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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. Click here for the most recent version of the errata for the print version.

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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] [Induced-Charge Effects] [DEP] [Solution Chemistry]

6.7 Supplementary reading [electroosmosis top]

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 [482949505152]. 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 electrokinetically-generated pressures due to nonuniform zeta potential [53], electrokinetic pumps [4445], the effect ofpermittivity on electrokinetic pumps [46], and detailed calculations of electrokinetic pumps without the many simplifying approximations used in this chapter [5455].

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., φ0. 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 (uinner) in terms of another (φ), but purely electroosmotic flows can be predicted after experimental measurements of φ0.

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.

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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] [Induced-Charge 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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