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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]
For uniform fluid properties, the Coulomb body force is the only electrostatic body force:
 (16.30) 
However, if the fluid properties vary (for example, because of temperature variations), we must also include a
dielectric force:
 (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 ρ_{E} in terms of ε and , substituting this into the charge conservation equation, and
neglecting convective charge transport leads to
 (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 timeaveraged 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 = expjωt, then the time averaged body force can be
written
 (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]
[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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