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  Место хранения:   014 | Институт теоретической и прикладной механики СО РАН | Новосибирск | Библиотека

Оглавление / Contents

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