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[资源] Theoretical Microfluidics

Contents
List of symbols xiii
1 Basic concepts in microfluidics 1
1.1 Lab-on-a-chip technology 1
1.2 Scaling laws in microfluidics 2
1.3 Fluids and fields 3
1.4 SI units and mathematical notation 7
1.5 Perturbation theory 11
1.6 Eigenfunction expansion 13
1.7 Further reading 15
1.8 Exercises 15
1.9 Solutions 17
2 Governing equations 19
2.1 Mass flux, conservation of mass, and the continuity equation 19
2.2 Momentum flux, force densities, and the equation of motion 21
2.3 Energy flux and the heat-transfer equation 28
2.4 Further reading 31
2.5 Exercises 32
2.6 Solutions 33
3 Basic flow solutions 37
3.1 Fluids in mechanical equilibrium 37
3.2 Liquid film flow on an inclined plane 39
3.3 Couette flow 40
3.4 Poiseuille flow 41
3.5 Poiseuille flow in shape-perturbed channels 51
3.6 Poiseuille flow for weakly compressible fluids 55
3.7 Stokes drag on a sphere moving in steady state 60
3.8 Exercises 63
3.9 Solutions 65
vii
viii Contents
4 Hydraulic resistance and compliance 71
4.1 Viscous dissipation of energy for incompressible fluids 71
4.2 Hydraulic resistance of some straight channels 74
4.3 Shape dependence of hydraulic resistance 75
4.4 Reynolds number for systems with two length scales 79
4.5 Hydraulic resistance, two connected straight channels 81
4.6 Compliance 83
4.7 Equivalent circuit theory and Kirchhoff’s laws 84
4.8 Exercises 86
4.9 Solutions 88
5 Diffusion 91
5.1 A random-walk model of diffusion 91
5.2 The convection-diffusion equation for solutions 93
5.3 The diffusion equation 95
5.4 The H-filter: separating solutes by diffusion 98
5.5 Taylor dispersion; a convection-diffusion example 100
5.6 Exercises 105
5.7 Solutions 106
6 Time-dependent flow 109
6.1 Starting a Couette flow 109
6.2 Stopping a Poiseuille flow by viscous forces 111
6.3 Flow induced by slowly oscillating boundaries 113
6.4 Accelerated motion of a spherical body in a liquid 116
6.5 Other time-dependent flows 117
6.6 Exercises 118
6.7 Solutions 118
7 Capillary effects 123
7.1 Surface tension 123
7.2 Contact angle 127
7.3 Capillary length and capillary rise 128
7.4 Capillary pumps 131
7.5 Marangoni effect; surface-tension gradients 134
7.6 Exercises 134
7.7 Solutions 136
8 Electrohydrodynamics 141
8.1 Polarization and dipole moments 141
8.2 Electrokinetic effects 143
8.3 The Debye layer near charged surfaces 145
8.4 Further reading 152
8.5 Exercises 152
8.6 Solutions 154
Contents ix
9 Electroosmosis 157
9.1 Electrohydrodynamic transport theory 157
9.2 Ideal electro-osmotic flow 157
9.3 Debye-layer overlap 161
9.4 Ideal EO flow with backpressure 162
9.5 The many-channel EO pump 165
9.6 The cascade EO pump 166
9.7 Further reading 169
9.8 Exercises 169
9.9 Solutions 170
10 Dielectrophoresis 173
10.1 Induced polarization and dielectric forces; heuristically 173
10.2 A point dipole in a dielectric fluid 174
10.3 A dielectric sphere in a dielectric fluid; induced dipole 175
10.4 The dielectrophoretic force on a dielectric sphere 177
10.5 Dielectrophoretic particle trapping in microfluidics 178
10.6 The AC dielectrophoretic force on a dielectric sphere 180
10.7 Exercises 182
10.8 Solutions 184
11 Magnetophoresis 187
11.1 Magnetophoresis and bioanalysis 187
11.2 Magnetostatics 188
11.3 Basic equations for magnetophoresis 190
11.4 Calculation of magnetic-bead motion 191
11.5 Magnetophoretic lab-on-a-chip systems 193
11.6 Further reading 194
11.7 Exercises 194
11.8 Solutions 195
12 Thermal transfer 197
12.1 Thermal effects in hydrostatics 198
12.2 Poiseuille flow in a transverse temperature gradient 201
12.3 Equivalent circuit model for heat transfer 205
12.4 The PCR biochip 208
12.5 Exercises 210
12.6 Solutions 211
13 Two-phase flow 213
13.1 Two-phase Poiseuille flow 213
13.2 Capillary and gravity waves 215
13.3 Gas bubbles in microfluidic channels 220
13.4 Droplets in microfluidic junctions and digital fluidics 224
13.5 Further reading 226
13.6 Exercises 226
13.7 Solutions 228
x Contents
14 Complex flow patterns 231
14.1 Pressure-driven flow in shape-perturbed microchannels 231
14.2 Streamlines in a shape-perturbed channel 235
14.3 Lubrication theory 237
14.4 The staggered herring-bone mixer 238
14.5 Induced-charge electrolytic flow 240
14.6 Exercises 248
14.7 Solutions 249
15 Acoustofluidics 255
15.1 The acoustic-wave equation for zero viscosity 256
15.2 Acoustic waves in first-order perturbation theory 258
15.3 Viscous damping of first-order acoustic waves 260
15.4 Acoustic resonances 262
15.5 Acoustic waves in multilayer systems 264
15.6 Second-order acoustic fields 267
15.7 Further reading 270
15.8 Exercises 271
15.9 Solutions 272
16 Optofluidics 275
16.1 The optical wave equation in electrolytes 276
16.2 Molecular absorption and Beer–Lambert’s law 278
16.3 Molecular fluorescence and phosphorescence 281
16.4 Onchip waveguides 282
16.5 Onchip laser sources 283
16.6 Photonic bandgap structures in optofluidics 286
16.7 Further reading 288
16.8 Exercises 288
16.9 Solutions 289
17 Nanofluidics 291
17.1 Investigation of the no-slip boundary condition 291
17.2 Capillary filling of nanochannels 294
17.3 Squeeze flow in nanoimprint lithography 298
17.4 Nanofluidics and molecular dynamics 302
17.5 Exercises 304
17.6 Solutions 305
Appendix A Physical constants 309
A.1 Water 309
A.2 Viscosity 309
A.3 Diffusivity 310
A.4 Surface tension and contact angle 310
Contents xi
Appendix B Dimensionless numbers 311
Appendix C Curvilinear co-ordinates 313
C.1 Cartesian co-ordinates 313
C.2 Cylindrical polar co-ordinates 314
C.3 Spherical polar co-ordinates 316
Appendix D The chemical potential 319
D.1 The partition function and the free energy 319
D.2 The chemical potential of a solution 320
Appendix E The wave equation 321
Appendix F Numerical simulations 325
F.1 The finite-element method (FEM) 325
F.2 The level set method and motion of interfaces 329
Bibliography 333
Index 33

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附件 1 : Theoretical_Microfluidics_-_Henrik_Bruus_(Oxford_Master_Series_In_Physics,_Oxford_University_Press,_Usa,_2007)(Isbn0199235090).pdf

2016-09-16 00:09:56, 9.66 M