- Cover image
- Title page
- Table of Contents
- Copyright
- Dedication
- Preface
- Acknowledgement
- List of Figures
- List of Tables
- List of Listings
- List of Acronyms
- List of Abbreviations
- List of Symbols
- List of Constants
- List of Chemicals
- Conversions
- I: Fundamentals
- II: Bulk Fluid Flows
- Chapter 9: Fluids
- Chapter 10: Conservation of Mass: The Continuity Equation
- Chapter 11: Conservation of Momentum: The Navier-Stokes Equation
- 11.1 Introduction
- 11.2 Momentum Transfer Into and Out of a Control Volume
- 11.3 Momentum by in- and Outflowing Mass
- 11.4 Momentum by Shear Forces
- 11.5 Momentum by Volume Forces
- 11.6 Balance of Momentum
- 11.7 Navier-Stokes Equation for Incompressible Newtonian Fluids
- 11.8 Dimensional Analysis
- 11.9 Conclusion
- Chapter 12: Conservation of Energy: The Energy Equation and the Thermodynamic Equation of State
- Chapter 13: Continuity and Navier-Stokes Equations in Different Coordinate Systems
- Chapter 14: The Circular Flow Tube
- Chapter 15: Analytical Solutions to the Navier-Stokes Equation
- Chapter 16: Analytical Solutions to Poiseuille Flow Problems in Different Geometries
- Chapter 17: Hydraulic Resistance
- Chapter 18: Analytical Solutions to Transient Flow Problems
- Chapter 19: Taylor-Aris Dispersion
- III: Fluid Surface Effects
- Chapter 20: Surface Tension
- Chapter 21: Capillarity
- Chapter 22: Measuring Surface Tension and Free Surface Energy
- Chapter 23: Plateau-Rayleigh Instability
- Chapter 24: The Shape of Drops
- 24.1 Introduction
- 24.2 Derivation
- 24.3 Bashforth and Adams: Curvature Expressed as Z (X)
- 24.4 Brien, Ben, and Van den Brule: Curvature Expressed as Function of θ (Sessile Drops)
- 24.5 Del Río and Neumann: Curvature Expressed as Function of S (Pendant Drop)
- 24.6 Comparison With Experimental Data
- 24.7 Drops Inside of a Fluid
- 24.8 Historical Development of Drop-Shape Analysis
- 24.9 Summary
- IV: Numerics
- Chapter 25: Numerical Methods for Linear Systems of Equations
- Chapter 26: Numerical Solutions to Nonlinear Systems: Newton’s Method
- Chapter 27: Numerical Methods for Solving Differential Equations
- 27.1 Introduction
- 27.2 Numerical Solutions to Ordinary Differential Equations
- 27.3 Numerical Solutions to Higher-Order Ordinary Differential Equations and Systems of Coupled Ordinary Differential Equations
- 27.4 Numerical Solutions to Systems of Ordinary Differential Equations with Boundary Conditions
- 27.5 Summary
- Chapter 28: Numerical Solutions to the Navier-Stokes Equation
- Chapter 29: Computational Fluid Dynamics
- Chapter 30: Finite Difference Method
- Chapter 31: Finite Volume Method
- 31.1 Introduction
- 31.2 Conservative form Notation
- 31.3 Integral form of the Conservative Notation
- 31.4 Discretization
- 31.5 Function Reconstruction
- 31.6 Example: One-Dimensional Heat Equation
- 31.7 Two-Dimensional Problems of First Order in Time and Space
- 31.8 Two-Dimensional Problems of First Order in Time and Second-Order in Space
- 31.9 Summary
- Chapter 32: Finite Element Method
- Chapter 33: Numerical Solutions to Transient Flow Problems
- Chapter 34: Numerical Solutions to Three-Dimensional Flow Problems
- Bibliography
- Index
Microfluidics: Modeling, Mechanics, and Mathematics
Bastian E. Rapp
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