Brian J. Kirby, PhD Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY

1. Powerpoint Slides to AccompanyMicro- 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. Ch6: 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. Ch6: 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 • Electroosmoticmobilities are of the order of 1e-8 m2/Vs

13. Startup of Electroosmosis • The outer solution for electroosmosisbetween 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