Microfluidics: Modeling, Mechanics and Mathematics, Second Edition provides a practical, lab-based approach to nano- and microfluidics, including a wealth of practical techniques, protocols and experiments ready to be put into practice in both research and industrial settings. This practical approach is ideally suited to researchers and R&D staff in industry. Additionally, the interdisciplinary approach to the science of nano- and microfluidics enables readers from a range of different academic disciplines to broaden their understanding. Alongside traditional fluid/transport topics, the book contains a wealth of coverage of materials and manufacturing techniques, chemical modification/surface functionalization, biochemical analysis, and the biosensors involved.
This fully updated new edition also includes new sections on viscous flows and centrifugal microfluidics, expanding the types of platforms covered to include centrifugal, capillary and electro kinetic platforms.
1. Chapter 1 Introduction - p. 3 2. Chapter 2 Introduction to Maple - p. 9 3. Chapter 3 Engineering mathematics - p. 21 4. 3.1: Differential equations - p. 21 5. 3.2: Important functions - p. 31 6. 3.3: Commonly used tricks - p. 48 7. 3.4: Summary - p. 51 8. Chapter 4 Series - p. 53 9. 4.1: Introduction - p. 53 10. 4.2: Taylor series - p. 54 11. 4.3: Fourier series - p. 63 12. 4.4: Fourier-Bessel series - p. 78 13. 4.5: Conclusion - p. 82 14. Chapter 5 Transforms - p. 83 15. Chapter 6 Thermodynamics - p. 95 16. 6.1: Atomic model - p. 95 17. 6.2: Weights and concentrations - p. 97 18. 6.3: Important terms and concepts in thermodynamics - p. 101 19. 6.4: Ideal gases - p. 102 20. 6.5: Idealized thermodynamic processes - p. 111 21. 6.6: First law of thermodynamics - p. 112 22. 6.7: Second law of thermodynamics - p. 115 23. 6.8: Third law of thermodynamics - p. 128 24. 6.9: Heat and mass transfer - p. 128 25. 6.10: Summary - p. 138 26. Chapter 7 Vector calculus - p. 141 27. 7.1: Scalars and vectors - p. 141 28. 7.2: Important theorems in vector calculus - p. 147 29. 7.3: Coordinate system transformation - p. 151 30. 7.4: Position, velocity and acceleration - p. 159 31. 7.5: Jacobian matrix - p. 163 32. 7.6: Operators transformed into the different coordinate systems - p. 166 33. 7.6.1: Cylindrical coordinates - p. 166 34. 7.6.2: Polar coordinates - p. 177 35. 7.6.3: Spherical coordinates - p. 178 36. 7.7: Summary - p. 196 37. Chapter 8 Differential equations - p. 197 38. 8.1: Important differential equations - p. 197 39. 8.2: General solutions to selected ordinary differential equations - p. 203 40. 8.3: General solutions to selected partial differential equations - p. 214 41. 8.3.1: Introduction - p. 214 42. 8.3.2: The method of characteristics: the transport equation - p. 214 43. 8.3.3: Substitution and separation of variables: the one-dimensional heat equation - p. 217 44. 8.3.4: Important solutions for substitution and separation of variables approaches - p. 223 45. 8.3.5: Wave equation solved by substitution and separation of variables - p. 236 46. 8.3.6: Fourier transform: the one-dimensional diffusion equation - p. 242 47. 8.3.7: Laplace transform: the one-dimensional wave and heat equations - p. 247 48. 8.3.8: Two-dimensional partial differential equations: the diffusion equation - p. 252 49. 8.3.9: Time-dependent higher-order partial differential equations by substitution and separation of variables: the time-dependent diffusion equation in three dimensions - p. 255 50. 8.3.10: Summary - p. 257 51. Chapter 9 Fluids - p. 261 52. Chapter 10 Conservation of mass: the continuity equation - p. 283 53. Chapter 11 Conservation of momentum: the Navier-Stokes equation - p. 291 54. Chapter 12 Conservation of energy: the energy equation and the thermodynamic equation of state - p. 311 55. Chapter 13 Continuity and Navier-Stokes equation in different coordinate systems - p. 323 56. Chapter 14 The circular flow tube - p. 331 57. Chapter 15 Analytical solutions to the Navier-Stokes equation - p. 337 58. Chapter 16 Analytical solutions to Poiseuille flow problems in different geometries - p. 345 59. 16.1: Elliptical and circular profiles - p. 345 60. 16.2: Planar infinitesimally extended channel cross-sections - p. 348 61. 16.3: Flows in circular cross-sections: Hagen-Poiseuille flow - p. 351 62. 16.4: Flows in rectangular cross-sections: solution to Poisson and Laplace equations - p. 358 63. 16.5: Summary - p. 373 64. Chapter 17 Hydraulic resistance - p. 375 65. Chapter 18 Analytical solutions to transient flow problems - p. 397 66. 18.1: Time-dependent transient effects: acceleration and deceleration - p. 397 67. 18.2: Time-dependent Couette flow - p. 399 68. 18.3: Time-dependent Hagen-Poiseuille flow - p. 406 69. 18.4: Time-dependent flow in rectangular cross-sections - p. 411 70. 18.5: Entrance effects in Hagen-Poiseuille flow - p. 420 71. 18.6: Summary - p. 426 72. Chapter 19 Taylor-Aris dispersion - p. 427 73. Chapter 20 Surface tension - p. 447 74. Chapter 21 Capillarity - p. 471 75. Chapter 22 Measuring surface tension and free surface energy - p. 481 76. Chapter 23 Plateau-Rayleigh instability - p. 495 77. Chapter 24 The shape of drops - p. 507 78. Chapter 25 Numerical methods for linear systems of equations - p. 525 79. 25.1: Introduction - p. 525 80. 25.2: Solutions to linear systems of equations - p. 528 81. 25.3: Numerical solutions to linear systems of equations - p. 537 82. 25.3.1: Introduction - p. 537 83. 25.3.2: Jacobi method - p. 537 84. 25.3.3: Gauß-Seidel method - p. 542 85. 25.3.4: Successive over-relaxation - p. 543 86. 25.3.5: LU-decomposition - p. 547 87. 25.3.6: Sequential dense LU-decomposition - p. 557 88. 25.3.7: Substitution - p. 562 89. 25.3.8: Tridiagonal matrix algorithm: Thomas algorithm - p. 563 90. 25.3.9: Export to CoreFunctions.txt - p. 566 91. 25.3.10: Summary - p. 566 92. 25.4: Summary - p. 566 93. Chapter 26 Numerical solutions to nonlinear systems: Newton's method - p. 567 94. Chapter 27 Numerical methods for solving differential equations - p. 581 95. 27.1: Numerical solutions to ordinary differential equations - p. 581 96. 27.1.1: Introduction - p. 581 97. 27.1.2: First-order methods: Euler's method - p. 582 98. 27.1.3: First-order methods: backward Euler method - p. 587 99. 27.1.4: Other important first-order methods: forward and backward finite distance - p. 591 100. 27.1.5: Important second-order methods - p. 592 101. 27.1.6: Second- and fourth-order finite difference schemes - p. 596 102. 27.1.7: Multistep methods: Adams-Bashforth methods - p. 597 103. 27.1.8: Predictor-corrector methods: Adams-Moulton methods - p. 602 104. 27.1.9: Modern one-step methods: Runge-Kutta methods - p. 605 105. 27.1.10: Richardson extrapolation - p. 614 106. 27.2: Numerical solutions to higher-order ordinary differential equations and systems of coupled ordinary differential equations - p. 619 107. 27.3: Numerical solutions to systems of ordinary differential equations with boundary conditions - p. 629 108. 27.4: Summary - p. 637 109. Chapter 28 Numerical solutions to the Navier-Stokes equation - p. 639 110. Chapter 29 Computational fluid dynamics - p. 653 111. Chapter 30 Finite difference method - p. 667 112. Chapter 31 Finite volume method - p. 677 113. 31.1: Introduction - p. 677 114. 31.2: Conservative form notation - p. 677 115. 31.3: Integral form of the conservative notation - p. 678 116. 31.4: Discretization - p. 681 117. 31.5: Function reconstruction - p. 682 118. 31.6: Example: one-dimensional heat equation - p. 689 119. 31.7: Two-dimensional problems of first order in time and space - p. 693 120. 31.8: Two-dimensional problems of first order in time and second-order in space - p. 696 121. 31.9: Summary - p. 698 122. Chapter 32 Finite element method - p. 701 123. 32.1: Introduction - p. 701 124. 32.2: Discretization - p. 701 125. 32.3: Lagrangian coordinates - p. 701 126. 32.4: Basis functions - p. 705 127. 32.5: One-dimensional example: flow in infinitesimally extended channels - p. 707 128. 32.6: Two-dimensional example: flow in rectangular channels11 Published in [1]. - p. 715 129. 32.7: Summary - p. 725 130. Chapter 33 Numerical solutions to transient flow problems - p. 727 131. Chapter 34 Numerical solutions to three-dimensional flow problems - p. 747 132. 34.1: Introduction - p. 747 133. 34.2: Derivation - p. 747 134. 34.2.1: Four equations - p. 747 135. 34.2.2: Pressure recovery - p. 748 136. 34.2.3: Schemes for stationary and instationary flows - p. 753 137. 34.3: Implementation of a stationary-flow numerical solver - p. 762 138. 34.4: Usage of the numerical solver - p. 773 139. 34.5: Summary - p. 788 140. Index - p. 789
Microfluidics: Modeling, Mechanics and Mathematics, Second Edition provides a practical, lab-based approach to nano- and microfluidics, including a wealth of practical techniques, protocols and experiments ready to be put into practice in both research and industrial settings. This practical approach is ideally suited to researchers and R&D staff in industry. Additionally, the interdisciplinary approach to the science of nano- and microfluidics enables readers from a range of different academic disciplines to broaden their understanding. Alongside traditional fluid/transport topics, the book contains a wealth of coverage of materials and manufacturing techniques, chemical modification/surface functionalization, biochemical analysis, and the biosensors involved.
This fully updated new edition also includes new sections on viscous flows and centrifugal microfluidics, expanding the types of platforms covered to include centrifugal, capillary and electro kinetic platforms.
1. Chapter 1 Introduction - p. 3 2. Chapter 2 Introduction to Maple - p. 9 3. Chapter 3 Engineering mathematics - p. 21 4. 3.1: Differential equations - p. 21 5. 3.2: Important functions - p. 31 6. 3.3: Commonly used tricks - p. 48 7. 3.4: Summary - p. 51 8. Chapter 4 Series - p. 53 9. 4.1: Introduction - p. 53 10. 4.2: Taylor series - p. 54 11. 4.3: Fourier series - p. 63 12. 4.4: Fourier-Bessel series - p. 78 13. 4.5: Conclusion - p. 82 14. Chapter 5 Transforms - p. 83 15. Chapter 6 Thermodynamics - p. 95 16. 6.1: Atomic model - p. 95 17. 6.2: Weights and concentrations - p. 97 18. 6.3: Important terms and concepts in thermodynamics - p. 101 19. 6.4: Ideal gases - p. 102 20. 6.5: Idealized thermodynamic processes - p. 111 21. 6.6: First law of thermodynamics - p. 112 22. 6.7: Second law of thermodynamics - p. 115 23. 6.8: Third law of thermodynamics - p. 128 24. 6.9: Heat and mass transfer - p. 128 25. 6.10: Summary - p. 138 26. Chapter 7 Vector calculus - p. 141 27. 7.1: Scalars and vectors - p. 141 28. 7.2: Important theorems in vector calculus - p. 147 29. 7.3: Coordinate system transformation - p. 151 30. 7.4: Position, velocity and acceleration - p. 159 31. 7.5: Jacobian matrix - p. 163 32. 7.6: Operators transformed into the different coordinate systems - p. 166 33. 7.6.1: Cylindrical coordinates - p. 166 34. 7.6.2: Polar coordinates - p. 177 35. 7.6.3: Spherical coordinates - p. 178 36. 7.7: Summary - p. 196 37. Chapter 8 Differential equations - p. 197 38. 8.1: Important differential equations - p. 197 39. 8.2: General solutions to selected ordinary differential equations - p. 203 40. 8.3: General solutions to selected partial differential equations - p. 214 41. 8.3.1: Introduction - p. 214 42. 8.3.2: The method of characteristics: the transport equation - p. 214 43. 8.3.3: Substitution and separation of variables: the one-dimensional heat equation - p. 217 44. 8.3.4: Important solutions for substitution and separation of variables approaches - p. 223 45. 8.3.5: Wave equation solved by substitution and separation of variables - p. 236 46. 8.3.6: Fourier transform: the one-dimensional diffusion equation - p. 242 47. 8.3.7: Laplace transform: the one-dimensional wave and heat equations - p. 247 48. 8.3.8: Two-dimensional partial differential equations: the diffusion equation - p. 252 49. 8.3.9: Time-dependent higher-order partial differential equations by substitution and separation of variables: the time-dependent diffusion equation in three dimensions - p. 255 50. 8.3.10: Summary - p. 257 51. Chapter 9 Fluids - p. 261 52. Chapter 10 Conservation of mass: the continuity equation - p. 283 53. Chapter 11 Conservation of momentum: the Navier-Stokes equation - p. 291 54. Chapter 12 Conservation of energy: the energy equation and the thermodynamic equation of state - p. 311 55. Chapter 13 Continuity and Navier-Stokes equation in different coordinate systems - p. 323 56. Chapter 14 The circular flow tube - p. 331 57. Chapter 15 Analytical solutions to the Navier-Stokes equation - p. 337 58. Chapter 16 Analytical solutions to Poiseuille flow problems in different geometries - p. 345 59. 16.1: Elliptical and circular profiles - p. 345 60. 16.2: Planar infinitesimally extended channel cross-sections - p. 348 61. 16.3: Flows in circular cross-sections: Hagen-Poiseuille flow - p. 351 62. 16.4: Flows in rectangular cross-sections: solution to Poisson and Laplace equations - p. 358 63. 16.5: Summary - p. 373 64. Chapter 17 Hydraulic resistance - p. 375 65. Chapter 18 Analytical solutions to transient flow problems - p. 397 66. 18.1: Time-dependent transient effects: acceleration and deceleration - p. 397 67. 18.2: Time-dependent Couette flow - p. 399 68. 18.3: Time-dependent Hagen-Poiseuille flow - p. 406 69. 18.4: Time-dependent flow in rectangular cross-sections - p. 411 70. 18.5: Entrance effects in Hagen-Poiseuille flow - p. 420 71. 18.6: Summary - p. 426 72. Chapter 19 Taylor-Aris dispersion - p. 427 73. Chapter 20 Surface tension - p. 447 74. Chapter 21 Capillarity - p. 471 75. Chapter 22 Measuring surface tension and free surface energy - p. 481 76. Chapter 23 Plateau-Rayleigh instability - p. 495 77. Chapter 24 The shape of drops - p. 507 78. Chapter 25 Numerical methods for linear systems of equations - p. 525 79. 25.1: Introduction - p. 525 80. 25.2: Solutions to linear systems of equations - p. 528 81. 25.3: Numerical solutions to linear systems of equations - p. 537 82. 25.3.1: Introduction - p. 537 83. 25.3.2: Jacobi method - p. 537 84. 25.3.3: Gauß-Seidel method - p. 542 85. 25.3.4: Successive over-relaxation - p. 543 86. 25.3.5: LU-decomposition - p. 547 87. 25.3.6: Sequential dense LU-decomposition - p. 557 88. 25.3.7: Substitution - p. 562 89. 25.3.8: Tridiagonal matrix algorithm: Thomas algorithm - p. 563 90. 25.3.9: Export to CoreFunctions.txt - p. 566 91. 25.3.10: Summary - p. 566 92. 25.4: Summary - p. 566 93. Chapter 26 Numerical solutions to nonlinear systems: Newton's method - p. 567 94. Chapter 27 Numerical methods for solving differential equations - p. 581 95. 27.1: Numerical solutions to ordinary differential equations - p. 581 96. 27.1.1: Introduction - p. 581 97. 27.1.2: First-order methods: Euler's method - p. 582 98. 27.1.3: First-order methods: backward Euler method - p. 587 99. 27.1.4: Other important first-order methods: forward and backward finite distance - p. 591 100. 27.1.5: Important second-order methods - p. 592 101. 27.1.6: Second- and fourth-order finite difference schemes - p. 596 102. 27.1.7: Multistep methods: Adams-Bashforth methods - p. 597 103. 27.1.8: Predictor-corrector methods: Adams-Moulton methods - p. 602 104. 27.1.9: Modern one-step methods: Runge-Kutta methods - p. 605 105. 27.1.10: Richardson extrapolation - p. 614 106. 27.2: Numerical solutions to higher-order ordinary differential equations and systems of coupled ordinary differential equations - p. 619 107. 27.3: Numerical solutions to systems of ordinary differential equations with boundary conditions - p. 629 108. 27.4: Summary - p. 637 109. Chapter 28 Numerical solutions to the Navier-Stokes equation - p. 639 110. Chapter 29 Computational fluid dynamics - p. 653 111. Chapter 30 Finite difference method - p. 667 112. Chapter 31 Finite volume method - p. 677 113. 31.1: Introduction - p. 677 114. 31.2: Conservative form notation - p. 677 115. 31.3: Integral form of the conservative notation - p. 678 116. 31.4: Discretization - p. 681 117. 31.5: Function reconstruction - p. 682 118. 31.6: Example: one-dimensional heat equation - p. 689 119. 31.7: Two-dimensional problems of first order in time and space - p. 693 120. 31.8: Two-dimensional problems of first order in time and second-order in space - p. 696 121. 31.9: Summary - p. 698 122. Chapter 32 Finite element method - p. 701 123. 32.1: Introduction - p. 701 124. 32.2: Discretization - p. 701 125. 32.3: Lagrangian coordinates - p. 701 126. 32.4: Basis functions - p. 705 127. 32.5: One-dimensional example: flow in infinitesimally extended channels - p. 707 128. 32.6: Two-dimensional example: flow in rectangular channels11 Published in [1]. - p. 715 129. 32.7: Summary - p. 725 130. Chapter 33 Numerical solutions to transient flow problems - p. 727 131. Chapter 34 Numerical solutions to three-dimensional flow problems - p. 747 132. 34.1: Introduction - p. 747 133. 34.2: Derivation - p. 747 134. 34.2.1: Four equations - p. 747 135. 34.2.2: Pressure recovery - p. 748 136. 34.2.3: Schemes for stationary and instationary flows - p. 753 137. 34.3: Implementation of a stationary-flow numerical solver - p. 762 138. 34.4: Usage of the numerical solver - p. 773 139. 34.5: Summary - p. 788 140. Index - p. 789
