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ОбложкаConlisk A.T. Essentials of micro- and nanofluidics: with applications to the biological and chemical sciences. - New York: Cambridge University Press, 2013. - xix, 537 p.: ill. - Bibliogr.: p.515-532. - Ind.: p.533-537. - ISBN 978-0-521-88168-5
Шифр: (И/Е0-С74) 02
 

Место хранения: 02 | Отделение ГПНТБ СО РАН | Новосибирск

Оглавление / Contents
 
 
Preface ........................................................ xv

1  Introduction and Overview .................................... 1
   1.1  Micro- and nanofluidics ................................. 1
   1.2  Some micro- and nanofluidic devices ..................... 3
   1.3  What is it about the nanoscale? ......................... 7
   1.4  Nanotechnology ......................................... 11
   1.5  What is a fluid? ....................................... 13
   1.6  Historical perspectives ................................ 14
        1.6.1  Fluid mechanics ................................. 15
        1.6.2  Heat and mass transfer .......................... 17
        1.6.3  Electrokinetic phenomena ........................ 19
   1.7  The thermal sciences ................................... 20
   1.8  Electrostatics ......................................... 23
   1.9  Electrolyte solutions .................................. 25
   1.10 The electrical double layer ............................ 26
   1.11 Colloidal systems ...................................... 29
   1.12 Molecular biology ...................................... 32
   1.13 The convergence of molecular biology and engineering ... 34
   1.14 Design of micro- and nanofluidic devices ............... 35
   1.15 Unit systems ........................................... 37
   1.16 A word about notation .................................. 37
   1.17 Chapter summary ........................................ 38
2  Preparatory Concepts ........................................ 40
   2.1  Introduction ........................................... 40
   2.2  Important constitutive laws ............................ 41
   2.3  Determining transport properties ....................... 45
        2.3.1  Viscosity ....................................... 45
        2.3.2  Diffusion coefficient ........................... 48
        2.3.3  Thermal conductivity ............................ 52
        2.3.4  Electrical permittivity ......................... 54
        2.3.5  Surface tension and wettability ................. 55
   2.4  Classification of fluid flows .......................... 59
   2.5  Elements of thermodynamics ............................. 62
   2.6  The nature of frictional losses in channels and pipes .. 68
   2.7  Chapter summary ........................................ 70
3  The Governing Equations for an Electrically Conducting
   Fluid ....................................................... 74
   3.1  Introduction ........................................... 74
   3.2  The continuum approximation and its limitations ........ 75
   3.3  Kinematics ............................................. 77
   3.4  Surface and body forces ................................ 83
   3.5  The continuity equation ................................ 87
   3.6  The Navier-Stokes equations ............................ 88
   3.7  Mass transport ......................................... 93
        3.7.1  Definitions ..................................... 93
        3.7.2  Governing equation .............................. 97
   3.8  Electrostatics ........................................ 100
   3.9  Energy transport ...................................... 102
   3.10 Two-dimensional, steady, and incompressible flow ...... 106
   3.11 Boundary and initial conditions ....................... 106
        3.11.1  Velocity boundary conditions .................. 107
        3.11.2  Mass transfer boundary conditions ............. 113
        3.11.3  Electrostatics boundary conditions ............ 114
        3.11.4  Temperature boundary conditions ............... 116
        3.11.5  Other boundary conditions ..................... 117
   3.12 Dimensional analysis and similarity ................... 117
   3.13 Fluid, electrostatics, and heat and mass transfer
        analogies ............................................. 123
        3.13.1  Mole fraction and temperature similarity ...... 123
        3.13.2  Velocity and electrical potential similarity .. 125
   3.14 Other stress-strain relationships ..................... 126
   3.15 Mathematical character of partial differential
        equations ............................................. 128
        3.15.1 Introduction ................................... 128
        3.15.2 Mathematical classification of second-order
               partial differential equations ................. 128
        3.15.3 Characteristic curves .......................... 129
        3.15.4 Boundary and initial conditions ................ 130
        3.15.5 Classification of the governing equations of
               micro- and nanofluidics ........................ 131
   3.16 Well-posed problems ................................... 131
   3.17 The role of fabrication, experiments, and theory in
        micro- and nanofluidics ............................... 132
   3.18 Chapter summary ....................................... 134
4  The Essentials of Viscous Flow ............................. 140
   4.1  Introduction .......................................... 140
   4.2  The structure of flow in a pipe or channel ............ 141
   4.3  Poiseuille flow in a pipe or channel .................. 143
   4.4  The velocity in slip flow ............................. 146
        4.4.1  Gases .......................................... 146
        4.4.2  Liquids ........................................ 147
   4.5  Flow in a thin film under gravity ..................... 148
   4.6  The boundary layer on a flat plate .................... 150
   4.7  Fully developed suction flows ......................... 155
   4.8  Developing suction flows .............................. 158
   4.9  The lubrication approximation ......................... 162
   4.10 A surface tension-driven flow ......................... 166
   4.11 Stokes flow past a sphere ............................. 169
   4.12 Sedimentation of a solid particle ..................... 172
   4.13 A simple model for blood flow ......................... 173
   4.14 Chapter summary ....................................... 174
5  Heat and Mass Transfer Phenomena in Channels and Tubes ..... 180
   5.1  Introduction .......................................... 180
   5.2  One-dimensional temperature distributions in channel
        flow .................................................. 181
   5.3  Thermal and mass transfer entrance regions ............ 184
   5.4  The temperature distribution in fully developed tube
        flow .................................................. 189
   5.5  The Graetz problem for a channel ...................... 189
   5.6  Mass transfer in thin films ........................... 192
   5.7  Classical Taylor-Aris dispersion ...................... 194
   5.8  The stochastic nature of diffusion: Brownian motion ... 199
   5.9  Unsteady mass transport in uncharged membranes ........ 201
   5.10 Temperature and concentration boundary layers ......... 205
   5.11 Chapter summary ....................................... 207
6  Introduction to Electrostatics ............................. 213
   6.1  Introduction .......................................... 213
   6.2  Coulomb's law: The electric field ..................... 214
   6.3  The electric field due to an isolated large flat
        plate ................................................. 216
   6.4  Gauss's law ........................................... 218
   6.5  The electric potential ................................ 219
   6.6  The electric dipole and polar molecules ............... 221
   6.7  Poisson's equation .................................... 222
   6.8  Current and current density ........................... 225
   6.9  Maxwell's equations ................................... 226
   6.10 Chapter summary ....................................... 227
7  Elements of Electrochemistry and the Electrical Double
   Layer ...................................................... 230
   7.1  Introduction .......................................... 230
   7.2  The structure of water and ionic species .............. 231
   7.3  Chemical bonds in biology and chemistry ............... 233
   7.4  Hydration of ions ..................................... 234
   7.5  Chemical potential .................................... 236
   7.6  The Gibbs function and chemical equilibrium ........... 240
   7.7  Electrochemical potential ............................. 243
   7.8  Acids, bases, and electrolytes ........................ 244
   7.9  Site-binding models of the silica surface ............. 246
   7.10 Polymer surfaces ...................................... 249
   7.11 Qualitative description of the electrical double
        layer ................................................. 251
   7.12 Electrolyte and potential distribution in the
        electrical double layer ............................... 253
   7.13 Multivalent asymmetric mixtures ....................... 259
   7.14 The f potential and surface charge density: Putting
        it all together ....................................... 260
        7.14.1 The classical liquid-side view for
               a symmetric electrolyte ........................ 260
        7.14.2 The solid-side view and connection to the
               liquid side .................................... 262
   7.15 The electrical double layer on a cylinder ............. 265
   7.16 The electrical double layer on a sphere ............... 266
   7.17 Electrical conductivity in an electrolyte solution .... 267
   7.18 Semi-permeable membranes .............................. 270
   7.19 The Derjaguin approximation ........................... 275
   7.20 Chapter summary ....................................... 278
8  Elements of Molecular and Cell Biology ..................... 283
   8.1  Introduction .......................................... 283
   8.2  Nucleic acids and polysaccharides ..................... 285
   8.3  Proteins .............................................. 287
        8.3.1  Protein function ............................... 288
        8.3.2  Protein structure .............................. 289
        8.3.3  Some common proteins ........................... 292
        8.3.4  Few polypeptide chains are useful .............. 295
   8.4  Protein binding ....................................... 295
   8.5  Cells ................................................. 298
   8.6  The cell membrane ..................................... 300
   8.7  Membrane transport and ion channels ................... 301
   8.8  Chapter summary ....................................... 304
9  Electrokinetic Phenomena ................................... 306
   9.1  Introduction .......................................... 306
   9.2  Electro-osmosis ....................................... 307
        9.2.1  The relationship between velocity and
               potential ...................................... 307
        9.2.2  The Debye-Hьckel approximation reviewed ........ 312
        9.2.3  Another similarity revealed .................... 312
        9.2.4  Asymptotic solution for binary electrolytes
               of arbitrary valence ........................... 313
        9.2.5  Walls with different Ј potentials .............. 316
        9.2.6  Species velocities in electro-osmotic flow:
               Electromigration ............................... 318
        9.2.7  Current and current density in electro-
                osmotic flow .................................. 320
        9.2.8  Electro-osmotic flow in an annulus ............. 322
        9.2.9  Electro-osmotic flow in nozzles and diffusers .. 324
        9.2.10 Dispersion in electro-osmotic flow ............. 328
   9.3  Electrophoresis: Single particles ..................... 331
        9.3.1  Introduction ................................... 331
        9.3.2  Electrophoretic mobility ....................... 332
        9.3.3  Henry's solution ............................... 334
        9.3.4  The full nonlinear problem ..................... 336
   9.4  Streaming potential ................................... 338
   9.5  Sedimentation potential ............................... 341
   9.6  Joule heating ......................................... 342
   9.7  Chapter summary ....................................... 344
10 Essential Numerical Methods ................................ 348
   10.1 Introduction .......................................... 348
   10.2 Types of errors ....................................... 350
   10.3 Taylor series ......................................... 351
   10.4 Zeros of functions .................................... 353
   10.4.1 Numerical methods ................................... 353
   10.4.2 Polynomials ......................................... 358
   10.5 Interpolation ......................................... 359
        10.5.1 Linear interpolation ........................... 360
        10.5.2 The difference table ........................... 361
        10.5.3 Lagrangian polynomial interpolation ............ 362
        10.5.4 Newton interpolation formulas .................. 363
        10.5.5 Matlab interpolation functions ................. 365
        10.5.6 Cubic spline interpolation ..................... 366
   10.6 Curve fitting ......................................... 370
   10.7 Numerical differentiation ............................. 373
        10.7.1 Derivatives from Taylor series ................. 373
        10.7.2 A more accurate forward formula for the first
               derivative ..................................... 375
   10.8 Numerical integration ................................. 376
        10.8.1 The trapezoidal rule ........................... 377
        10.8.2 Simpson's rules ................................ 380
        10.8.3 Matlab integration functions ................... 382
        10.8.4 The indefinite integral ........................ 382
        10.8.5 Other formulas ................................. 383
        10.8.6 Grid (mesh) size ............................... 383
        10.8.7 Singularities .................................. 384
   10.9  Solution of linear systems ........................... 386
        10.9.1 Solving sets of linear equations  in Matlab .... 389
        10.9.2 Iterative solution to linear systems ........... 390
        10.9.3 Tridiagonal systems ............................ 393
        10.9.4 Ill-conditioning and stability ................. 396
   10.10 Solution of boundary value problems .................. 398
        10.10.1 Introduction .................................. 398
        10.10.2 Linear equations .............................. 399
        10.10.3 Nonlinear equations ........................... 403
        10.10.4 Systems of ordinary differential equations .... 405
        10.10.5 Derivative boundary conditions ................ 407
        10.10.6 Convergence tests and Richardson
                extrapolation ................................. 409
        10.10.7 Solving boundary value problems with Matlab
                functions ..................................... 410
   10.11 Solution of initial value problems ................... 411
        10.11.1 Introduction .................................. 411
        10.11.2 Taylor series method .......................... 413
        10.11.3 Euler methods ................................. 414
        10.11.4 Runge-Kutta methods ........................... 416
        10.11.5 Adams-Moulton methods ......................... 419
        10.11.6 Symplectic integrators ........................ 419
        10.11.7 Stiff equations and stability ................. 424
        10.11.8 Solving initial value problems using Matlab
                functions ..................................... 428
   10.12 Numerical solution of the PNP system ................. 428
   10.13 Partial differential equations ....................... 430
        10.13.1 Elliptic equations ............................ 431
        10.13.2 Parabolic equations ........................... 432
        10.13.3 The Matlab PDE solver ......................... 435
   10.14 Verification and validation of numerical solutions ... 435
   10.15 Chapter summary ...................................... 438
11 Molecular Simulations ...................................... 447
   11.1 Introduction .......................................... 447
   11.2 The molecular world ................................... 449
   11.3 Ensembles ............................................. 451
   11.4 The potentials ........................................ 451
   11.5 Using the Lennard-Jones potential ..................... 453
   11.6 Molecular models for water ............................ 456
   11.7 Periodic boundary conditions .......................... 457
   11.8 The Ewald sum ......................................... 460
   11.9 Numerical issues ...................................... 463
        11.9.1 Time integration ............................... 463
        11.9.2 Truncation of interactions ..................... 464
        11.9.3 Boundary conditions ............................ 465
   11.10 Postprocessing ....................................... 465
   11.11 Nonequilibrium molecular dynamics .................... 467
        11.11.1 Introduction .................................. 467
        11.11.2 Poiseuille flow ............................... 468
        11.11.3 Electro-osmotic flow .......................... 469
   11.12 Molecular dynamics packages .......................... 471
        11.12.1 Introduction .................................. 471
        11.12.2 What MD/NEMD simulators do .................... 471
   11.13 Summary .............................................. 472
12 Applications ............................................... 475
   12.1 Introduction .......................................... 475
   12.2 DNA transport ......................................... 476
        12.2.1 How does DNA move? ............................. 477
        12.2.2 Mathematical model ............................. 479
        12.2.3 Results ........................................ 481
        12.2.4 DNA current .................................... 482
        12.2.5 Comparison with experiment ..................... 483
   12.3 Development of an artificial kidney ................... 484
        12.3.1 Background ..................................... 484
        12.3.2 The nanopore membrane for filtration ........... 486
        12.3.3 Hindered transport ............................. 487
   12.4 Biochemical sensing ................................... 491
        12.4.1 Introduction ................................... 491
        12.4.2 What is a biosensor? ........................... 492
        12.4.3 Receptor-based classification of biosensors .... 493
        12.4.4 Transducer-based classification of biosensors .. 494
        12.4.5 Evaluation of biosensor performance ............ 495
        12.4.6 Nanopores and nanopore membranes for
               biochemical sensing ............................ 496
   12.5 Chapter summary ....................................... 498
Appendix A  Matched Asymptotic Expansions ..................... 501
   A.l  Introduction .......................................... 501
   A.2  Terminology ........................................... 501
   A.3  Asymptotic sequences and expansions ................... 502
   A.4  Regular perturbations ................................. 503
   A.5  Singular perturbations ................................ 504
Appendix В  Vector Operations in Curvilinear Coordinates ...... 508
   B. 1 Cylindrical coordinates ............................... 508
   B.2 Spherical coordinates .................................. 508
   B.3  Rectangular coordinates ............................... 509
Appendix C WebSites ........................................... 510
   C.l Fluid dynamics and micro-and nanofluidics .............. 510
   C.2  General nanotechnology ................................ 511
   C.3  Wikipedia ............................................. 511
Appendix D  A Semester Course Syllabus ........................ 512

Bibliography .................................................. 515
Index ......................................................... 533


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