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The Microfluidics Module User's Guide

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The Microfluidics Module User's Guide Microfluidics Module User’s Guide Microfluidics Module User’s Guide © 1998–2017 COMSOL Protected by U.S. Patents listed on www.comsol.com/patents, and U.S. Patents 7,519,518; 7,596,474; 7,623,991; 8,457,932; 8,954,302; 9,098,106; 9,146,652; 9,323,503; 9,372,673; and 9,454,625. Patents pending. This Documentation and the Programs described herein are furnished under the COMSOL Software License Agreement (www.comsol.com/comsol-license-agreement) and may be used or copied only under the terms of the license agreement. COMSOL, the COMSOL logo, COMSOL Multiphysics, Capture the Concept, COMSOL Desktop, LiveLink, and COMSOL Server are either registered trademarks or trademarks of COMSOL AB. All other trademarks are the property of their respective owners, and COMSOL AB and its subsidiaries and products are not affiliated with, endorsed by, sponsored by, or supported by those trademark owners. For a list of such trademark owners, see www.comsol.com/trademarks. Version: COMSOL 5.3 Contact Information Visit the Contact COMSOL page at www.comsol.com/contact to submit general inquiries, contact Technical Support, or search for an address and phone number. You can also visit the Worldwide Sales Offices page at www.comsol.com/contact/offices for address and contact information. If you need to contact Support, an online request form is located at the COMSOL Access page at www.comsol.com/support/case. Other useful links include: • Support Center: www.comsol.com/support • Product Download: www.comsol.com/product-download • Product Updates: www.comsol.com/support/updates • COMSOL Blog: www.comsol.com/blogs • Discussion Forum: www.comsol.com/community • Events: www.comsol.com/events • COMSOL Video Gallery: www.comsol.com/video • Support Knowledge Base: www.comsol.com/support/knowledgebase Part number: CM021901 Contents Chapter 1: Introduction About the Microfluidics Module 14 About Microfluidics . 14 About the Microfluidics Module . 15 The Microfluidics Module Physics Interface Guide . 15 Coupling to Other Physics Interfaces . 18 The Microfluidics Module Study Capabilities by Physics Interface . 19 Common Physics Interface and Feature Settings and Nodes. 20 The Liquids and Gases Materials Database . 21 Where Do I Access the Documentation and Application Libraries? . 21 Overview of the User’s Guide 25 Chapter 2: Microfluidic Modeling Physics and Scaling in Microfluidics 28 Dimensionless Numbers in Microfluidics 31 Dimensionless Numbers Important for Solver Stability . 31 Other Dimensionless Numbers . 33 Modeling Microfluidic Fluid Flows 36 Selecting the Right Physics Interface. 36 Single-Phase Flow. 37 Multiphase Flow . 39 Porous Media Flow . 40 The Relationship Between the Physics Interfaces . 43 Modeling Coupled Phenomena in Microfluidics 45 Chemical Transport and Reactions . 45 Electrohydrodynamics . 47 CONTENTS | 3 Heat Transfer . 54 Coupling to Other Physics Interfaces . 56 Modeling Rarefied Gas Flows 57 The Flow Regimes . 57 Slip Flow . 58 References for the Theory of Microfluidics . 59 Chapter 3: Single-Phase Flow Interfaces The Laminar Flow and Creeping Flow Interfaces 62 The Creeping Flow Interface . 62 The Laminar Flow Interface . 63 Domain, Boundary, Pair, and Point Nodes for Single-Phase Flow . 68 Fluid Properties . 68 Volume Force . 70 Initial Values. 71 Wall. 71 Inlet. 74 Outlet . 77 Symmetry . 78 Open Boundary . 79 Boundary Stress . 80 Periodic Flow Condition . 81 Pipe Connection. 82 Flow Continuity . 82 Pressure Point Constraint . 83 Point Mass Source . 83 Line Mass Source . 84 Gravity . 85 Theory for the Single-Phase Flow Interfaces 86 General Single-Phase Flow Theory . 87 Compressible Flow . 89 Weakly Compressible Flow . 89 The Mach Number Limit . 89 4 | CONTENTS Incompressible Flow . 90 The Reynolds Number. 91 Non-Newtonian Flow: The Power Law and the Carreau Model . 92 The Boussinesq Approximation . 93 Theory for the Wall Boundary Condition . 94 Prescribing Inlet and Outlet Conditions . 98 Laminar Inflow. 99 Laminar Outflow . 100 Mass Flow . 101 No Viscous Stress . 102 Normal Stress Boundary Condition. 102 Pressure Boundary Condition . 103 Mass Sources for Fluid Flow . 105 Numerical Stability — Stabilization Techniques for Fluid Flow . 107 Solvers for Laminar Flow . 108 Pseudo Time Stepping for Laminar Flow Models . 111 Discontinuous Galerkin Formulation . 112 Particle Tracing in Fluid Flow . 113 References for the Single-Phase Flow, Laminar Flow Interfaces. 114 Chapter 4: Multiphase Flow, Two-Phase Flow Interfaces The Laminar Two-Phase Flow, Level Set and Laminar Two-Phase Flow, Phase Field Interfaces 118 The Laminar Two-Phase Flow, Level Set Interface . 118 The Turbulent Two-Phase Flow, Level Set Interface . 119 Two-Phase Flow, Level Set Coupling Features . 120 The Wetted Wall Coupling Feature . 122 The Laminar Two-Phase Flow, Phase Field Interface . 124 The Turbulent Two-Phase Flow, Phase Field Interface . 125 The Two-Phase Flow, Phase Field Coupling Features . 126 Domain, Boundary, Point, and Pair Nodes for the Laminar Flow, Two-Phase, Level Set and Phase Field Interfaces . 128 CONTENTS | 5 The Laminar Three-Phase Flow, Phase Field Interface 129 The Laminar Three-Phase Flow, Phase Field Interface . 129 The Three-Phase Flow, Phase Field Coupling Feature . 130 Domain, Boundary, Point, and Pair Nodes for the Laminar Three-Phase Flow, Phase Field Interface . 131 The Laminar Two-Phase Flow, Moving Mesh Interface 133 Domain, Boundary, Edge, Point, and Pair Nodes for the Laminar Two-Phase Flow, Moving Mesh Interface . 135 Free Deformation . 137 Prescribed Mesh Displacement . 137 Initial Values. 138 Fixed Mesh . 138 Prescribed Mesh Velocity . 138 Fluid-Fluid Interface . 139 External Fluid Interface . 140 Wall. 141 Wall-Fluid Interface . 143 Navier Slip . 144 Theory for the Level Set and Phase Field Interfaces 146 Level Set and Phase Field Equations . 146 Conservative and Nonconservative Formulations . 149 Phase Initialization . 149 Numerical Stabilization . 151 References for the Level Set and Phase Field Interfaces . 151 Theory for the Three-Phase Flow, Phase Field Interface 152 Governing Equations of the Three-Phase Flow, Phase Field Interface . 152 Reference for the Three-Phase Flow, Phase Field Interface . 155 Theory for the Two Phase Flow Moving Mesh Interface 156 Domain Level Fluid Flow . 156 About the Moving Mesh . 157 About the Fluid Interface Boundary Conditions . 158 Wall Fluid Interface Boundary Conditions . 162 References for the Two-Phase Flow, Moving Mesh Interface. 163 6 | CONTENTS Chapter 5: Mathematics, Moving Interfaces The Level Set Interface 166 Domain, Boundary, and Pair Nodes for the Level Set Interface . 167 Level Set Model . 167 Initial Values. 168 Inlet. 169 Initial Interface. 169 No Flow . 169 The Phase Field Interface 170 Domain, Boundary, and Pair Nodes for the Phase Field Interface . 171 Phase Field Model . 171 Initial Values. 172 Inlet. 173 Initial Interface. 174 Wetted Wall . 174 The Ternary Phase Field Interface 175 Domain, Boundary, and Pair Nodes for the Ternary Phase Field Interface. 176 Mixture Properties . 176 Initial Values. 177 Inlet. 177 Outlet . 178 Symmetry . 178 Wetted Wall . 178 Theory for the Level Set Interface 180 The Level Set Method . 180 Conservative and Non-Conservative Form . 182 Initializing the Level Set Function . 182 Variables For Geometric Properties of the Interface . 183 Reference for the Level Set Interface . 184 Theory for the Phase Field Interface 185 About the Phase Field Method. 185 CONTENTS | 7 The Equations for the Phase Field Method . 185 Conservative and Non-Conservative Forms . 187 Additional Sources of Free Energy . 187 Initializing the Phase Field Function . 188 Variables and Expressions . 188 Reference for the Phase Field Interface . 189 Theory for the Ternary Phase Field interface 190 About the Phase Field Method. 190 The Equations of the Ternary Phase Field Method . 190 Reference for the Ternary Phase Field Interface . 192 Chapter 6: Porous Media Flow Interfaces The Darcy’s Law Interface 194 Domain, Boundary, Edge, Point, and Pair Nodes for the Darcy’s Law Interface . 195 Fluid and Matrix Properties . 197 Mass Source . 198 Initial Values. 198 Pressure . 198 Mass Flux. 199 Inlet. 199 Symmetry . 199 No Flow . ..
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