brian j. kirby, phd sibley school of mechanical and aerospace engineering, cornell university,...

© Cambridge University Press 2010

Brian J. Kirby, PhD

Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY

Powerpoint Slides to AccompanyMicro- and Nanoscale Fluid Mechanics: Transport in Microfluidic Devices

Chapter6


• 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

Ch 6: Electroosmosis


• Electroosmosis consists of a bulk flow driven exclusively by body forces near walls

Ch 6: Electroosmosis


• 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

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

Sec 6.1: Matched Asymptotics


• 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

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

Sec 6.2: Integral Analysis of Electroosmotic Flow


• If several constraints are satisfied, electrosmotic velocity is everywhere proportional to the local electric field, which is irrotational

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

Sec 6.3 Solving Navier-Stokes in the thin-EDL limit


• 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

Sec 6.4 Electrokinetic Potential and Electroosmotic Mobility


• Electroosmotic mobilities are of the order of 1e-8 m2/Vs

Sec 6.4 Electrokinetic Potential and Electroosmotic Mobility


• 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

Startup of Electroosmosis


• 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

Sec 6.5 Electrokinetic Pumps

brian j. kirby, phd sibley school of mechanical and aerospace engineering, cornell university,...

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