 | Karniadakis G. Microflows and nanoflows: fundamentals and simulation / G.Karniadakis, A.Beskok, N.Aluru; foreword by Chih-Ming Ho. - New York: Springer, 2005. - xxi, 817 p.: ill. - (Interdisciplinary applied mathematics; Vol.29). - Bibliogr.: p.757-807. - Ind.: p.808-817. - ISBN-10 0387286764; ISBN-13 9780387286761
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Foreword by Chih-Ming Ho ........................................ v
Preface ....................................................... vii
1 Basic Concepts and Technologies .............................. 1
1.1 New Flow Regimes in Microsystems ........................ 1
1.2 The Continuum Hypothesis ................................ 8
1.2.1 Molecular Magnitudes ............................ 13
1.2.2 Mixed Flow Regimes .............................. 18
1.2.3 Experimental Evidence ........................... 19
1.3 The Pioneers ........................................... 24
1.4 Modeling of Microflows ................................. 30
1.5 Modeling of Nanoflows .................................. 34
1.6 Numerical Simulation at All Scales ..................... 37
1.7 Full-System Simulation of Microsystems ................. 38
1.7.1 Reduced-Order Modeling .......................... 40
1.7.2 Coupled Circuit/Device Modeling ................. 41
2 Governing Equations and Slip Models ......................... 51
2.1 The Basic Equations of Fluid Dynamics .................. 51
2.1.1 Incompressible Flow ............................. 54
2.1.2 Reduced Models .................................. 56
2.2 Compressible Flow ...................................... 57
2.2.1 First-Order Models .............................. 59
2.2.2 The Role of the Accommodation Coefficients ...... 61
2.3 High-Order Models ...................................... 66
2.3.1 Derivation of High-Order Slip Models ............ 67
2.3.2 General Slip Condition .......................... 70
2.3.3 Comparison of Slip Models ....................... 74
3 Shear-Driven Flows .......................................... 79
3.1 Couette Flow: Slip Flow Regime ......................... 79
3.2 Couette Flow: Transition and Free-Molecular Flow
Regimes ................................................ 83
3.2.1 Velocity Model .................................. 83
3.2.2 Shear Stress Model .............................. 86
3.3 Oscillatory Couette Flow ............................... 90
3.3.1 Quasi-Steady Flows .............................. 91
3.3.2 Unsteady Flows .................................. 96
3.3.3 Summary ........................................ 109
3.4 Cavity Flow ........................................... 110
3.5 Grooved Channel Flow .................................. 112
4 Pressure-Driven Flows ...................................... 117
4.1 Slip Flow Regime ...................................... 117
4.1.1 Isothermal Compressible Flows .................. 118
4.1.2 Adiabatic Compressible Flows - Fanno Theory .... 126
4.1.3 Validation of Slip Models with DSMC ............ 131
4.1.4 Effects of Roughness ........................... 136
4.1.5 Inlet Flows .................................... 137
4.2 Transition and Free-Molecular Regimes ................. 140
4.2.1 Burnett Equations .............................. 144
4.2.2 A Unified Flow Model ........................... 146
4.2.3 Summary ........................................ 166
5 Thermal Effects in Microscales ............................. 167
5.1 Thermal Creep (Transpiration) ......................... 167
5.1.1 Simulation Results ............................. 169
5.1.2 A Thermal Creep Experiment ..................... 173
5.1.3 Knudsen Compressors ............................ 174
5.2 Other Temperature-Induced Flows ....................... 175
5.3 Heat Conduction and the Ghost Effect .................. 177
5.4 Heat Transfer in Poiseuille Microflows ................ 179
5.4.1 Pressure-Driven Flows .......................... 179
5.4.2 Force-Driven Flows ............................. 186
5.5 Heat Transfer in Couette Microflows ................... 188
6 Prototype Applications of Gas Flows ........................ 195
6.1 Gas Damping and Dynamic Response of Microsystems ...... 196
6.1.1 Reynolds Equation .............................. 199
6.1.2 Squeezed Film Effects in Accelerometers ........ 210
6.2 Separated Internal Flows .............................. 214
6.3 Separated External Flows .............................. 221
6.4 Flow Past a Sphere: Stokes Flow Regime ................ 224
6.4.1 External Flow .................................. 224
6.4.2 Sphere-in-a-Pipe ............................... 225
6.5 Microfilters .......................................... 227
6.5.1 Drag Force Characteristics ..................... 232
6.5.2 Viscous Heating Characteristics ................ 234
6.5.3 Short Channels and Filters ..................... 234
6.5.4 Summary ........................................ 239
6.6 Micropropulsion and Micronozzle Flows ................. 239
6.6.1 Micropropulsion Analysis ....................... 240
6.6.2 Rarefaction and Other Effects .................. 245
7 Electrokinetic Flows ....................................... 255
7.1 Electrokinetic Effects ................................ 256
7.2 The Electric Double Layer (EDL) ....................... 258
7.2.1 Near-Wall Potential Distribution ............... 261
7.3 Governing Equations ................................... 263
7.4 Electroosmotic Flows .................................. 266
7.4.1 Channel Flows .................................. 266
7.4.2 Time-Periodic and AC Flows ..................... 272
7.4.3 EDL/Bulk Flow Interface Velocity Matching
Condition ...................................... 279
7.4.4 Slip Condition ................................. 280
7.4.5 A Model for Wall Drag Force .................... 281
7.4.6 Joule Heating .................................. 282
7.4.7 Applications ................................... 283
7.5 Electrophoresis ....................................... 292
7.5.1 Governing Equations ............................ 294
7.5.2 Classification ................................. 295
7.5.3 Taylor Dispersion .............................. 297
7.5.4 Charged Particle in a Pipe ..................... 302
7.6 Dielectrophoresis ..................................... 302
7.6.1 Applications ................................... 304
8 Surface Tension-Driven Flows ............................... 311
8.1 Basic Concepts ........................................ 312
8.2 General Form of Young's Equation ...................... 317
8.3 Governing Equations for Thin Films .................... 319
8.4 Dynamics of Capillary Spreading ....................... 321
8.5 Thermocapillary Pumping ............................... 324
8.6 Electrocapillary ...................................... 328
8.6.1 Generalized Young-Lippmann Equation ............ 333
8.6.2 Optoelectrowetting ............................. 335
8.7 Bubble Transport in Capillaries ....................... 337
9 Mixers and Chaotic Advection ............................... 343
9.1 The Need for Mixing at Microscales .................... 344
9.2 Chaotic Advection ..................................... 346
9.3 Micromixers ........................................... 349
9.4 Quantitative Characterization of Mixing ............... 357
10 Simple Fluids in Nanochannels .............................. 365
10.1 Atomistic Simulation of Simple Fluids ................. 366
10.2 Density Distribution .................................. 368
10.3 Diffusion Transport.................................... 375
10.4 Validity of the Navier-Stokes Equations ............... 381
10.5 Boundary Conditions at Solid-Liquid Interfaces ........ 387
10.5.1 Experimental and Computational Results ......... 387
10.5.2 Conceptual Models of Slip ...................... 396
10.5.3 Reynolds-Vinogradova Theory for Hydrophobic
Surfaces ....................................... 401
11 Water in Nanochannels ...................................... 407
11.1 Definitions and Models ................................ 407
11.1.1 Atomistic Models .............................. 409
11.2 Static Behavior ....................................... 416
11.2.1 Density Distribution and Dipole Orientation .... 417
11.2.2 Hydrogen Bonding ............................... 422
11.2.3 Contact Angle .................................. 427
11.2.4 Dielectric Constant ............................ 429
11.3 Dynamic Behavior ...................................... 430
11.3.1 Basic Concepts ................................. 430
11.3.2 Diffusion Transport ............................ 435
11.3.3 Filling and Emptying Kinetics .................. 437
12 Electroosmotic Flow in Nanochannels ........................ 447
12.1 The Need for Atomistic Simulation ..................... 447
12.2 Ion Concentrations .................................... 452
12.2.1 Modified Poisson-Boltzmann Equation ................ 455
12.3 Velocity Profiles ..................................... 457
12.4 Slip Condition ........................................ 461
12.5 Charge Inversion and Flow Reversal .................... 464
13 Functional Fluids and Functionalized Nanotubes ............. 471
13.1 Colloidal Particles and Self-Assembly ................. 472
13.1.1 Magnetorheological (MR) Fluids ................ 475
13.1.2 Electrophoretic Deposition ..................... 486
13.2 Electrolyte Transport Through Carbon Nanotubes ........ 490
13.2.1 Carbon Nanotubes ............................... 491
13.2.2 Ion Channels in Biological Membranes ........... 493
13.2.3 Transport Through Unmodified Nanotubes ......... 495
13.2.4 Transport Through Nanotubes with Charges at
the Ends ....................................... 497
13.2.5 Transport Through Functionalized Nanotubes ..... 498
13.2.6 Anomalous Behavior ............................. 499
14 Numerical Methods for Continuum Simulation ................. 509
14.1 Spectral Element Method: The μFlow Program ............ 510
14.1.1 Incompressible Flows ........................... 514
14.1.2 Compressible Flows ............................. 517
14.1.3 Verification Example: Resolution of the
Electric Double Layer .......................... 524
14.1.4 Moving Domains ................................. 525
14.2 Meshless Methods ...................................... 531
14.2.1 Domain Simulation .............................. 532
14.2.2 Boundary-Only Simulation ....................... 537
14.3 Particulate Microflows ................................ 542
14.3.1 Hydrodynamic Forces on Spheres ................. 543
14.3.2 The Force Coupling Method (FCM) ................ 547
15 Multiscale Modeling of Gas Flows ........................... 559
15.1 Direct Simulation Monte Carlo (DSMC) Method ........... 560
15.1.1 Limitations and Errors in DSMC ................. 562
15.1.2 DSMC for Unsteady Flows ........................ 567
15.1.3 DSMC: Information-Preservation Method .......... 569
15.2 DSM: Continuum Coupling ............................... 572
15.2.1 The Schwarz Algorithm .......................... 575
15.2.2 Interpolation Between Domains .................. 577
15.3 Multiscale Analysis of Microfilters ................... 578
15.3.1 Stokes/DSMC Coupling ........................... 579
15.3.2 Navier-Stokes/DSMC Coupling .................... 584
15.4 The Boltzmann Equation ................................ 588
15.4.1 Classical Solutions ............................ 592
15.4.2 Sone's Asymptotic Theory ....................... 596
15.4.3 Numerical Solutions ............................ 606
15.4.4 Nonisothermal Flows ............................ 611
15.5 Lattice-Boltzmann Method (LBM) ........................ 611
15.5.1 Boundary Conditions ............................ 618
15.5.2 Comparison with Navier-Stokes Solutions ........ 618
15.5.3 LBM Simulation of Microflows ................... 620
16 Multiscale Modeling of Liquid Flows ........................ 625
16.1 Molecular Dynamics (MD) Method ........................ 626
16.1.1 Intermolecular Potentials ...................... 628
16.1.2 Calculation of the Potential Function .......... 634
16.1.3 Thermostats .................................... 638
16.1.4 Data Analysis .................................. 640
16.1.5 Practical Guidelines ........................... 646
16.1.6 MD Software .................................... 648
16.2 MD-Continuum Coupling ................................. 648
16.3 Embedding Multiscale Methods .......................... 656
16.3.1 Application to the Poisson-Boltzmann
Equation ....................................... 657
16.3.2 Application to Navier-Stokes Equations ......... 659
16.4 Dissipative Particle Dynamics (DPD) ................... 663
16.4.1 Governing Equations ............................ 665
16.4.2 Numerical Integration .......................... 668
16.4.3 Boundary Conditions ............................ 673
17 Reduced-Order Modeling ..................................... 677
17.1 Classification ........................................ 677
17.1.1 Quasi-Static Reduced-Order Modeling ............ 678
17.1.2 Dynamical Reduced-Order Modeling ............... 679
17.2 Generalized Kirchhofhan Networks ...................... 680
17.2.1 Equivalent Circuit Representation .............. 681
17.2.2 Description Languages .......................... 689
17.3 Black Box Models ...................................... 695
17.3.1 Nonlinear Static Models ........................ 695
17.3.2 Linear Dynamic Models .......................... 697
17.3.3 Nonlinear Dynamic Models ....................... 701
17.4 Galerkin Methods ...................................... 705
17.4.1 Linear Galerkin Methods ........................ 705
17.4.2 Nonlinear Galerkin Methods ..................... 717
18 Reduced-Order Simulation ................................... 721
18.1 Circuit and Device Models for Lab-on-a-Chip Systems ... 721
18.1.1 Electrical Model ............................... 723
18.1.2 Fluidic Model .................................. 725
18.1.3 Chemical Reactions: Device Models .............. 730
18.1.4 Separation: Device Model ....................... 731
18.1.5 Integration of the Models ...................... 733
18.1.6 Examples ....................................... 733
18.2 Macromodeling of Squeezed Film Damping ................ 745
18.2.1 Equivalent Circuit Models ...................... 747
18.2.2 Galerkin Methods ............................... 749
18.2.3 Mixed-Level Simulation ......................... 751
18.2.4 Black Box Models ............................... 752
18.3 Compact Model for Electrowetting ...................... 753
18.4 Software .............................................. 754
Bibliography .................................................. 757
Index ......................................................... 808
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