Microfluidics: Modeling, Mechanics and Mathematics

Microfluidics: Modeling, Mechanics and Mathematics

by Bastian E. Rapp
Released December 2016
Publisher(s): Elsevier
ISBN: 9781455731510

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Book description

This practical, lab-based approach to nano- and microfluidics provides readers with a wealth of practical techniques, protocols, and experiments ready to be put into practice in both research and industrial settings. The 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.

Dr Rapp fully engages with the multidisciplinary nature of the subject. Alongside traditional fluid/transport topics, there is a wealth of coverage of materials and manufacturing techniques, chemical modification/surface functionalization, biochemical analysis, and the biosensors involved.

As well as providing a clear and concise overview to get started into the multidisciplinary field of microfluidics and practical guidance on techniques, pitfalls and troubleshooting, this book supplies:

  • A set of hands-on experiments and protocols that will help setting up lab experiments but which will also allow a quick start into practical work.

  • A collection of microfluidic structures, with 3D-CAD and image data that can be used directly (files provided on a companion website).
  • A practical guide to the successful design and implementation of nano- and microfluidic processes (e.g. biosensing) and equipment (e.g., biosensors, such as diabetes blood glucose sensors)
  • Provides techniques, experiments, and protocols ready to be put to use in the lab, in an academic, or industry setting
  • A collection of 3D-CAD and image files is provided on a companion website

Table of contents

  1. Cover image
  2. Title page
  3. Table of Contents
  4. Copyright
  5. Dedication
  6. Preface
  7. Acknowledgement
  8. List of Figures
  9. List of Tables
  10. List of Listings
  11. List of Acronyms
  12. List of Abbreviations
  13. List of Symbols
  14. List of Constants
  15. List of Chemicals
  16. Conversions
  17. I: Fundamentals
    1. Chapter 1: Introduction
      1. 1.1 What is Microfluidics?
      2. 1.2 A Brief History of Microfluidics
      3. 1.3 Commercial Aspects
      4. 1.4 About This Book
      5. 1.5 Structure of This Book
    2. Chapter 2: Introduction to Maple
      1. 2.1 Introduction
      2. 2.2 Elementary Maple Commands
      3. 2.3 The File Core.txt
      4. 2.4 The File Corefunctions.txt
      5. 2.5 The Neptunlib
      6. 2.6 Summary
    3. Chapter 3: Engineering Mathematics
      1. 3.1 Differential Equations
      2. 3.2 Important Functions
      3. 3.3 Commonly Used Calculus Tricks
      4. 3.4 Summary
    4. Chapter 4: Series
      1. 4.1 Introduction
      2. 4.2 Taylor Series
      3. 4.3 Fourier Series
      4. 4.4 Fourier-Bessel Series
      5. 4.5 Conclusion
    5. Chapter 5: Transforms
      1. 5.1 Fourier Transform
      2. 5.2 Laplace Transform
      3. 5.3 Summary
    6. Chapter 6: Thermodynamics
      1. 6.1 Atomic Model
      2. 6.2 Weights and Concentrations
      3. 6.3 Important Terms and Concepts in Thermodynamics
      4. 6.4 Ideal Gases
      5. 6.5 Idealized Thermodynamic Processes
      6. 6.6 First Law of Thermodynamics
      7. 6.7 Second Law of Thermodynamics
      8. 6.8 Third Law of Thermodynamics
      9. 6.9 Heat and Mass Transfer
      10. 6.10 SUMMARY
    7. Chapter 7: Vector Calculus
      1. 7.1 Scalars and Vectors
      2. 7.2 Important Theorems in Vector Calculus
      3. 7.3 Coordinate System Transformation
      4. 7.4 Position, Velocity, and Acceleration
      5. 7.5 Jacobian Matrix
      6. 7.6 Operators Transformed into the different Coordinate Systems
      7. 7.7 Summary
    8. Chapter 8: Differential Equations
      1. 8.1 Important Differential Equations
      2. 8.2 General Solutions to Selected Ordinary Differential Equations
      3. 8.3 General Solutions to Selected Partial Differential Equations
  18. II: Bulk Fluid Flows
    1. Chapter 9: Fluids
      1. 9.1 Introduction
      2. 9.2 Solids, Liquids, and Gases at the Atomic Scale
      3. 9.3 Control Volumes
      4. 9.4 Fluid Properties
      5. 9.5 Momentum Transport
      6. 9.6 Heat Transport
      7. 9.7 Mass Transport
      8. 9.8 Boundary Conditions
      9. 9.9 Dimensionless Numbers
      10. 9.10 Summary
    2. Chapter 10: Conservation of Mass: The Continuity Equation
      1. 10.1 Fluid Flow in the Bulk
      2. 10.2 Continuity Equation
      3. 10.3 Integral Representation of the Flowrate
      4. 10.4 Mass Balance
      5. 10.5 Derivation using Gauss’s Theorem
      6. 10.6 Combined Convection and Diffusion: The Convection-Diffusion Equation
      7. 10.7 Summary
    3. Chapter 11: Conservation of Momentum: The Navier-Stokes Equation
      1. 11.1 Introduction
      2. 11.2 Momentum Transfer Into and Out of a Control Volume
      3. 11.3 Momentum by in- and Outflowing Mass
      4. 11.4 Momentum by Shear Forces
      5. 11.5 Momentum by Volume Forces
      6. 11.6 Balance of Momentum
      7. 11.7 Navier-Stokes Equation for Incompressible Newtonian Fluids
      8. 11.8 Dimensional Analysis
      9. 11.9 Conclusion
    4. Chapter 12: Conservation of Energy: The Energy Equation and the Thermodynamic Equation of State
      1. 12.1 Introduction
      2. 12.2 Energy Transfer by Convection
      3. 12.3 Heat Flow by Conduction
      4. 12.4 Work Flow by Boundary Forces
      5. 12.5 Heat Flow by Volume Effects
      6. 12.6 Work Flow by Volume Forces
      7. 12.7 Balance of Contributions
      8. 12.8 Thermodynamic Equation of State
      9. 12.9 Summary
    5. Chapter 13: Continuity and Navier-Stokes Equations in Different Coordinate Systems
      1. 13.1 Cartesian Coordinates
      2. 13.2 Cylindrical Coordinates
      3. 13.3 Polar Coordinates
      4. 13.4 Spherical Coordinates
      5. 13.5 Summary
    6. Chapter 14: The Circular Flow Tube
      1. 14.1 Introduction
      2. 14.2 Conservation of Mass: The Continuity Equation
      3. 14.3 Conservation of Momentum: The Navier-Stokes Equation
      4. 14.4 Euler Equation
      5. 14.5 Bernoulli Equation
      6. 14.6 Conservation of Energy
      7. 14.7 Deriving the Euler Equation by a Coordinate System Transformation
      8. 14.8 Summary
    7. Chapter 15: Analytical Solutions to the Navier-Stokes Equation
      1. 15.1 Hydrostatics and Aerostatics
      2. 15.2 Shear Force-Driven Flow: Couette Flow
      3. 15.3 Gravity-Driven Flow
      4. 15.4 Pressure-Driven Flow: Poiseuille Flow
      5. 15.5 Summary
    8. Chapter 16: Analytical Solutions to Poiseuille Flow Problems in Different Geometries
      1. 16.1 Elliptical and Circular Profiles
      2. 16.2 Planar Infinitesimally Extended Channel Cross-Sections
      3. 16.3 Flows in Circular Cross-Sections: Hagen-Poiseuille Flow
      4. 16.4 Flows in Rectangular Cross-Sections: Solution to Poisson and Laplace Equations
      5. 16.5 Summary
    9. Chapter 17: Hydraulic Resistance
      1. 17.1 Introduction
      2. 17.2 Viscous Dissipation
      3. 17.3 Hydraulic Resistance of Important flow Channel Geometries
      4. 17.4 Simplification Approaches to Hydraulic Resistances
      5. 17.5 Equivalent Circuit Theory
      6. 17.6 Summary
    10. Chapter 18: Analytical Solutions to Transient Flow Problems
      1. 18.1 Time-Dependent Transient Effects: Acceleration and Deceleration
      2. 18.2 Time-Dependent Couette Flow
      3. 18.3 Time-Dependent Hagen-Poiseuille Flow
      4. 18.4 Time-Dependent Flow in Rectangular Cross-Sections
      5. 18.5 Entrance Effects in Hagen-Poiseuille Flow
      6. 18.6 Summary
    11. Chapter 19: Taylor-Aris Dispersion
      1. 19.1 Introduction
      2. 19.2 Dispersion
      3. 19.3 Convection-Diffusion Equation for Cylindrical Cross-Sections
      4. 19.4 Mass Concentration Function
      5. 19.5 Convection-Diffusion Equation
      6. 19.6 Solving for P
      7. 19.7 Solving for P
      8. 19.8 Validity of the Solution
      9. 19.9 Example
      10. 19.10 SUMMARY
  19. III: Fluid Surface Effects
    1. Chapter 20: Surface Tension
      1. 20.1 Fluid Effects at Interfaces
      2. 20.2 Contact Angle Measurement
      3. 20.3 Surfactants
      4. 20.4 Marangoni Effect
      5. 20.5 Summary
    2. Chapter 21: Capillarity
      1. 21.1 Capillary Pressure
      2. 21.2 Capillary Length
      3. 21.3 Meniscus Formation
      4. 21.4 Summary
    3. Chapter 22: Measuring Surface Tension and Free Surface Energy
      1. 22.1 Introduction
      2. 22.2 Measuring the Surface Tension of Liquids
      3. 22.3 MEASURING THE FREE SURFACE ENERGY
      4. 22.4 Summary
    4. Chapter 23: Plateau-Rayleigh Instability
      1. 23.1 Introduction
      2. 23.2 Stability Considerations
      3. 23.3 Fluid Jets
      4. 23.4 Instability
      5. 23.5 Standing Waves on a Fluid Jet
      6. 23.6 Characteristic Breakup Time
      7. 23.7 Applicability of the Plateau-Rayleigh Instability
      8. 23.8 Summary
    5. Chapter 24: The Shape of Drops
      1. 24.1 Introduction
      2. 24.2 Derivation
      3. 24.3 Bashforth and Adams: Curvature Expressed as Z (X)
      4. 24.4 Brien, Ben, and Van den Brule: Curvature Expressed as Function of θ (Sessile Drops)
      5. 24.5 Del Río and Neumann: Curvature Expressed as Function of S (Pendant Drop)
      6. 24.6 Comparison With Experimental Data
      7. 24.7 Drops Inside of a Fluid
      8. 24.8 Historical Development of Drop-Shape Analysis
      9. 24.9 Summary
  20. IV: Numerics
    1. Chapter 25: Numerical Methods for Linear Systems of Equations
      1. 25.1 Introduction
      2. 25.2 Solutions to Linear Systems of Equations
      3. 25.3 Numerical Solutions to Linear Systems of Equations
      4. 25.4 Summary
    2. Chapter 26: Numerical Solutions to Nonlinear Systems: Newton’s Method
      1. 26.1 Introduction
      2. 26.2 An Example: The Loran System
      3. 26.3 Newton’s Method
      4. 26.4 A Solver Implemented in Maple
      5. 26.5 Summary
    3. Chapter 27: Numerical Methods for Solving Differential Equations
      1. 27.1 Introduction
      2. 27.2 Numerical Solutions to Ordinary Differential Equations
      3. 27.3 Numerical Solutions to Higher-Order Ordinary Differential Equations and Systems of Coupled Ordinary Differential Equations
      4. 27.4 Numerical Solutions to Systems of Ordinary Differential Equations with Boundary Conditions
      5. 27.5 Summary
    4. Chapter 28: Numerical Solutions to the Navier-Stokes Equation
      1. 28.1 Introduction
      2. 28.2 Solution to the Poisson Equation
      3. 28.3 Solution to the Poisson Equation Using SOR
      4. 28.4 Summary
    5. Chapter 29: Computational Fluid Dynamics
      1. 29.1 Introduction
      2. 29.2 Galerkin Method
      3. 29.3 Summary
    6. Chapter 30: Finite Difference Method
      1. 30.1 Introduction
      2. 30.2 Advantages and Disadvantages
      3. 30.3 FDM in Microsoft Excel
      4. 30.4 Summary
    7. Chapter 31: Finite Volume Method
      1. 31.1 Introduction
      2. 31.2 Conservative form Notation
      3. 31.3 Integral form of the Conservative Notation
      4. 31.4 Discretization
      5. 31.5 Function Reconstruction
      6. 31.6 Example: One-Dimensional Heat Equation
      7. 31.7 Two-Dimensional Problems of First Order in Time and Space
      8. 31.8 Two-Dimensional Problems of First Order in Time and Second-Order in Space
      9. 31.9 Summary
    8. Chapter 32: Finite Element Method
      1. 32.1 Introduction
      2. 32.2 Discretization
      3. 32.3 Lagrangian Coordinates
      4. 32.4 Basis Functions
      5. 32.5 One-Dimensional Example: Flow in Infinitesimally Extended Channels
      6. 32.6 Two-Dimensional Example: Flow in Rectangular Channels
      7. 32.7 Summary
    9. Chapter 33: Numerical Solutions to Transient Flow Problems
      1. 33.1 Introduction
      2. 33.2 A Numerical Solver for Two-dimensional Time-Dependent Flow Problems
      3. 33.3 A Numerical Solver for Two-Dimensional Entrance Flow Problems
      4. 33.4 Summary
    10. Chapter 34: Numerical Solutions to Three-Dimensional Flow Problems
      1. 34.1 Introduction
      2. 34.2 Derivation
      3. 34.3 Implementation of a Stationary Flow Numerical Solver
      4. 34.4 Usage of the Numerical Solver
      5. 34.5 Summary
  21. Bibliography
  22. Index

Product information

  • Title: Microfluidics: Modeling, Mechanics and Mathematics
  • Author(s): Bastian E. Rapp
  • Release date: December 2016
  • Publisher(s): Elsevier
  • ISBN: 9781455731510