Powerpoint Slides to Accompany
Micro- and Nanoscale Fluid Mechanics:
Transport in Microfluidic Devices
Brian J. Kirby, PhD
Sibley School of
Mechanical and
Aerospace Engineering,
Cornell University, Ithaca,
NY
© Cambridge University Press 2010
Chapter
6
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
© Cambridge University Press 2010
Ch 6: Electroosmosis
• Electroosmosis consists of a bulk
flow driven exclusively by body
forces near walls
© Cambridge University Press 2010
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
© Cambridge University Press 2010
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
© Cambridge University Press 2010
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
© Cambridge University Press 2010
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
© Cambridge University Press 2010
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
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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
© Cambridge University Press 2010
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
© Cambridge University Press 2010
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
© Cambridge University Press 2010
Sec 6.4 Electrokinetic Potential and
Electroosmotic Mobility
• Electroosmotic mobilities are of
the order of 1e-8 m2/Vs
© Cambridge University Press 2010
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
© Cambridge University Press 2010
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
© Cambridge University Press 2010