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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. 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] [Induced-Charge 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 boundary-driven 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 low-Re, high-Pe limit
 4.5 Laminar flow patterning in microdevices
 4.6 Taylor-Aris 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 electrolyte-filled 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 Navier-Stokes 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 Navier-Stokes 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 Micro-PIV
 8.5 Summary
 8.6 Supplementary reading
 8.7 Exercises
9 The diffuse structure of the electrical double layer
 9.1 The Gouy-Chapman electrical double layer
 9.2 Fluid flow in the Gouy-Chapman electrical double layer
 9.3 Convective surface conductivity
 9.4 Accuracy of the Boltzmann and Debye-Hückel approximations
 9.5 Modified Poisson-Boltzmann 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′′, φ0, and ζ
 10.4 Observed electrokinetic potentials on microfluidic substrates
 10.5 Modifying the zeta potential
 10.6 Chemical and fluid-mechanical 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: Nernst-Planck equations
 11.3 Conservation of charge
 11.4 Logarithmic transform of the Nernst-Planck equations
 11.5 Microfluidic application: scalar-imagevelocimetry
 11.6 Summary
 11.7 Supplementary reading
 11.8 Exercises
12 Microchip chemical separations
 12.1 Microchip separations: experimental realization
 12.2 1-DBand 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 molecular-scale and thick-double-layer systems
 15.1 Unidirectional transport in infinitely long nanochannels
 15.2 Transport through nanostructures with interfaces or cross-sectional area changes
 15.3 Supplementary reading
 15.4 Exercises
16 AC electrokinetics and the dynamics of diffuse charge
 16.1 Electroosmosis with temporally-varying interfacial potential
 16.2 Equivalentcircuits
 16.3 Induced-charge 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 Poisson-Boltzmann Equation
 D.3 Continuity Equation
 D.4 Navier-Stokes Equations
 D.5 Supplementary Reading
E Nondimensionalization and characteristic parameters
 E.1 Buckingham Π-theorem
 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 Kramers-Krönig 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] [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.