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.
[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]
[InducedCharge Effects]
[DEP]
[Solution Chemistry]
Chapter 7 Potential fluid flow
This chapter discusses the physical relevance of potential fluid flowto flows in microfluidic devices and describes
analytical tools for creating potential flow solutions. While Appendix F focuses on a mathematical
approach—solving theLaplace Equation, this chapter focuses more on the physics of the potential flow
problem and the solution approach of the potential flow technique. This chapter also focuses on the
use of complex mathematics for twodimensional potential problems with plane symmetry. These
planesymmetric flows are relevant for microsystems, since microchannels are often shallower than
they are wide and thus depthaveraged properties are often wellapproximated by twodimensional
analysis.
In particular, we want to retain perspective on the engineering importance of these flows as well as the relative
importance of analysis versus numerics. The Laplace equation is rather straightforward to solve numerically, and
therefore numerical simulation is a suitable approach for most Laplace equation systems. For example, simulation of
the electroosmotic flow within a microdevice with a complicated geometry would be simulated, since analytical
solution would be impossible. Despite the importance of numerics, the analytical solutions are important because
they lend physical insight, and because simple analytical solutions for important cases (for example, the potential
flow around a sphere) facilitate expedient solution to more complicated problems. For example, study of
electrophoresis of a suspension of charged spheres is typically analyzed with techniques informed by the analytical
solution for potential flow around a sphere and not with detailed and extensive numerical solutions of the Laplace
equation.
[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]
[InducedCharge 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.
