Numerical modeling of electroosmotically driven flows in complex micro-geometries

Electroosmotic phenomena are analyzed and simulated for two-dimensional micro-geometries, and the means of building pressure in micro-channels are explored. In the first part of the dissertation, analytical results for the velocity distribution, mass flow rate, pressure gradient, wall shear stress and vorticity in mixed electroosmotic/pressure driven flows are presented for two-dimensional straight channel geometries. We particularly analyze the electric double layer (EDL) region near the walls for steady flows, and define three new concepts based on the electroosmotic potential distribution. We show that the Helmholtz-Smoluchowski velocity is the appropriate slip velocity on the walls.; In the second part of the dissertation, analytical solutions of time periodic electroosmotic flows are obtained as a function of a nondimensional parameter, κ, which is based on the EDL thickness, kinematic viscosity, and the frequency of an externally applied electric field. A parametric study as a function of κ reveals very interesting physics ranging from oscillatory “plug like” flow in the quasi-steady state to flows analogous to Stokes' second problem. The latter case differs from the Stokes' second solution within the EDL, since the flow is driven with an oscillatory electric field, rather than a moving surface. Unlike the steady electroosmotic flow, the vorticity for time periodic flows is not confined in the EDL.; In the third part of the dissertation, a spectral element algorithm is developed to analyze the Navier-Stokes equations under the action of inertia, viscous, pressure, and electrokinetic forces in arbitrary micro-geometries. Numerical simulation results for combined electroosmotic/pressure driven flows in complex micro-geometries, such as cross-flow, Y-split junction and T-junction geometry are presented. Flow control in the Stokes flow regime is shown to have linear dependence on the magnitude of the externally applied electric field. Electroosmotic action is also applied in step channel and groove channel geometries by proper selection of surface materials and electric field directions to eliminate flow separation. Finally, we present global and point-wise comparisons of experimental measurements and numerical simulation results of electroosmotically driven flows in grooved micro-channels.