Essentials of Micro- and Nanofluidics : With Applications to the Biological and Chemical Sciences

"This book introduces students to the basic physical principles to analyze fluid flow in micro and nano-size devices. This is the first book that unifies the thermal sciences with electrostatics and electrokinetics and colloid science; electrochemistry; and molecular biology. The author discusses key concepts and principles, such as the essentials of viscous flows, an introduction to electrochemistry, heat and mass transfer phenomena, elements of molecular and cell biology, and much more. This textbook presents state-of-the-art analytical and computational approaches to problems in all of these areas, especially electrokinetic flows, and gives examples of the use of these disciplines to design devices used for rapid molecular analysis, biochemical sensing, drug delivery, DNA analysis, the design of an artificial kidney, and other transport phenomena. This textbook includes exercise problems, modern examples of the applications of these sciences, and a solutions manual available to qualified instructors"--Provided by publisher. Contents 8 Preface 16 1 Introduction and Overview 22 1.1 Micro- and nanofluidics 22 1.2 Some micro- and nanofluidic devices 24 1.3 What is it about the nanoscale? 28 1.4 Nanotechnology 32 1.5 What is a fluid? 34 1.6 Historical perspectives 35 1.6.1 Fluid mechanics 36 1.6.2 Heat and mass transfer 38 1.6.3 Electrokinetic phenomena 40 1.7 The thermal sciences 41 1.8 Electrostatics 44 1.9 Electrolyte solutions 46 1.10 The electrical double layer 47 1.11 Colloidal systems 50 1.12 Molecular biology 53 1.13 The convergence of molecular biology and engineering 55 1.14 Design of micro- and nanofluidic devices 56 1.15 Unit systems 58 1.16 A word about notation 58 1.17 Chapter summary 59 2 Preparatory Concepts 61 2.1 Introduction 61 2.2 Important constitutive laws 62 2.3 Determining transport properties 66 2.3.1 Viscosity 66 2.3.2 Diffusion coefficient 69 2.3.3 Thermal conductivity 73 2.3.4 Electrical permittivity 75 2.3.5 Surface tension and wettability 76 2.4 Classification of fluid flows 80 2.5 Elements of thermodynamics 83 2.6 The nature of frictional losses in channels and pipes 89 2.7 Chapter summary 91 Exercises 92 3 The Governing Equations for an Electrically Conducting Fluid 95 3.1 Introduction 95 3.2 The continuum approximation and its limitations 96 3.3 Kinematics 98 3.4 Surface and body forces 104 3.5 The continuity equation 108 3.6 The Navier--Stokes equations 109 3.7 Mass transport 114 3.7.1 Definitions 114 3.7.2 Governing equation 118 3.8 Electrostatics 121 3.9 Energy transport 123 3.10 Two-dimensional, steady, and incompressible flow 127 3.11 Boundary and initial conditions 127 3.11.1 Velocity boundary conditions 128 3.11.2 Mass transfer boundary conditions 134 3.11.3 Electrostatics boundary conditions 135 3.11.4 Temperature boundary conditions 137 3.11.5 Other boundary conditions 138 3.12 Dimensional analysis and similarity 138 3.13 Fluid, electrostatics, and heat and mass transfer analogies 144 3.13.1 Mole fraction and temperature similarity 144 3.13.2 Velocity and electrical potential similarity 146 3.14 Other stress--strain relationships 147 3.15 Mathematical character of partial differential equations 149 3.15.1 Introduction 149 3.15.2 Mathematical classification of second-order partialdifferential equations 149 3.15.3 Characteristic curves 150 3.15.4 Boundary and initial conditions 151 3.15.5 Classification of the governing equations of micro- and nanofluidics 152 3.16 Well-posed problems 152 3.17 The role of fabrication, experiments, and theory in micro- and nanofluidics 153 3.18 Chapter summary 155 Exercises 92 4 The Essentials of Viscous Flow 161 4.1 Introduction 161 4.2 The structure of flow in a pipe or channel 162 4.3 Poiseuille flow in a pipe or channel 164 4.4 The velocity in slip flow 167 4.4.1 Gases 167 4.4.2 Liquids 168 4.5 Flow in a thin film under gravity 169 4.6 The boundary layer on a flat plate 171 4.7 Fully developed suction flows 176 4.8 Developing suction flows 179 4.9 The lubrication approximation 183 4.10 A surface tension--driven flow 187 4.11 Stokes flow past a sphere 190 4.12 Sedimentation of a solid particle 193 4.13 A simple model for blood flow 194 4.14 Chapter summary 195 Exercises 92 5 Heat and Mass Transfer Phenomena in Channels and Tubes 201 5.1 Introduction 201 5.2 One-dimensional temperature distributions in channel flow 202 5.3 Thermal and mass transfer entrance regions 205 5.4 The temperature distribution in fully developed tube flow 210 5.5 The Graetz problem for a channel 210 5.6 Mass transfer in thin films 213 5.7 Classical Taylor--Aris dispersion 215 5.8 The stochastic nature of diffusion: Brownian motion 220 5.9 Unsteady mass transport in uncharged membranes 222 5.10 Temperature and concentration boundary layers 226 5.11 Chapter summary 228 Exercises 92 6 Introduction to Electrostatics 234 6.1 Introduction 234 6.2 Coulomb's law: The electric field 235 6.3 The electric field due to an isolated large flat plate 237 6.4 Gauss's law 239 6.5 The electric potential 240 6.6 The electric dipole and polar molecules 242 6.7 Poisson's equation 243 6.8 Current and current density 246 6.9 Maxwell's equations 247 6.10 Chapter summary 248 Exercises 92 7 Elements of Electrochemistry and the Electrical Double Layer 251 7.1 Introduction 251 7.2 The structure of water and ionic species 252 7.3 Chemical bonds in biology and chemistry 254 7.4 Hydration of ions 255 7.5 Chemical potential 257 7.6 The Gibbs function and chemical equilibrium 261 7.7 Electrochemical potential 264 7.8 Acids, bases, and electrolytes 265 7.9 Site-binding models of the silica surface 267 7.10 Polymer surfaces 270 7.11 Qualitative description of the electrical double layer 272 7.12 Electrolyte and potential distribution in the electrical double layer 274 7.13 Multivalent asymmetric mixtures 280 7.14 The potential and surface charge density: Putting it all together 281 7.14.1 The classical liquid-side view for a symmetric electrolyte 281 7.14.2 The solid-side view and connection to the liquid side 283 7.15 The electrical double layer on a cylinder 286 7.16 The electrical double layer on a sphere 287 7.17 Electrical conductivity in an electrolyte solution 288 7.18 Semi-permeable membranes 291 7.19 The Derjaguin approximation 296 7.20 Chapter summary 299 Exercises 92 8 Elements of Molecular and Cell Biology 304 8.1 Introduction 304 8.2 Nucleic acids and polysaccharides 306 8.3 Proteins 308 8.3.1 Protein function 309 8.3.2 Protein structure 310 8.3.3 Some common proteins 313 8.3.4 Few polypeptide chains are useful 316 8.4 Protein binding 316 8.5 Cells 319 8.6 The cell membrane 321 8.7 Membrane transport and ion channels 322 8.8 Chapter summary 325 Exercises 92 9 Electrokinetic Phenomena 327 9.1 Introduction 327 9.2 Electro-osmosis 328 9.2.1 The relationship between velocity and potential 328 9.2.2 The Debye--Huckel approximation reviewed 333 9.2.3 Another similarity revealed 333 9.2.4 Asymptotic solution for binary electrolytes of arbitrary valence 334 9.2.5 Walls with different potentials 337 9.2.6 Species velocities in electro-osmotic flow: Electromigration 339 9.2.7 Current and current density in electro-osmotic flow 341 9.2.8 Electro-osmotic flow in an annulus 343 9.2.9 Electro-osmotic flow in nozzles and diffusers 345 9.2.10 Dispersion in electro-osmotic flow 349 9.3 Electrophoresis: Single particles 352 9.3.1 Introduction 352 9.3.2 Electrophoretic mobility 353 9.3.3 Henry's solution 355 9.3.4 The full nonlinear problem 357 9.4 Streaming potential 359 9.5 Sedimentation potential 362 9.6 Joule heating 363 9.7 Chapter summary 365 Exercises 366 10 Essential Numerical Methods 369 10.1 Introduction 369 10.2 Types of errors 371 10.3 Taylor series 372 10.4 Zeros of functions 374 10.4.1 Numerical methods 374 10.4.2 Polynomials 379 10.5 Interpolation 380 10.5.1 Linear interpolation 381 10.5.2 The difference table 382 10.5.3 Lagrangian polynomial interpolation 383 10.5.4 Newton interpolation formulas 384 10.5.5 Matlab interpolation functions 386 10.5.6 Cubic spline interpolation 387 10.6 Curve fitting 391 10.7 Numerical differentiation 394 10.7.1 Derivatives from Taylor series 394 10.7.2 A more accurate forward formula for the first derivative 396 10.8 Numerical integration 397 10.8.1 The trapezoidal rule 398 10.8.2 Simpson's rules 401 10.8.3 Matlab integration functions 403 10.8.4 The indefinite integral 403 10.8.5 Other formulas 404 10.8.6 Grid (mesh) size 404 10.8.7 Singularities 405 10.9 Solution of linear systems 407 10.9.1 Solving sets of linear equations in Matlab 410 10.9.2 Iterative solution to linear systems 411 10.9.3 Tridiagonal systems 414 10.9.4 Ill-conditioning and stability 417 10.10 Solution of boundary value problems 419 10.10.1 Introduction 419 10.10.2 Linear equations 420 10.10.3 Nonlinear equations 424 10.10.4 Systems of ordinary differential equations 426 10.10.5 Derivative boundary conditions 428 10.10.6 Convergence tests and Richardson extrapolation 430 10.10.7 Solving boundary value problems with Matlab functions 431 10.11 Solution of initial value problems 432 10.11.1 Introduction 432 10.11.2 Taylor series method 434 10.11.3 Euler methods 435 10.11.4 Runge-Kutta methods 437 10.11.5 Adams--Moulton methods 440 10.11.6 Symplectic integrators 440 10.11.7 Stiff equations and stability 445 10.11.8 Solving initial value problems using Matlab functions 449 10.12 Numerical solution of the PNP system 449 10.13 Partial differential equations 451 10.13.1 Elliptic equations 452 10.13.2 Parabolic equations 453 10.13.3 The Matlab PDE solver 456 10.14 Verification and validation of numerical solutions 456 10.15 Chapter summary 459 Exercises 460 11 Molecular Simulations 468 11.1 Introduction 468 11.2 The molecular world 470 11.3 Ensembles 472 11.4 The potentials 472 11.5 Using the Lennard--Jones potential 474 11.6 Molecular models for water 477 11.7 Periodic boundary conditions 478 11.8 The Ewald sum 481 11.9 Numerical issues 484 11.9.1 Time integration 484 11.9.2 Truncation of interactions 485 11.9.3 Boundary conditions 486 11.10 Postprocessing 486 11.11 Nonequilibrium molecular dynamics 488 11.11.1 Introduction 488 11.11.2 Poiseuille flow 489 11.11.3 Electro-osmotic flow 490 11.12 Molecular dynamics packages 492 11.12.1 Introduction 492 11.12.2 What MD/NEMD simulators do 492 11.13 Summary 493 Exercises 92 12 Applications 496 12.1 Introduction 496 12.2 DNA transport 497 12.2.1 How does DNA move? 498 12.2.2 Mathematical model 500 12.2.3 Results 502 12.2.4 DNA current 503 12.2.5 Comparison with experiment 504 12.3 Development of an artificial kidney 505 12.3.1 Background 505 12.3.2 The nanopore membrane for filtration 507 12.3.3 Hindered transport 508 12.4 Biochemical sensing 512 12.4.1 Introduction 512 12.4.2 What is a biosensor? 513 12.4.3 Receptor-based classification of biosensors 514 12.4.4 Transducer-based classification of biosensors 515 12.4.5 Evaluation of biosensor performance 516 12.4.6 Nanopores and nanopore membranes for biochemical sensing 517 12.5 Chapter summary 519 Exercises 366 Appendix A: Matched Asymptotic Expansions 522 A.1 Introduction 522 A.2 Terminology 522 A.3 Asymptotic sequences and expansions 523 A.4 Regular perturbations 524 A.5 Singular perturbations 525 Appendix B: Vector Operations in Curvilinear Coordinates 529 B.1 Cylindrical coordinates 529 B.2 Spherical coordinates 529 B.3 Rectangular coordinates 530 Appendix C: Web Sites 531 C.1 Fluid dynamics and micro- and nanofluidics 531 C.2 General nanotechnology 532 C.3 Wikipedia 532 Appendix D: A Semester Course Syllabus 533 Bibliography 536 Index 554 "This book introduces students to the basic physical principles to analyze fluid flow in micro and nano-size devices. This is the first book that unifies the thermal sciences with electrostatics and electrokinetics and colloid science; electrochemistry; and molecular biology. The author discusses key concepts and principles, such as the essentials of viscous flows, an introduction to electrochemistry, heat and mass transfer phenomena, elements of molecular and cell biology, and much more. This textbook presents state-of-the-art analytical and computational approaches to problems in all of these areas, especially electrokinetic flows, and gives examples of the use of these disciplines to design devices used for rapid molecular analysis, biochemical sensing, drug delivery, DNA analysis, the design of an artificial kidney, and other transport phenomena. This textbook includes exercise problems, modern examples of the applications of these sciences, and a solutions manual available to qualified instructors"--Résumé de l'éditeur This textbook introduces students to the basic physical principles to analyse fluid flow in micro- and nano-size devices. This is the first book that unifies the thermal sciences with electrostatics and electrokinetics and colloid science; electrochemistry; and molecular biology. Key concepts and principles are discussed, such as the essentials of viscous flows, introductory electrochemistry, heat and mass transfer phenomena, elements of molecular and cell biology and much more. State-of-the-art analytical and computational approaches to problems in all of these areas are presented, especially electrokinetic flows, and examples are given of the use of these approaches to design devices used for rapid molecular analysis, biochemical sensing, drug delivery, DNA analysis, the design of an artificial kidney and other transport phenomena. There are exercise problems and modern examples of applications, as well as a solutions manual available for qualified instructors. Machine generated contents note: 1. Introduction and overview; 2. Preparatory concepts; 3. The governing equations for an electrically conducting fluid; 4. The essentials of viscous flow; 5. Heat and mass transfer phenomena in channels and tubes; 6. Introduction to electrostatics; 7. Elements of electrochemistry and the electrical double layer; 8. Elements of molecular and cell biology; 9. Electrokinetic phenomena; 10. Essential numerical methods; 11. Molecular dynamics and simulations; 12. Applications; Appendix 1. Matched asymptotic expansions; Appenedix 2. Vector operations in curvilinear coordinates. This textbook introduces students to the physical principles used to analyse fluid flow in micro- and nano-size devices. It is the first to unify thermal sciences with electrostatics and electrokinetics and colloid science; electrochemistry; and molecular biology. Included are exercises, modern examples and applications, and a solutions manual for instructors.