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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]

E.5 Exercises [nondimensionalization top]

  1. Derive Equation E.12 from the dimensional Navier-Stokes equations by substituting in the relations in Equations E.2E.6.
  2. We wish to study the flow of water through a circular microchannel with radius r = 4 μm and mean velocity 100 μms. 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.

  3. Consider the Navier-Stokes 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 ρU2. Show that this nondimensionalization, in the limit where Re 0, leads to the equation
    microfluidics textbook nanofluidics textbook Brian Kirby Cornell
    (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.

  4. Derive the nondimensional passive scalar mass transfer equation (Equation E.15) from the dimensional passive scalar mass transfer equation (Equation E.14.)

  5. From the standpoint of dimensional analysis, define the physical parameters and the fundamental physical quantities for the Poisson-Boltzmann 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] [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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