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.
[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]
In this chapter, we present relations for flow through hydraulic circuits. Hydraulic circuit analysis uses the
infinite-tube Poiseuille flow solution to approximate the pressure-flow relations in long channels, using the
Hagen-Poiseuille relation:
as well as the definition of hydraulic resistance:
The mechanical compliance of a channel is described using a hydraulic capacitance, and the net response of a
channel to sinusoidal forcing is given by its hydraulic impedance:
To consider time-varying pressures and flowrates, we adopt analytic representations of these properties and use
the complex hydraulic impedance of the circuit elements in the equations. The resulting equations
are analogous to electrical circuit relations, where the Hagen-Poiseuille law and continuity replace
Ohm’s law and Kirchoff’s law. Physically, the hydraulic system has pumps, channels, and microchannel
compliance in the same role that voltage sources, resistors, and capacitors play in electrical circuits.
Mathematically, pressure, volumetric flowrate, and hydraulic resistance replace voltage, current, and electrical
resistance from electrical circuit modeling. These hydraulic circuit analysis techniques provide useful
engineering approximations to flow rates in channel networks, which are common in microfluidic
systems.
[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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