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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.
[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]
The NavierStokes equations can be solved analytically if certain simplifications were made. In particular, the
convection term ⋅∇ is the most mathematically difficult term in the NavierStokes equations to handle, and this
chapter examines flows for which the geometry was so simple that we can assume away any spatial dependence that
leads to nonzero net convective flux. This approach leads to steady solutions for Couette flow, i.e., flow between
two infinite parallel plates:
and HagenPoiseuille flow, i.e., pressuredriven flow through a circular channel:
The startup of these flows highlights differences between forces, velocities and accelerations. During startup, the
acceleration is proportional to the force, which is a sum of the pressure and viscous forces. At equilibrium, the
acceleration is by definition zero, and the concavity of the velocity distribution (which is proportional
to the viscous force) is proportional to the local pressure gradient. Thus steady Couette flow, which
has no pressure gradient, has no concavity in the velocity distribution, while steady Poiseuille flow,
which has a uniform pressure gradient, has uniform concavity in the velocity profile. Development of
these flows includes nonzero convective terms, which are nonlinear and preclude general analytical
solution.
[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.
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.
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