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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.

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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]

Contents

1 Kinematics, Conservation Equations, and Boundary Conditions for Incompressible Flow
2 Unidirectional flow
 2.1 Steady pressure- and boundary-driven flow through long channels
  2.1.1 Couette flow
  2.1.2 Poiseuille flow
 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
  3.2.1 Analytic representation of sinusoidal pressures and flowrates
  3.2.2 Hydraulic impedance
  3.2.3 Hydraulic circuit relations
  3.2.4 Series and parallel component rules
 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
  4.1.1 Scalar fluxes and constitutive properties
  4.1.2 Scalar conservation equation
 4.2 Physics of mixing
 4.3 Measuring and quantifying mixing and related parameters
 4.4 The low-Re, high-Pe limit
  4.4.1 The high-Pe limit
  4.4.2 The low-Re 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
  5.1.1 Electrical potential and electric field
  5.1.2 Coulomb’s Law, Gauss’s Law for electricity in a material, curl of electric field
  5.1.3 Polarization of matter and electric permittivity
  5.1.4 Material, frequency, and electric field dependence of electrical permittivity
  5.1.5 Poisson and Laplace equations
  5.1.6 Classification of material types
  5.1.7 Electrostatic boundary conditions
  5.1.8 Solution of electrostatic equations
  5.1.9 Maxwell stress tensor
  5.1.10 Effects of electrostatic fields on multipoles
 5.2 Electrodynamics
  5.2.1 Charge conservation equation
  5.2.2 Electrodynamic boundary conditions
  5.2.3 Field lines at substrate walls
 5.3 Analytic representations of electrodynamic quantities: complex permittivity and conductivity
  5.3.1 Complex description of dielectric loss
 5.4 Electrical circuits
  5.4.1 Components and properties
  5.4.2 Electrical impedance
  5.4.3 Circuit relations
  5.4.4 Series and parallel component rules
 5.5 Equivalent circuits for flow and current in electrolyte-filled microchannels
  5.5.1 Electrical circuit equivalents of hydraulic components
 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
  6.3.1 Outer solution
  6.3.2 Replacing the electrical double layer with an effective slip boundary condition
  6.3.3 Replacing the Navier-Stokes equations with the Laplace equation: flow-current similitude
  6.3.4 Reconciling the no-slip condition with irrotational flow
 6.4 Electroosmotic mobility and the electrokinetic potential
  6.4.1 Electrokinetic coupling matrix representation of electroosmosis
 6.5 Electrokinetic pumps
  6.5.1 A planar electrokinetic pump
  6.5.2 Types of 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
  7.2.1 Laplace equation for the velocity potential
  7.2.2 No-slip condition
 7.3 Potential flows with plane symmetry
  7.3.1 Complex algebra and its use in plane-symmetric potential flow
  7.3.2 Monopolar flow: plane-symmetric (line) source with volume outflow per unit depth Λ
  7.3.3 Plane-symmetric vortex with counterclockwise circulation per unit depth Γ
  7.3.4 Dipolar flow: plane-symmetric doublet with dipole moment κ
  7.3.5 Uniform flow with speed U
  7.3.6 Flow around a corner
  7.3.7 Flow over a circular cylinder
  7.3.8 Conformal mapping
 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
  8.1.1 Different forms of the Stokes flow equations
  8.1.2 Analytical vs. numerical solutions of the Stokes flow equations
 8.2 Bounded Stokes flows
  8.2.1 Hele-Shaw flows
  8.2.2 Numerical solution of general bounded Stokes flow problems
 8.3 Unbounded Stokes flows
  8.3.1 Stokes flow over a sphere in an infinite domain
  8.3.2 General solution for Stokes flow over a sphere in an infinite domain
  8.3.3 Flow over prolate ellipsoids
  8.3.4 Stokes flow over particles in finite domains
  8.3.5 Stokes flow over multiple particles
 8.4 Micro-PIV
  8.4.1 Deterministicparticle lag
  8.4.2 Brownianmotion
 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
  9.1.1 Boltzmann statistics for ideal solutions of ions
  9.1.2 Ion distributions and potential: Boltzmann relation
  9.1.3 Ion distributions and potential: Poisson-Boltzmann equation
  9.1.4 Simplified forms of the nonlinear Poisson-Boltzmann equation
  9.1.5 Solutions of the Poisson-Boltzmann equation
 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
  9.4.1 Debye-Hückel approximation
  9.4.2 Limitations of the ideal solution approximation
 9.5 Modified Poisson-Boltzmann equations
  9.5.1 Steric correction to ideal solution statistics
  9.5.2 Modified Poisson-Boltzmann equation
  9.5.3 Importance and limitations of Poisson-Boltzmann modifications
 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
  10.2.1 Electrochemical potentials
  10.2.2 Potential-determining ions
  10.2.3 Nernstian and non-Nernstian surfaces
 10.3 Relations between q′′, φ0, and ζ
  10.3.1 Extended interface models: modifications to φ0
  10.3.2 Fluid inhomogeneity models: relation between φ0 and ζ
  10.3.3 Slip and multiphase interface models: hydrophobic surfaces
 10.4 Observed electrokinetic potentials on microfluidic substrates
  10.4.1 Electrolyte concentration
  10.4.2 pH dependence
 10.5 Modifying the zeta potential
  10.5.1 Indifferent electrolyte concentrations
  10.5.2 Surface-active agents
  10.5.3 Chemical functionalizations
 10.6 Chemical and fluid-mechanical techniques for measuring interfacial properties
  10.6.1 Charge titration
  10.6.2 Electroosmotic flow
  10.6.3 Streaming current and potential
 10.7 Summary
 10.8 Supplementary reading
 10.9 Exercises
11 Species and charge transport
 11.1 Modes of species transport
  11.1.1 Species diffusion
  11.1.2 Convection
  11.1.3 Relating diffusivity and electrophoretic mobility: the viscous mobility
 11.2 Conservation of species: Nernst-Planck equations
  11.2.1 Species fluxes and constitutive properties
  11.2.2 Nernst-Planck equations
 11.3 Conservation of charge
  11.3.1 Charge conservation equation
  11.3.2 Diffusivity, electrophoretic mobility, and molar conductivity
 11.4 Logarithmic transform of the Nernst-Planck equations
 11.5 Microfluidic application: scalar-imagevelocimetry
  11.5.1 SIV using caged-dyeimaging
  11.5.2 SIV using photobleaching
 11.6 Summary
 11.7 Supplementary reading
 11.8 Exercises
12 Microchip chemical separations
 12.1 Microchip separations: experimental realization
  12.1.1 Sample injection
  12.1.2 Resolution
 12.2 1-DBand broadening
  12.2.1 Analyte transport: quiescent flow, no electric field
  12.2.2 Transport of analytes: electroosmoticflow andelectrophoresis
 12.3 Microchip electrophoresis: motivation and experimental issues
  12.3.1 Thermal dissipation
  12.3.2 Compact, folded, long-pathlength channels
 12.4 Experimental challenges
  12.4.1 Pressure-driven flow
  12.4.2 Analyteband dispersion in turns and expansions
 12.5 Protein and peptide separation
  12.5.1 Protein properties
  12.5.2 Protein separationtechniques
  12.5.3 Isotachophoresisandfield-amplified sample stacking
  12.5.4 Capillaryelectrochromatography
 12.6 Multidimensionalseparations
  12.6.1 2-D slab gels
 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
  13.2.1 Smoluchowski velocity:large particles, small zeta
  13.2.2 Henry’s function: effect of finite double layers for small φ0
  13.2.3 Large surface potential—effect of counterion distribution
 13.3 Summary
 13.4 Supplementary reading
 13.5 Exercises
14 DNA transport and analysis
 14.1 Physicochemical structure of DNA
  14.1.1 Chemical structure of DNA
  14.1.2 Physical properties of dsDNA
 14.2 DNA transport
  14.2.1 DNA transport in bulk aqueous solution
 14.3 Ideal chain models for bulk DNA physical properties
  14.3.1 Idealized models for bulk DNA properties
  14.3.2 Dependence of transport properties on contour length
 14.4 Real polymer models
 14.5 dsDNA in confining geometries
  14.5.1 Energy and entropy of controlled polymer extension
  14.5.2 Energy and entropy of confinement for ideal polymers
  14.5.3 DNA diffusion in confined geometries
  14.5.4 DNA electrophoretic mobility in confined geometries
 14.6 DNA analysis techniques
  14.6.1 DNA amplification
  14.6.2 DNA separation
  14.6.3 DNA microarrays
 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
  15.1.1 Fluid transport
  15.1.2 Electrokinetic coupling matrix for thick double layer transport
  15.1.3 Circuit models for nanoscale channels
 15.2 Transport through nanostructures with interfaces or cross-sectional area changes
  15.2.1 Quasielectroneutral model
  15.2.2 Large molecule and particle transport
 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
  16.2.1 The double layer as a capacitor
 16.3 Induced-charge flow phenomena
  16.3.1 Induced-charge double layers
  16.3.2 Flow due to induced-charge double layers—induced-charge electroosmosis
  16.3.3 Flow due to induced-charge double layers—AC electroosmosis
 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
  17.1.1 Inferring the Coulomb force on an enclosed volume from the electric field outside the volume
  17.1.2 The force on an uncharged, uniform, isotropic sphere in a linearly varying electric field with uniform, isotropic phase
  17.1.3 Maxwellian equivalent body for inhomogeneous, spherically symmetric particles
  17.1.4 Dielectrophoresis of charged spheres
  17.1.5 Dielectrophoresis of non-spherical objects
  17.1.6 Nonuniform and anisotropic phase effects
 17.2 Particle magnetophoresis
  17.2.1 Origin of magnetic fields in materials
  17.2.2 Attributes of magnetism
  17.2.3 Magnetic properties of superparamagnetic beads
  17.2.4 Magnetophoretic forces
  17.2.5 DC magnetophoresis of spheres—linear limit
 17.3 Digital microfluidics
  17.3.1 Electrowetting-on-dielectric
 17.4 Summary
 17.5 Supplementary reading
 17.6 Exercises
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.3.1 pH, pKa, and the Henderson-Hasselbach equation
  B.3.2 Conjugate acids and bases; buffers
  B.3.3 Ionization of water
  B.3.4 Solubility product of weakly-soluble salts
  B.3.5 Ideal solution limit and activity
  B.3.6 Electrochemical potentials
 B.4 Effects of solutes
  B.4.1 Dielectric increments
 B.5 Summary
 B.6 Supplementary reading
 B.7 Exercises
C Coordinate systems and vector calculus
 C.1 Coordinate systems
  C.1.1 3D coordinate systems
  C.1.2 2D coordinate systems
 C.2 Vector calculus
  C.2.1 Scalars, vectors, and tensors
  C.2.2 Vector operations
  C.2.3 Del or nabla operations
  C.2.4 Vector identities
  C.2.5 Dyadic operations
 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.2.1 Nondimensionalization of Navier-Stokes: Reynolds number
  E.2.2 Nondimensionalization of the passive scalar transfer equation: Peclet number
  E.2.3 Nondimensionalization of the Poisson-Boltzmann equation: Debye length and thermal voltage
 E.3 Summary
 E.4 Supplementary reading
 E.5 Exercises
F Multipolar solutions to the Laplace and Stokes equations
 F.1 Laplace equation
  F.1.1 Laplace equation solutions for axisymmetric spherical coordinates: separation of variables and multipolar expansions
  F.1.2 Systems with plane symmetry: 2D cylindrical coordinates
 F.2 Stokes equations
  F.2.1 Green’s function for Stokes flow with a point source
 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.1.1 Arithmetic operations
  G.1.2 Calculus operations
 G.2 Using complex variables to combine orthogonal parameters
 G.3 Analytic representation of harmonic parameters
  G.3.1 Mathematical rules for using the analytic representation of harmonic parameters
 G.4 Kramers-Krönig relations
 G.5 Conformal mapping
  G.5.1 Joukowski transform
  G.5.2 Schwarz-Christoffel transform
 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.1.1 Monopole pair potentials
  H.1.2 Spherically-symmetric multipole pair potentials
 H.2 Liquid state theories
  H.2.1 Integral techniques for concentration profiles
  H.2.2 Why the direct correlation function does not describe concentration profiles
  H.2.3 Total correlation functions and the Ornstein-Zernike equation
 H.3 Excluded volume calculations
 H.4 Atomistic simulations
  H.4.1 Defining atomic forces and accelerations
  H.4.2 Water models
  H.4.3 Nondimensionalization in MD 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.