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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.

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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]

Chapter 8
Stokes flow

The Navier-Stokes equations have not been solved analytically in the general case, and the only available analytical solutions arise from simple geometries (for example, the 1D flow geometries discussed in Chapter 2). Because of this, our analytical approach for solving fluid flow problems is often to solve a simpler equation that applies in a specific limit. Some examples of these simplified equations include the Stokes equations(applicable when the Reynolds number is low, as is usually the case in microfluidic devices) and the Laplace equation(applicable when the flow has no vorticity, as is the case for purely electrokinetic flows in certain limits). These simplified equations guide engineering analysis of fluid systems.

In this chapter, we discuss Stokes flow (equivalently termed creeping flow), in which case the Reynolds number is so low that viscous forces dominate over inertial forces. We show the approximation that leads from the Navier-Stokes equations to the Stokes equations, and discuss analytical results. The Stokes flow equations provide useful solutions to describe the fluid forces on small particles in micro- and nanofluidic systems, because these particles are often well approximated by simple geometries (for example, spheres) for which the Stokes flow equations can be solved analytically. The Stokes flow equations also lead to simple solutions (Hele-Shaw flows) for wide, shallow microchannels of uniform depths.

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.