1. Powerpoint Slides to Accompany Micro- and Nanoscale Fluid Mechanics: Transport in Microfluidic Devices
Chapter 6
Brian J. Kirby, PhD
Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY

2. Ch 6: Electroosmosis
The presence of a surface charge at a solid-electrolyte interface generates an electrical double layer
Electroosmosis describes the fluid flow when an extrinsic field actuates the electrical double layer
For thin double layers, the observed OUTER flow is everywhere proportional to the local electric field

3. Ch 6: Electroosmosis
Electroosmosis consists of a bulk flow driven exclusively by body forces near walls

4. Sec 6.1: Matched Asymptotics
Analysis of the electrical double layer involves a matched asymptotic analysis
Near the wall (inner solution), we assume that the extrinsic electric field is uniform
Far from the wall (outer solution), we assume that the fluid’s net charge density is zero

5. Sec 6.1: Matched Asymptotics
The two solutions are matched to form a composite solution
This chapter uses an integral analysis of the EDL to find outer solutions

6. Sec 6.2: Integral Analysis of Electroosmotic Flow
If the electrical potential drop across the double layer is assumed known, the integral effect on the fluid flow can be determined by use of an integral analysis

7. Sec 6.2: Integral Analysis of Electroosmotic Flow
This analysis does not determine the potential and velocity distribution inside the electrical double layer, but it determines the relation between the two
The integral analysis also determines the freestream velocity for electroosmotic flow

8. Sec 6.3 Solving Navier-Stokes in the thin-EDL limit
If several constraints are satisfied, electrosmotic velocity is everywhere proportional to the local electric field, which is irrotational

9. Sec 6.3 Solving Navier-Stokes in the thin-EDL limit
If several constraints are satisfied, electrosmotic velocity is everywhere proportional to the local electric field, which is irrotational

10. Sec 6.3 Solving Navier-Stokes in the thin-EDL limit
Irrotational outer flow is possible in the presence of viscous boundaries because the Coulomb body force perfectly balances out the vorticity caused by the viscous boundary condition

11. Sec 6.4 Electrokinetic Potential and Electroosmotic Mobility
The relation between the outer flow velocity and the local electric field is called the electroosmotic mobility
The electroosmotic mobility is a simple function of the surface potential and fluid permittivity and viscosity if the interface is simple
The electrokinetic potential is an experimental observable that is related to but not identical to the surface potential boundary condition

12. Sec 6.4 Electrokinetic Potential and Electroosmotic Mobility
Electroosmotic mobilities are of the order of 1e-8 m2/Vs

13. Startup of Electroosmosis
The outer solution for electroosmosis between two plates is identical to Couette flow between two plates
Electroosmosis startup is described by the startup of Couette flow
Couette flow startup can be solved by use of separation of variables and harmonic (sin, cos) eigenfunctions

14. Sec 6.5 Electrokinetic Pumps
Electroosmosis can be used to generate flow in an isobaric system
Electroosmosis can be used to generate pressure in a no-net-flow system
The system is linear, and all conditions in between are possible