Copyright Brian J. Kirby. With questions, contact Prof. Kirby here.
This material may not be distributed without the author's consent. When linking to these pages, please use the URL http://www.kirbyresearch.com/textbook.
This web posting is a draft, abridged version of the Cambridge University Press text. Follow the links to buy at Cambridge or Amazon or Powell's or Barnes and Noble. Contact Prof. Kirby
here.
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Jump To:
[Kinematics]
[Couette/Poiseuille Flow]
[Fluid Circuits]
[Mixing]
[Electrodynamics]
[Electroosmosis]
[Potential Flow]
[Stokes Flow]
[Debye Layer]
[Zeta Potential]
[Species Transport]
[Separations]
[Particle Electrophoresis]
[DNA]
[Nanofluidics]
[InducedCharge Effects]
[DEP]
[Solution Chemistry]
Chapter 6 Electroosmosis
When electric fields are applied across capillaries or microchannels, bulk fluid motion is observed. The
velocity of this motion is linearly proportional to the applied electric field, and dependent on both (a)
the material used to construct the microchannel and (b) the solution in contact with the channel wall.
This motion is referred to aselectroosmosis, and stems from electrical forces on ions in the electrical
double layer, a thin layer of ions that is located near a wall exposed to an aqueous solution. If the fluid
velocity is interrogated at micrometer resolution, for example, by observing the fluid flow with a light
microscope, the fluid flow in a channel of uniform crosssection appears to be uniform. If the fluid
velocity were interrogated with nanometer resolution (which is experimentally difficult), the fluid
velocity would be uniform far from the wall, but it would decay to zero at the wall over a length scale
λ_{D} ranging from approximately 0.5–200 nm. Figure 6.1 illustrates the velocity profile in an electroosmotic
flow.
This fluid flow can be immensely useful in microfluidic systems, because it is often much more straightforward
experimentally to address voltage signals sent to electrodes rather than implement and control a miniaturized
mechanical pressure pump. This flow, however, comes with its own complications, as its velocity distribution is
different from pressure driven flow, it is sensitive to chemical features at the interface, and because the act of
applying electric fields can also move particles relative to the fluid or cause Joule heating (i.e., resistive heating)
throughout the fluid.
Just as our impressions of the fluid flow vary depending on the spatial resolution of our velocity observations,
our mathematical descriptions of this system can take different forms depending on what level of detail is required.
A full description of the flow requires that the NavierStokes equations be combined with a Coulomb body
force term caused by the net charge density near the wall, and that the Poisson equation be solved in
conjunction with an equilibrium Boltzmann distribution of ions to determine the spatial variation of this body
force. This treatment describes the fluid velocity in complete detail. However, this level of detail is not
required to describe electroosmotic flows at micrometer resolution, and we therefore start by describing
electroosmosis with simpler relations that are dependent on properties of the wall but ignore the details of the
flow near the wall. In developing simpler relations, we use an integral analysis of the flow near the
wall to derive a result for the outer solution of this flow, i.e., the solution far from the wall. In this
chapter, many details of the inner solution of this flow, i.e., the solution close to the wall, are left
unspecified.
Our approach in this chapter is to use a onedimensional integral analysis of the electrical double layer to relate
the electroosmotic mobility of a solidliquid interface to the electrical potential at the wall (called the surface
potential), which is a chemical property of both the wall material and the electrolyte solution. This electroosmotic
mobility describes the apparent slip at the wall if the observer ignores the portion of the fluid velocity distribution
proximal to the wall.
The solutions presented in this chapter provide no information about the size of the electrical double layer, its
physical underpinnings, or its structure, though these solutions do require that we assume that the double layer is a
boundary layer, i.e., it is relatively thin as compared to the flowfield dimensions. However, despite these omissions,
the 1D analysis leads to several important conclusions about purely electroosmotically driven flows: (1) the velocity
field near the wall is proportional to the voltage difference between that point and the wall; (2) the velocity at the
edge of the boundary layer is proportional to the local electric field and the voltage difference between the bulk fluid
and the wall; and (3) if the fluid conductivity and electroosmotic mobility are uniform, the velocity at any point far
from the wall is proportional to the local electric field, and thus the velocity field far from the wall is
irrotational.
[Return to Table of Contents]
Jump To:
[Kinematics]
[Couette/Poiseuille Flow]
[Fluid Circuits]
[Mixing]
[Electrodynamics]
[Electroosmosis]
[Potential Flow]
[Stokes Flow]
[Debye Layer]
[Zeta Potential]
[Species Transport]
[Separations]
[Particle Electrophoresis]
[DNA]
[Nanofluidics]
[InducedCharge Effects]
[DEP]
[Solution Chemistry]
Copyright Brian J. Kirby. Please contact Prof. Kirby here with questions or corrections.
This material may not be distributed without the author's consent. When linking to these pages, please use the URL http://www.kirbyresearch.com/textbook.
This web posting is a draft, abridged version of the Cambridge University Press text. Follow the links to buy at Cambridge or Amazon or Powell's or Barnes and Noble. Contact Prof. Kirby
here.
