or numerical models are developed, under some simplifying assumptions, for EO flow of non-Newtonian fluids in microchannels subject to various complicating factors. Through these models, the effects due to various geometrical and electro-hydrodynamic mechanisms coupled with nonlinear rheology can be revealed. Results of this study can be used not only to provide guidance for future experiments, but also to validate numerical models for more complicated problems.

The thesis comprises three parts. In the first part, EO flow of viscoplastic materials, characterized by the presence of a yield stress, is analytically solved. Effect of the yield stress on the EO flow is found to be significant. Surface heterogeneities, because of either manufacturing irregularities or intentional fabrication, are considered in the second part, where EO flow of power-law fluids is investigated by means of the lubrication approximation. Sinusoidal functions are used to describe wavy-like channel height and wall potential distribution. The cases in which whether or not the presence of a near-wall depletion layer is taken into account are examined. Interaction between two wall patterns, under the combined action of hydrodynamic and electric forcings, may result in a rich set of nonlinear behaviors. In the last part, models for rotating EO flows of Newtonian, Eyring and viscoplastic fluids are developed by means of eigenfunction expansion, perturbation analysis, and numerical methods, respectively. The aim is to look into the interplay between Coriolis force, viscous force, pressure gradient, electric forcing, and nonlinear rheology.