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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]

4.7 Summary [flow patterning/microfluidic mixing top]

In this chapter, we present the passive scalar transport equation:

microfluidics textbook nanofluidics textbook Brian Kirby Cornell

which can be nondimensionalized to the following form:

microfluidics textbook nanofluidics textbook Brian Kirby Cornell

This nondimensional form highlights the Peclet number Pe = Uℓ∕D, which indicates the relative magnitude of the convective fluxes as compared to the diffusive fluxes in the system.

Mixing is driven by diffusion processes, which proceed over a characteristic length proportional to microfluidics textbook nanofluidics textbook Brian Kirby Cornell. Flow processes can facilitate mixing by changing the characteristic length over which this diffusive mixing must occur. Microfluidic devices use flows with low Re and high Pe, leading to slow mixing. The net effect is that scalars in microfluidic systems are often unmixed over time scales relevant to experiments. This attribute facilitates laminar flow patterning but interferes with processes that require mixing. Chaotic advection facilitates mixing by shortening the required diffusion length scales, but this sort of advection occurs only if specifically designed for with carefully crafted microfluidic geometries.

When scalars are transported axially along microchannels, Taylor-Aris dispersion controls the effective axial diffusivity, leading to an effective diffusivity given by

microfluidics textbook nanofluidics textbook Brian Kirby Cornell

[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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