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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 2
Unidirectional flow

While the Navier-Stokes solutions cannot be solved analytically in the general case, we can still obtain solutions that guide engineering analysis of fluid systems. If we make certain geometric simplifications, specifically that the flow is unidirectional through a channel of infinite extent, the Navier-Stokes equations can be simplified and solved by direct integration. The key simplification enabled by this assumption is that the convective term of the Navier-Stokes equations can be neglected, because the fluid velocity and the velocity gradients are orthogonal. The solutions in this limit include laminar flow between two flat plates (Couette flow) and laminar flow in a pipe (Poiseuille flow). These flows are simultaneously the simplest solutions of the Navier-Stokes equations and the most common types of flows observed in long, narrow channels. Many microchannel flows are described by these solutions, their superposition, or a small perturbation of these flows. This chapter presents these solutions and interprets these solutions in terms of flow kinematics, viscous stresses, and Reynolds number.

[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.