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Copyright Brian J. Kirby. With questions, contact Prof. Kirby here.
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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. Click here for the most recent version of the errata for the print version.
[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]
The integral analysis that leads to the description of the bulk electrosmotic velocity as a function of the wall
potential can be found in many sources [48, 29, 49, 50, 51, 52]. Li [52] gives a detailed treatment of several
electrokinetic flows. Cummings [43] details the requirements for similitude in a more rigorous mathematical
fashion.
Relevant sources include discussion of electrokineticallygenerated pressures due to nonuniform zeta
potential [53], electrokinetic pumps [44, 45], the effect ofpermittivity on electrokinetic pumps [46], and
detailed calculations of electrokinetic pumps without the many simplifying approximations used in this
chapter [54, 55].
It is critical to highlight what we have and have not accomplished. We have assumed that we knew the electrical
potential at the wall, in which case we can evaluate the velocity far from the wall with an integral analysis. The
magnitude of the velocity of the flow far from the wall is independent of the spatial dependence of φ—the velocity
magnitude depends only on the total variation in electrical potential between the wall and the bulk fluid,
i.e., φ_{0}. However, many important issues are left unresolved. The chemistry of microdevice walls
typically leads to a surface charge density q′′_{wall}. Knowledge of this surface charge density would help us
know the electrical force on the wall and the net body force on the fluid as well. However, we cannot
evaluate any of these parameters without a detailed picture of the ion distribution near a charged wall,
which is modeled in Chapter 9. Our study of distributed body forces in 1D flow systems (for example,
Exercises 2.12), though, has shown us that velocities in these systems are a function of the distribution of the
body forces. We were able to get an outer velocity solution without knowledge of the details of the
inner solution only because of a coincidence—namely, that the mathematical form of the bulk velocity
(a 2nd spatial integral of the Coulomb force on a net charge density) and the mathematical form of
the wall potential (a 2nd spatial integral of the net charge density) are the same for this system. In
our result for the inner solution, we have succeeded only in writing one unknown (u_{inner}) in terms of
another (φ), but purely electroosmotic flows can be predicted after experimental measurements of
φ_{0}.
The tools developed in this chapter enable us to recast rather complicated flows in terms of simpler equations.
We expand on this in later chapters. First, in Chapter 7, we describe tools for irrotational flow, applicable for purely
electroosmotic flows with nonuniform electric fields (albeit only outside the electrical double layer). Then, in
Chapter 9, we describe the structure of the electrical double layer, and in so doing, describe the electroosmotic flow
near walls as well.
While the integral description used here to link surface potential to fluid velocity is a straightforward and
intuitive one, its ability to match experimental observations is a matter of debate, owing to questions about the
validity of the assumption that the fluid properties are everywhere uniform. This is discussed in more detail in
Chapter 10.
[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. Click here for the most recent version of the errata for the print version.
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