Microfluidics Module User’s Guide Microfluidics Module User’s Guide © 1998–2018 COMSOL Protected by 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, COMSOL Desktop, COMSOL Server, and LiveLink 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 5.4 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 . 42 Modeling Coupled Phenomena in Microfluidics 44 Chemical Transport and Reactions . 44 Electrohydrodynamics . 46 CONTENTS | 3 Heat Transfer . 53 Coupling to Other Physics Interfaces . 55 Modeling Rarefied Gas Flows 56 The Flow Regimes . 56 Slip Flow . 57 References for the Theory of Microfluidics . 58 Chapter 3: Single-Phase Flow Interfaces The Laminar Flow and Creeping Flow Interfaces 60 The Creeping Flow Interface . 60 The Laminar Flow Interface . 61 Fluid Properties . 66 Volume Force . 69 Initial Values . 69 Wall . 70 Inlet. 72 Outlet . 75 Symmetry . 77 Open Boundary . 78 Boundary Stress . 78 Periodic Flow Condition . 80 Flow Continuity . 81 Pressure Point Constraint . 81 Point Mass Source . 81 Line Mass Source. 82 Gravity . 83 Theory for the Single-Phase Flow Interfaces 85 General Single-Phase Flow Theory . 86 Compressible Flow . 88 Weakly Compressible Flow . 88 The Mach Number Limit . 88 Incompressible Flow . 89 The Reynolds Number. 90 4 | CONTENTS Non-Newtonian Flow . 91 Theory for the Wall Boundary Condition . 93 Prescribing Inlet and Outlet Conditions . 97 Mass Flow . 98 Fully Developed Flow (Inlet) . 100 Fully Developed Flow (Outlet). 101 No Viscous Stress . 102 Normal Stress Boundary Condition . 103 Pressure Boundary Condition . 103 Mass Sources for Fluid Flow . 105 Numerical Stability — Stabilization Techniques for Fluid Flow . 107 Solvers for Laminar Flow . 109 Pseudo Time Stepping for Laminar Flow Models . 111 Discontinuous Galerkin Formulation . 113 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 T he Two-Phase Flow, Level Set Coupling Feature . 119 The Wetted Wall Coupling Feature. 122 The Laminar Two-Phase Flow, Phase Field Interface . 124 The Two-Phase Flow, Phase Field Coupling Feature. 124 Domain, Boundary, Point, and Pair Nodes for the Laminar Flow, Two-Phase, Level Set and Phase Field Interfaces. 127 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 . 132 CONTENTS | 5 The Laminar Two-Phase Flow, Moving Mesh Interface 134 Select Laminar Flow Properties . 135 Deforming Domain . 135 Fluid-Fluid Interface . 136 External Fluid Interface . 137 Wall-Fluid Interface . 139 Theory for the Level Set and Phase Field Interfaces 141 Level Set and Phase Field Equations . 141 Conservative and Nonconservative Formulations . 144 Phase Initialization . 145 Numerical Stabilization . 146 References for the Level Set and Phase Field Interfaces . 146 Theory for the Three-Phase Flow, Phase Field Interface 148 Governing Equations of the Three-Phase Flow, Phase Field Interface . 148 Reference for the Three-Phase Flow, Phase Field Interface . 151 Theory for the Two-Phase Flow, Moving Mesh Interface 152 Domain Level Fluid Flow . 152 About the Moving Mesh . 153 About the Fluid Interface Boundary Conditions . 154 Wall-Fluid Interface Boundary Conditions . 158 References for the Two-Phase Flow, Moving Mesh Interface . 159 Chapter 5: Mathematics, Moving Interfaces The Level Set Interface 162 Domain, Boundary, and Pair Nodes for the Level Set Interface . 163 Level Set Model . 164 Initial Values . 164 Inlet. 165 Initial Interface. 166 No Flow . 166 Thin Barrier. 166 6 | CONTENTS The Phase Field Interface 167 Domain, Boundary, and Pair Nodes for the Phase Field Interface. 168 Phase Field Model . 169 Initial Values . 170 Inlet. 171 Initial Interface. 171 Wetted Wall . 171 Interior Wetted Wall . 172 The Ternary Phase Field Interface 173 Domain, Boundary, and Pair Nodes for the Ternary Phase Field Interface. 174 Mixture Properties . 174 Initial Values . 176 Inlet. 176 Outlet . 176 Symmetry . 177 Wetted Wall . 177 Theory for the Level Set Interface 179 The Level Set Method . 179 Conservative and Nonconservative Form . 181 Initializing the Level Set Function . 182 Variables For Geometric Properties of the Interface . 182 Reference for the Level Set Interface . 183 Theory for the Phase Field Interface 184 About the Phase Field Method. 184 The Equations for the Phase Field Method . 184 Conservative and Nonconservative Forms . 186 Additional Sources of Free Energy . 187 Initializing the Phase Field Function . 187 Variables and Expressions . 188 Reference for the Phase Field Interface . 188 Theory for the Ternary Phase Field Interface 189 About the Phase Field Method. 189 The Equations of the Ternary Phase Field Method . 189 CONTENTS | 7 Reference for the Ternary Phase Field Interface . 191 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 . 200 No Flow . 200 Flux Discontinuity . 200 Outlet . 201 Cross Section . 201 Thickness. 202 The Brinkman Equations Interface 203 Domain, Boundary, Point, and Pair Nodes for the Brinkman Equations Interface. 205 Fluid and Matrix Properties . 206 Forchheimer Drag . 207 Mass Source . ..