


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. For the errata for the Cambridge publication, click
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]
Micro and Nanoscale Fluid Mechanics: Transport in
Microfluidic Devices
Brian J. Kirby
September 11, 2009
Contents  Print Version Errata
1 Kinematics, Conservation Equations, and Boundary Conditions for
Incompressible Flow
2 Unidirectional flow
2.1 Steady pressure and boundarydriven flow through long channels
2.2 Startup and development of unidirectional flows
2.3 Summary
2.4 Supplementary reading
2.5 Exercises
3 Hydraulic circuit analysis
3.1 Hydraulic circuit analysis
3.2 Hydraulic circuit equivalents for fluid flow in microchannels
3.3 Solution techniques
3.4 Summary
3.5 Supplementary reading
3.6 Exercises
4 Passive scalar transport: dispersion, patterning, and mixing
4.1 Passive scalar transport equation
4.2 Physics of mixing
4.3 Measuring and quantifying mixing and related parameters
4.4 The lowRe, highPe limit
4.5 Laminar flow patterning in microdevices
4.6 TaylorAris dispersion
4.7 Summary
4.8 Supplementary reading
4.9 Exercises
5 Electrostatics and electrodynamics
5.1 Electrostatics in matter
5.2 Electrodynamics
5.3 Analytic representations of electrodynamic quantities: complex permittivity
and conductivity
5.4 Electrical circuits
5.5 Equivalent circuits for flow and current in electrolytefilled microchannels
5.6 Summary
5.7 Supplementary reading
5.8 Exercises
6 Electroosmosis
6.1 Matched asymptotics in electroosmotic flow
6.2 Integral analysis of Coulomb forces on the electrical double layer
6.3 Solving the NavierStokes equations for electroosmotic flow in the
thin double layer limit
6.4 Electroosmotic mobility and the electrokinetic potential
6.5 Electrokinetic pumps
6.6 Summary
6.7 Supplementary reading
6.8 Exercises
7 Potential fluid flow
7.1 Approach for finding potential flow solutions to the NavierStokes equations
7.2 Laplace equation for velocity potential and stream function
7.3 Potential flows with plane symmetry
7.4 Potential flow in axisymmetric systems in spherical coordinates
7.5 Summary
7.6 Supplementary reading
7.7 Exercises
8 Stokes flow
8.1 Stokes flow equation
8.2 Bounded Stokes flows
8.3 Unbounded Stokes flows
8.4 MicroPIV
8.5 Summary
8.6 Supplementary reading
8.7 Exercises
9 The diffuse structure of the electrical double layer
9.1 The GouyChapman electrical double layer
9.2 Fluid flow in the GouyChapman electrical double layer
9.3 Convective surface conductivity
9.4 Accuracy of the Boltzmann and DebyeHückel approximations
9.5 Modified PoissonBoltzmann equations
9.6 Stern Layer
9.7 Summary
9.8 Supplementary reading
9.9 Exercises
10 Zeta potential in microchannels
10.1 Definitions and notation
10.2 Chemical and physical origins of interfacial charge
10.3 Relations between q′′, φ_{0}, and ζ
10.4 Observed electrokinetic potentials on microfluidic substrates
10.5 Modifying the zeta potential
10.6 Chemical and fluidmechanical techniques for measuring interfacial properties
10.7 Summary
10.8 Supplementary reading
10.9 Exercises
11 Species and charge transport
11.1 Modes of species transport
11.2 Conservation of species: NernstPlanck equations
11.3 Conservation of charge
11.4 Logarithmic transform of the NernstPlanck equations
11.5 Microfluidic application: scalarimagevelocimetry
11.6 Summary
11.7 Supplementary reading
11.8 Exercises
12 Microchip chemical separations
12.1 Microchip separations: experimental realization
12.2 1DBand broadening
12.3 Microchip electrophoresis: motivation and experimental issues
12.4 Experimental challenges
12.5 Protein and peptide separation
12.6 Multidimensionalseparations
12.7 Summary
12.8 Supplementary reading
12.9 Exercises
13 Particle electrophoresis
13.1 Electrophoresis for simple geometries
13.2 Electrophoretic velocity dependence on particle size
13.3 Summary
13.4 Supplementary reading
13.5 Exercises
14 DNA transport and analysis
14.1 Physicochemical structure of DNA
14.2 DNA transport
14.3 Ideal chain models for bulk DNA physical properties
14.4 Real polymer models
14.5 dsDNA in confining geometries
14.6 DNA analysis techniques
14.7 Summary
14.8 Supplementary reading
14.9 Exercises
15 Nanofluidics: fluid and current flow in molecularscale and thickdoublelayer
systems
15.1 Unidirectional transport in infinitely long nanochannels
15.2 Transport through nanostructures with interfaces or crosssectional area changes
15.3 Supplementary reading
15.4 Exercises
16 AC electrokinetics and the dynamics of diffuse charge
16.1 Electroosmosis with temporallyvarying interfacial potential
16.2 Equivalentcircuits
16.3 Inducedcharge flow phenomena
16.4 Electrothermal fluid flow
16.5 Summary
16.6 Supplementary reading
16.7 Exercises
17 Particle and droplet actuation: dielectrophoresis, magnetophoresis, and
digital microfluidics
17.1 Dielectrophoresis
17.2 Particle magnetophoresis
17.3 Digital microfluidics
17.4 Summary
17.5 Supplementary reading
17.6 Exercises
Bibliography
A Units and fundamental constants
A.1 Units
A.2 Fundamental physical constants
B Properties of electrolyte solutions
B.1 Fundamental properties of water
B.2 Aqueous solutions and key parameters
B.3 Chemical reactions, rate constants, and equilibrium
B.4 Effects of solutes
B.5 Summary
B.6 Supplementary reading
B.7 Exercises
C Coordinate systems and vector calculus
C.1 Coordinate systems
C.2 Vector calculus
C.3 Summary
C.4 Supplementary reading
C.5 Exercises
D Governing Equation Reference
D.1 Scalar Laplace Equation
D.2 PoissonBoltzmann Equation
D.3 Continuity Equation
D.4 NavierStokes Equations
D.5 Supplementary Reading
E Nondimensionalization and characteristic parameters
E.1 Buckingham Πtheorem
E.2 Nondimensionalization of governing equations
E.3 Summary
E.4 Supplementary reading
E.5 Exercises
F Multipolar solutions to the Laplace and Stokes equations
F.1 Laplace equation
F.2 Stokes equations
F.3 Stokes multipoles: stresslet and rotlet
F.4 Summary
F.5 Supplementary reading
F.6 Exercises
G Complex Functions
G.1 Complex numbers and basic operations
G.2 Using complex variables to combine orthogonal parameters
G.3 Analytic representation of harmonic parameters
G.4 KramersKrönig relations
G.5 Conformal mapping
G.6 Summary
G.7 Supplementary Reading
G.8 Exercises
H Interaction potentials: atomistic modeling of solvents and solutes
H.1 Thermodynamics of intermolecular potentials
H.2 Liquid state theories
H.3 Excluded volume calculations
H.4 Atomistic simulations
H.5 Summary
H.6 Supplementary reading
H.7 Exercises
[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.


