Transport and Mixing in Laminar Flows: From Microfluidics to Oceanic Currents

This book provides readers from academia and industry with an up–to–date overview of important advances in the field, dealing with such fundamental fluid mechanics problems as nonlinear transport phenomena and optimal control of mixing at the micro– and nanoscale.
The editors provide both in–depth knowledge of the topic as well as vast experience in guiding an expert team of authors. The review style articles offer a coherent view of the micromixing methods, resulting in a much–needed synopsis of the theoretical models needed to direct experimental research and establish engineering principles for future applications.
Since these processes are governed by nonlinear phenomena, this book will appeal to readers from both communities: fluid mechanics and nonlinear dynamics.


Spis treści:
List of Contributors IX
Mixing in Laminar Fluid Flows: From Microfluidics to Oceanic Currents 1
Roman O. Grigoriev
Introduction 1
1 Resonances and Mixing in Near–Integrable Volume–Preserving Systems 5
Dmitri Vainchtein
1.1 Introduction 5
1.2 General Properties of Near–Integrable Flows and Different Types of the Resonance Surfaces 8
1.2.1 Metrics of Mixing 10
1.2.2 Correlations of Successive Jumps and Ergodicity 12
1.3 Separatrix Crossings in Volume–Preserving Systems 12
1.3.1 Flow Structure 14
1.3.2 Dynamics Near the Separatrix Surface 15
1.3.3 Finite Perturbations 16
1.4 Passages Through Resonances in Autonomous Flows 17
1.4.1 Scattering on Resonance 19
1.4.2 Capture Into Resonance 20
1.4.3 Improved AI 21
1.4.4 Jump of AI Between First– and Second–Layer Boundaries 22
1.4.5 Long–Time Dynamics and Adiabatic Diffusion 23
1.5 Passages Through Resonances in Nonautonomous Flows 24
1.5.1 Unperturbed Flow 25
1.5.2 Two Perturbations and Averaging 26
1.5.3 Resonant Phenomena 27
1.5.4 Vo lume of the Mixing Domain 29
References 31
2 Fluid Stirring in a Tilted Rotating Tank 35
Thomas Ward
2.1 Introduction and Background Information 35
2.2 Tilted–Rotating Tank Analysis 38
2.2.1 Tilted–Rotating Tank Model Equation 38
2.2.1.1 Asymptotic Analysis: Free Surface Vortex 40
2.2.1.2 Linear Analysis: Periodic Shearing 42
2.2.2 Comments on Laminar Flow 44
2.2.3 Analytical Results 45
2.3 Experiments 47
2.3.1 Setup and Procedure 47
2.3.1.1 Low Reynolds Number Experiments: Homogeneous Fluid 47
2.3.1.2 Laminar Flow Experiments: Homogeneous and Inhomogeneous Fluids 48
2.3.2 Results and Analysis 49
2.3.2.1 Low Reynolds Number 49
2.3.2.2 Laminar Flow: Homogeneous Fluid 51
2.3.2.3 Laminar Flow: Inhomogeneous Fluid 53
2.3.3 Brief Discussion 55
2.4 Conclusion 55
References 56
3 Lagrangian Coherent Structures 59
Shawn C. Shadden
3.1 Introduction 59
3.2 Background 61
3.3 Global Approach 64
3.3.1 FTLE 65
3.3.2 FTLE Ridges 67
3.3.3 Nature of Stretching 68
3.3.4 Objectivity 71
3.4 Computational Strategy 72
3.4.1 Grid–Based Computation 74
3.4.2 Integration Time 75
3.4.3 LCS Extraction 79
3.5 Robustness 82
3.6 Applications 83
3.7 Conclusions 83
References 84
4 Interfacial Transfer from Stirred Laminar Flows 91
Joseph D. Kirtland and Abraham D. Stroock
4.1 Introduction 91
4.2 Phenomena and Definitions 92
4.3 Experimental Methods 95
4.3.1 Protein Binding 95
4.3.2 Electrochemical Reactions 95
4.3.3 Heat Transfer from Macroscopic Coiled Pipe 97
4.3.4 Interphase Mass Transfer from Droplets 98
4.3.5 Summary of Experimental Observations 99
4.4 Modeling Approaches 100
4.4.1 Numerical Solutions in Eulerian Frame 100
4.4.2 Numerical Solutions in Lagrangian Frame 101
4.4.3 Macrotransport Approach 103
4.4.4 Theoretical Approaches 103
4.5 Conclusions 1 07
References 107
5 The Effects of Laminar Mixing on Reaction Fronts and Patterns 111
Tom Solomon
5.1 Introduction 111
5.2 Background 113
5.2.1 Laminar mixing – the Advection–Diffusion Equation 113
5.2.2 Short–Range Mixing 113
5.2.3 Long–Range Transport of Impurities 115
5.2.4 Nonlinear Reactions 117
5.2.5 Reaction–Diffusion Systems 117
5.3 Advection–Reaction–Diffusion: General Principles 118
5.4 Local Behavior of ARD Systems 120
5.5 Synchronization of Oscillating Reactions 122
5.6 Front Propagation in ARD Systems 125
5.7 Additional Comments 127
References 128
6 Microfluidic Flows of Viscoelastic Fluids 131
Mónica S. N. Oliveira, Manuel A. Alves, and Fernando T. Pinho
6.1 Introduction 131
6.1.1 Objectives and Organization of the Chapter 131
6.1.2 Microfluidics 131
6.1.2.1 Basic Principles, Relevance, and Applications 131
6.1.2.2 Complex Fluids in Microfluidic Flows 135
6.1.2.3 Continuum Approximation 136
6.2 Mixing in Microfluidics 138
6.2.1 Challenges of Micromixing 138
6.2.2 Overview of Methods for Micromixing Enhancement 139
6.3 Non–Newtonian Viscoelastic Fluids 141
6.3.1 Shear Viscosity 142
6.3.2 Normal Stresses 143
6.3.3 Storage and Loss Moduli 144
6.3.4 Extensional Viscosity 144
6.3.5 Other Rheological Properties 145
6.4 Governing Equations 146
6.4.1 Continuity and Momentum Equations 146
6.4.2 Rheological Constitutive Equation 147
6.4.2.1 Generalized Newtonian Fluid Model 148
6.4.2.2 Viscoelastic Stress Models 148
6.4.3 Equations for Electro–Osmosis 151
6.4.4 Thermal Energy Equation 153
6.5 Passive Mixing for Viscoelastic Fluids: Purely Elastic Flow Instabilities 154
6.5.1 General Considerations 154
6.5.2 The Underlying Physics 155
6.5.3 Viscoelastic Instabilities in Some Canonical Flows 156
6.5.4 Elastic Turbulence 160
6.6 Other Forcing Methods – Applications 162
6.6.1 Electro–Osmosis 162
6.6.2 Electrophoresis 164
6.7 Conclusions and Perspectives 165
References 166
Index 175

Nota biograficzna:
Roman Grigoriev got his PhD at the California Institute of Technology and became a Research Associate at the University of Chicago before he moved to Georgia Tech. Professor Grigoriev′s research on nonequilibrium systems such as fluids, lasers and living systems ranges from mixing in fluids, thin liquid films and wide aperture lasers to the heart muscle.
Heinz Georg Schuster is Professor of Theoretical Physics at the University of Kiel in Germany. He was a visiting professor at the Weizmann–Institute of Science in Israel and at the California Institute of Technology in Pasadena, USA. He authored and edited many books on nonlinear phenomena and chaos control.