Table of Contents
1.2 A Brief History of Microfluidics
Chapter 2: Introduction to Maple
2.4 The File Corefunctions.txt
Chapter 3: Engineering Mathematics
3.3 Commonly Used Calculus Tricks
6.2 Weights and Concentrations
6.3 Important Terms and Concepts in Thermodynamics
6.5 Idealized Thermodynamic Processes
6.6 First Law of Thermodynamics
6.7 Second Law of Thermodynamics
6.8 Third Law of Thermodynamics
7.2 Important Theorems in Vector Calculus
7.3 Coordinate System Transformation
7.4 Position, Velocity, and Acceleration
7.6 Operators Transformed into the different Coordinate Systems
Chapter 8: Differential Equations
8.1 Important Differential Equations
8.2 General Solutions to Selected Ordinary Differential Equations
8.3 General Solutions to Selected Partial Differential Equations
9.2 Solids, Liquids, and Gases at the Atomic Scale
Chapter 10: Conservation of Mass: The Continuity Equation
10.3 Integral Representation of the Flowrate
10.5 Derivation using Gauss’s Theorem
10.6 Combined Convection and Diffusion: The Convection-Diffusion Equation
Chapter 11: Conservation of Momentum: The Navier-Stokes Equation
11.2 Momentum Transfer Into and Out of a Control Volume
11.3 Momentum by in- and Outflowing Mass
11.5 Momentum by Volume Forces
11.7 Navier-Stokes Equation for Incompressible Newtonian Fluids
Chapter 12: Conservation of Energy: The Energy Equation and the Thermodynamic Equation of State
12.2 Energy Transfer by Convection
12.4 Work Flow by Boundary Forces
12.5 Heat Flow by Volume Effects
12.6 Work Flow by Volume Forces
12.8 Thermodynamic Equation of State
Chapter 13: Continuity and Navier-Stokes Equations in Different Coordinate Systems
Chapter 14: The Circular Flow Tube
14.2 Conservation of Mass: The Continuity Equation
14.3 Conservation of Momentum: The Navier-Stokes Equation
14.7 Deriving the Euler Equation by a Coordinate System Transformation
Chapter 15: Analytical Solutions to the Navier-Stokes Equation
15.1 Hydrostatics and Aerostatics
15.2 Shear Force-Driven Flow: Couette Flow
15.4 Pressure-Driven Flow: Poiseuille Flow
Chapter 16: Analytical Solutions to Poiseuille Flow Problems in Different Geometries
16.1 Elliptical and Circular Profiles
16.2 Planar Infinitesimally Extended Channel Cross-Sections
16.3 Flows in Circular Cross-Sections: Hagen-Poiseuille Flow
16.4 Flows in Rectangular Cross-Sections: Solution to Poisson and Laplace Equations
Chapter 17: Hydraulic Resistance
17.3 Hydraulic Resistance of Important flow Channel Geometries
17.4 Simplification Approaches to Hydraulic Resistances
17.5 Equivalent Circuit Theory
Chapter 18: Analytical Solutions to Transient Flow Problems
18.1 Time-Dependent Transient Effects: Acceleration and Deceleration
18.2 Time-Dependent Couette Flow
18.3 Time-Dependent Hagen-Poiseuille Flow
18.4 Time-Dependent Flow in Rectangular Cross-Sections
18.5 Entrance Effects in Hagen-Poiseuille Flow
Chapter 19: Taylor-Aris Dispersion
19.3 Convection-Diffusion Equation for Cylindrical Cross-Sections
19.4 Mass Concentration Function
19.5 Convection-Diffusion Equation
20.1 Fluid Effects at Interfaces
20.2 Contact Angle Measurement
Chapter 22: Measuring Surface Tension and Free Surface Energy
22.2 Measuring the Surface Tension of Liquids
22.3 MEASURING THE FREE SURFACE ENERGY
Chapter 23: Plateau-Rayleigh Instability
23.5 Standing Waves on a Fluid Jet
23.6 Characteristic Breakup Time
23.7 Applicability of the Plateau-Rayleigh Instability
Chapter 24: The Shape of Drops
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
24.8 Historical Development of Drop-Shape Analysis
Chapter 25: Numerical Methods for Linear Systems of Equations
25.2 Solutions to Linear Systems of Equations
25.3 Numerical Solutions to Linear Systems of Equations
Chapter 26: Numerical Solutions to Nonlinear Systems: Newton’s Method
26.2 An Example: The Loran System
26.4 A Solver Implemented in Maple
Chapter 27: Numerical Methods for Solving Differential Equations
27.2 Numerical Solutions to Ordinary Differential Equations
27.4 Numerical Solutions to Systems of Ordinary Differential Equations with Boundary Conditions
Chapter 28: Numerical Solutions to the Navier-Stokes Equation
28.2 Solution to the Poisson Equation
28.3 Solution to the Poisson Equation Using SOR
Chapter 29: Computational Fluid Dynamics
Chapter 30: Finite Difference Method
30.2 Advantages and Disadvantages
Chapter 31: Finite Volume Method
31.2 Conservative form Notation
31.3 Integral form of the Conservative Notation
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
Chapter 32: Finite Element Method
32.5 One-Dimensional Example: Flow in Infinitesimally Extended Channels
32.6 Two-Dimensional Example: Flow in Rectangular Channels
Chapter 33: Numerical Solutions to Transient Flow Problems
33.2 A Numerical Solver for Two-dimensional Time-Dependent Flow Problems
33.3 A Numerical Solver for Two-Dimensional Entrance Flow Problems
Chapter 34: Numerical Solutions to Three-Dimensional Flow Problems
34.3 Implementation of a Stationary Flow Numerical Solver