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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.

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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]

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 cross-section 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 λD 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.


microfluidics textbook nanofluidics textbook Brian Kirby CornellFigure 6.1: Cartoon ofelectrical double layer and electroosmotic flow. A negatively-charged wall in this figure coincides with a thin, positively charged electrical double layer. Coulomb forces in the electrical double layer induce a fluid flow that is approximately uniform outside the electrical double layer. The (typically nanoscale) thickness of the electrical double layer is exaggerated for the purposes of the figure. The difference between the local electrical potential and that of the bulk fluid is denoted by φ—this value is zero far from the wall but is finite near the wall.


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 Navier-Stokes 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 one-dimensional integral analysis of the electrical double layer to relate the electroosmotic mobility of a solid-liquid 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.

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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.