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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]
 Derive Equation E.12 from the dimensional NavierStokes equations by substituting in the relations
in Equations E.2–E.6.

We wish to study the flow of water through a circular microchannel with radius r = 4 μm and
mean velocity 100 μm∕s. We expect experimental resolution of the velocity profile to 1/100 of the
channel. Unfortunately, most experimental techniques for measuring fluid velocity cannot localize the
measurement to a region as small as 40 nm. Describe how you might select the channel size and fluid
such that you could make this measurement in a larger channel and achieve the desired resolution.
 Consider the NavierStokes equations and the nondimensionalization that leads to the Stokes flow
approximation. Rather than nondimensionalizing the pressure by ηU∕ℓ, one could nondimensionalize the
pressure by ρU^{2}. Show that this nondimensionalization, in the limit where Re → 0, leads to the
equation
 (E.27) 
Is it possible to solve this equation and the continuity equation if the only variables are the components of the
velocity vector? Comment on the mathematical form of the governing equations for momentum and mass as
they relate to pressure.

Derive the nondimensional passive scalar mass transfer equation (Equation E.15) from the dimensional
passive scalar mass transfer equation (Equation E.14.)
 From the standpoint of dimensional analysis, define the physical parameters and the fundamental physical
quantities for the PoissonBoltzmann equation, and explain why two of the nondimensional quantities that
govern the equation are the nondimensional voltage and nondimensional length.
[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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