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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]

8.5 Summary [Stokes flow top]

The Stokes equations are the limit of the Navier-Stokes equations as the Reynolds number approaches zero, in which case the unsteady and convective terms can be ignored. The Stokes equations are linear, and their solutions exhibit instantaneity, time-reversibility, linearity, and superposability. The Stokes equations are commonly written in any of three forms:

microfluidics textbook nanofluidics textbook Brian Kirby Cornell

microfluidics textbook nanofluidics textbook Brian Kirby Cornell

or

microfluidics textbook nanofluidics textbook Brian Kirby Cornell

Bounded Stokes flows are solved numerically for most geometries, but can be solved with separation of variables and the Laplace equation for Hele-Shaw flows. Unbounded Stokes flows can be treated analytically with the multipolar Stokeslet solutions, described in Appendix F. In particular, the flow around a sphere can be written analytically in terms of a Stokeslet, which describes the response of the fluid to the force applied to the particle, and a stresslet, which describes the irrotational response that the fluid would experience if there was a sphere with a full slip condition at the surface. A hydrodynamic interaction tensor is used to relate the velocity to the applied force:

microfluidics textbook nanofluidics textbook Brian Kirby Cornell

For large spacings of particles, the stresslet term is often ignored and the hydrodynamic interaction tensor is written as the Oseen-Burgers tensor:

microfluidics textbook nanofluidics textbook Brian Kirby Cornell

which provides the fundamental means for describing the hydrodynamic interaction of a collection of small particles with each other and with surfaces. Detailed modifications to these relations can be made for special cases, for example for ellipsoidal particles or for particles in proximity to walls.

Some examples of our research where Stokes flow analysis is relevant include our circulating tumor cell capture microchips and our dielectrophoretic manipulation of microparticles.

[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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