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 8 Stokes flow
The NavierStokes 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 NavierStokes 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 (HeleShaw 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]
[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.
