Cornell University - Visit www.cornell.edu Kirby Research Group at Cornell: Microfluidics and Nanofluidics : - Home College of Engineering - visit www.engr.cornell.edu Cornell University - Visit www.cornell.edu
Cornell University, College of Engineering Search Cornell
News Contact Info Login

Donations keep this resource free! Give here:

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.

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

16.4 Electrothermal fluid flow [AC electrokinetics top]

For uniform fluid properties, the Coulomb body force is the only electrostatic body force:
microfluidics textbook nanofluidics textbook Brian Kirby Cornell
(16.30)

However, if the fluid properties vary (for example, because of temperature variations), we must also include a dielectric force:
microfluidics textbook nanofluidics textbook Brian Kirby Cornell
(16.31)

The combined Coulomb and dielectric force drives flows in bulk fluid most often when temperature gradients exist in a microsystem; these flows are termed electrothermal flows. Unlike electroosmosis, for which the net charge density is an equilibrium phenomenon caused by a charged wall, electrothermal flows are driven by dynamic fluctuations in net charge density caused by spatial inhomogeneities in the fluid properties. Recall that, for uniform fluid properties far from walls, the charge conservation equation and Poisson’s equation both reduce to Laplace’s equation. However, if a localized temperature increase exists, the local conductivity is increased while the permittivity is decreased. Equilibrium conservation of charge indicates that the local electric field must be reduced, while an equilibrium Gauss’s law formulation indicates that the local electric field can only be reduced if a local charge density exists. Thus temperature fluctuations lead to dynamic fluctuations in net charge density, which in turn lead to electrostatic body forces.

Using Gauss’s law to write ρE in terms of ε and microfluidics textbook nanofluidics textbook Brian Kirby Cornell, substituting this into the charge conservation equation, and neglecting convective charge transport leads to
microfluidics textbook nanofluidics textbook Brian Kirby Cornell
(16.32)

Simplifying this relation with a perturbation expansion and substituting it into Equation 16.31 leads to a solution for the body force (see Exercise 16.14). If we assume that the applied field is sinusoidal, we can use the analytic representation of the field to calculate a time-averaged force. Further, this force can be written in terms of the field that would have existed but for the temperature perturbations. Writing the analytic representation of this applied field as microfluidics textbook nanofluidics textbook Brian Kirby Cornell = microfluidics textbook nanofluidics textbook Brian Kirby Cornellexpjωt, then the time averaged body force can be written
microfluidics textbook nanofluidics textbook Brian Kirby Cornell
(16.33)

where σ and ε have been assumed temporally constant.

[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] [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.


Ad revenue from these pages is used to support student research. The presence of an advertisement on these pages does not constitute an endorsement by the Kirby Research Group or Cornell University.

Donations keep this resource free! Give here: