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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]

10.1 Definitions and notation [zeta potential top]

Here we must define the difference between several terms, namely thezeta potential, the electrokinetic potential, the interfacial potential, the double layer potential, and the surface potential. These terms have different meanings and are used differently by various authors. Further, some of these terms become equivalent if specific models are used to describe the interface, but have different meanings if other models are used.

Surfacepotential (or, equivalently, interfacial potential or double layer potential) typically implies the difference between the potential in a bulk, electroneutral solution and the potential at the wall. The wall here is defined as the point at which the material in the solid phase ends. We write the surface potential in this text as φ0, but the reader should be aware that this potential is often denoted in other sources as ϕ0, ψ, ψ0, or ζ. The surface potential is well defined if the electrical double layer is thin, since interfacial effects decay on a shorter length scale than any spatial variation in the bulk electric field. In this case, we define a “bulk” location that simultaneously is (a) close enough to the wall that it experiences the same extrinsic electric field as the wall; and (b) is far enough from the wall that the net charge density is zero and interfacial effects on the potential can be neglected. The surface potential is also well defined if the bulk electric field is uniform, as is the case for flow over an infinite flat plate or over a small particle. In this case, the bulk is straightforward to define even when double layers are thick. When double layers are thick and the extrinsic field is nonuniform, the definition of a surface potential becomes much more difficult.

Electrokineticpotential is specific to a phenomenon (e.g., electroosmosis or electrophoresis). For electroosmosis, the electrokinetic potential is given by -μEOηbulk∕εbulk, which is the potential that need be inserted into aHelmholtz-Smoluchowski-type equation (e.g., Equation 6.14) to explain observed electroosmotic flow. We denote the electrokinetic potential as ζ [V] in this text. The electrokinetic potential has units of voltage by definition, but need not correspond to a physical potential or potential difference.

The distinction between the electrokinetic potential and the surface potential is critical—φ0 is a measure of the interfacial potential while ζ is a measure of fluid or particle flow—but this distinction is confounded by widely varying use of terminology and symbology as well as the fact that the two quantities are equivalent if the spatially-uniform property, integral analysis of Chapter 6 is employed. The terms electrokinetic potential, zeta potential, double layer potential, surface potential, and interfacial potential are often used interchangeably, and the meaning implied by specific use of these terms is often ambiguous. We use the terms surface potential, interfacial potential, or double layer potential and the symbol φ0 to denote the difference in potential between the bulk solution and the interface between the wall and the solution. We use the terms zeta potential or electrokinetic potential and the symbol ζ to denote -μEOηbulk∕εbulk for electroosmosis or μEPηbulk∕εbulk for electrophoresis.

Recall from Chapter 6 that the bulk velocity for electroosmosis over a flat plate for a system with uniform fluid properties and ion distributions described by Boltzmann statistics is given by μEO = -εφ0∕η, which implies that

microfluidics textbook nanofluidics textbook Brian Kirby Cornell

for such a system. However, ion crowding or adhesion limits the application of Boltzmann statistics, and the high electric fields and high ion densities give the potential for breakdown of the uniform-property assumption employed in Chapter 6.

Related work on zeta potential from our research group can be found 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]

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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