Open Microfluidics

Jean Berthier is a scientist at the CEA/LETI and teaches at the University of Grenoble. He received an engineering diploma from the Institut National Polytechnique, and an MS in mathematics from the University of Grenoble, France. He is presently involved in the development of microdevices for liquid-liquid extraction (LLE), flow focusing devices (FFD) for bio-encapsulation of live cells, microfluidic resonators for high sensitivity biodetection and numerical methods for the prediction of droplets and interfaces behavior in microsystems.He is the first author of the book The Physics of Microdroplets (Wiley-Scrivener 2012). Kenneth Brakke is Professor of Mathematics and Computer Science at Susquehanna University in Pennsylvania. He received his PhD in Mathematics from Princeton University, in the field of Geometric Measure Theory. Since 1988 he has written and maintained his freely-available Surface Evolver software, which shows computer models of liquid surfaces. He is the second author of the book The Physics of Microdroplets (Wiley-Scrivener 2012). Erwin Berthier is the VP of R&D of Tasso, Inc, a biotechnology startup that is developing blood sample collection and analysis technologies based on open microfluidic concepts as well as an affiliate professor in the Department of Chemistry at the University of Washington. He has received a PhD in Biomedical Engineering at the University of Wisconsin-Madison where he became an expert in user-centered microfluidic technologies. His believes that technologies must be made simpler to disseminate, be widely adopted, and find killer applications.

• Acknowledgements xiPreface xiiiOnline Materials xvIntroduction 11 Theory of Spontaneous Capillary Flows 131.1 Introduction 131.2 Quasi-static Approach to SCF 161.2.1 Open and Confined Systems 171.2.2 Theoretical Approach 171.2.3 Numerical Approach 211.2.3.1 Numerical Verification of the Capillary Force 221.2.3.2 Composite Confined Channel 221.2.3.3 Composite Open Channel 231.2.3.4 Fiber Bundle 241.2.3.5 Usual Geometries 271.2.3.6 Conclusion 271.2.4 Dynamic Aspects 271.2.4.1 Generalization of the Lucas-Washburn-Rideal Law to Composite, Confined Microchannels of Arbitrary Cross-section 301.2.4.2 Theory 301.2.4.3 Magnitude of Capillary Velocities 361.2.4.4 Experimental Results for Confined Channels 381.2.4.5 Conclusion 391.3 The Dynamics of Spontaneous Capillary Flows in Open-surface Channels 401.3.1 The Dynamics of SCF 401.3.2 Confined Rectangular Channels 421.3.3 Open Rectangular U-grooves 441.3.4 Suspended Rectangular Channels 451.3.5 Experiments 461.3.6 Comparison 461.4 Dynamic Contact Angle 491.5 Conclusion 531.6 References 532 Capillary Filaments 572.1 Introduction 572.2 Concus-Finn Theory 572.2.1 Numerical Approach 602.2.2 Example of Capillary Filaments in a Micro-beaker 602.2.3 Example of a Capillary Filament in a Micro Petri Dish 602.2.4 Extended Concus-Finn Relation 622.2.5 Capillary Filaments in a Non-ideal Corner 632.3 Capillary Filaments in Rectangular U-grooves 652.3.1 Capillary Flow Regimes with No Capillary Filaments (> 45°) 662.3.2 Capillary Flow Regimes with Capillary Filaments (<45°) 662.3.2.1 SCF Self-dividing into Filaments 672.3.2.2 Initially Separated Concus-Finn Filaments 692.3.2.3 Metastability of CF Filaments 702.3.2.4 Discussion 722.3.2.5 Imperfect Grooves 732.3.3 Example of a Varying Cross-sectional Area Channel 732.4 Capillary Filaments in V-grooves 742.4.1 Perfect V-grooves 742.4.2 Imperfect V-grooves 752.4.3 Parallel V-grooves 772.4.4 Imperfect Groovy Surface 792.5 Examples of Capillary Filaments 812.5.1 Capillary Filling of PCR Devices 822.5.2 Whole Blood Capillary Flow in V-grooves 822.6 Conclusions 852.7 References 86Appendix 2.1 Capillary Flow in a Cylindrical Cavity 883 Spontaneous Capillary Flows in Open U-grooves 913.1 Introduction: SCF in Open “U-grooves” 913.2 Quasi-static Approach 923.3 Bulk SCF in Uniform Cross-section U-grooves 933.3.1 Single Wall Wettability 933.3.1.1 Theoretical Approach 933.3.1.2 Evolver Numerical Approach 973.3.2 Composite Walls 973.3.2.1 Rectangular Open Channel 983.3.2.2 Trapezoidal Open Channel 993.3.2.3 Roll-embossed Channel 1003.4 Slightly Pressurized Open-surface Capillary Flow 1003.5 SCF in Winding Channels 1023.5.1 SCF in Winding, Open Channels, > 45° 1033.5.2 Concus-Finn Filaments in Sharp Curves, > 45° 1033.6 Extrapolation to the Coiling of the Flow Around a Curved Corner 1043.7 Converging U-channels 1053.8 Diverging U-channels 1053.8.1 No CF Filaments 1063.8.2 CF Filaments 1083.9 U-groove with a Sudden Enlargement 1083.9.1 Smooth Enlargement 1093.9.2 Enlargement with Sharp Edges 1103.9.3 U-groove Exiting into a Cylinder 1123.9.4 U-groove Crossing a Polygonal Cavity 1133.10 Open Capillary Valves 1143.10.1 Capillary Stop Valves 1143.10.2 Trigger Valves 1153.11 Bifurcation 1163.12 Capillary Filtration 1183.13 Capillary Flow Mixing 1193.14 Generalization: Substrate Patterned with Parallel Rectangular U-grooves 1193.14.1 Substrate Patterned with U-grooves 1193.14.2 Open, Rectangular U-groove with Sub-grooves in the Bottom Plate 1203.14.3 Applications 1213.15 Conclusion 1213.16 References 1224 Dynamics of Capillary Flow in a Channel with Constrictions and Enlargements 1254.1 Introduction 1254.2 Channel Constriction and Enlargement 1264.2.1 Theory 1264.2.2 Numerical Results and Discussion 1304.2.2.1 Straight Channel 1314.2.2.2 Channel with a Constricted Section 1314.2.2.3 Channel with an Enlarged Section 1324.2.3 Experimental Results 1344.2.3.1 Constriction 1354.2.3.2 Enlargement 1364.2.4 Conclusion 1374.3 SCF in a U-groove with Multiple Change of Cross-section 1374.3.1 Theoretical Approach 1384.3.2 Experimental Approach 1404.3.2.1 Winding Open Rectangular U-groove 1404.3.2.2 Open Rectangular U-groove with Constricted Sections 1414.3.2.3 Open Rectangular U-groove with Cylindrical Chambers 1444.3.3 Comparison with the Numerical Approach 1454.4 Conclusion 1464.5 References 149Appendix 4.1 Velocity Model for Open Rectangular Channels 150Appendix 4.2 Velocity Model for Cylindrical Tubes 152Appendix 4.3 Friction in a Rectangular Open Channel 1555 Suspended Capillary Flows 1575.1 Introduction 1575.2 Theory 1585.3 Quasi-static Numerical Approach 1595.3.1 Effect of Gravity 1625.4 Dynamic Approach 1625.4.1 Closed-form Expression of the Velocity for Newtonian Fluids 1625.4.2 Channel Characteristics Corresponding to Maximum Velocities 1645.4.3 Examples from Experiments 1665.4.3.1 Suspended Channel Fabrication 1675.4.3.2 Preparation of the Solutions and Liquid Characterization 1685.4.3.3 Tinted Water 1685.4.3.4 IPA Solutions 1695.4.3.5 Whole Blood 1695.4.3.6 Alginate Solutions 1715.5 Comparison of a U-channel and a Suspended Channel 1745.6 Suspended Microfluidics in Channels of Varying Section 1755.6.1 Diverging Straight Walls 1755.6.2 Sudden Enlargement of Suspended Channels 1795.6.2.1 Quasi-static Approach 1795.6.2.2 Dynamic Approach 1835.6.3 Converging Suspended Channels 1835.6.4 X-shape Suspended Channels 1845.7 Capillary Flow in a Suspended Tapering Channel 1865.8 Suspended Microfluidics in Suspended V-shaped Channels 1885.9 Capillary Flow Over a Hole 1895.10 Introduction to Two-phase Suspended Microflows 1915.10.1 Parallel Walls 1945.10.2 Tapered Walls 1975.10.2.1 Converging Channel 1975.10.2.2 Diverging Channel 1985.10.3 Examples and Applications of Suspended Microfluidics 1995.10.3.1 Formation of μDots 1995.10.3.2 Towards a Giant Polymeric Micromembrane 2015.10.3.3 Suspended Microfluidics for Measurement of Contact Angles 2015.11 Conclusion 2035.12 References 2036 Spontaneous Capillary Flow Between Horizontal Rails 2076.1 Introduction 2076.2 Spontaneous Capillary Flows Between Rails 2096.3 Winding Channels 2106.4 Diverging Rails 2116.5 Rails with Lateral Enlargement 2126.6 Converging Rails 2126.7 Rails with Constriction 2126.8 Stopping a Capillary Flow at a Neck 2136.9 SCF in Sinusoidal Railed Channels 2156.10 Divisions and Bifurcations 2176.10.1 Flow Separation 2176.10.2 Flow Around a Hole 2176.10.2.1 Two Plates Pierced by a Hole 2186.10.2.2 Bottom Plate Pierced by a Hole 2216.10.2.3 Rails Around a Hole 2216.10.3 Capillary Flow Around Pillars 2246.10.3.1 Single Pillar 2246.10.3.2 Multiple Pillars 2256.11 Conclusion 2276.12 References 2277 Paper-based Microfluidics 2297.1 Introduction 2297.2 Principles of Labs-on-Paper and Paper-based Devices 2307.3 Paper-based Microfluidics 2317.3.1 Spontaneous Imbibition-wicking 2317.3.2 Fully Wetted Medium – Darcy’s law 2347.3.3 Velocity in Paper Strips of Piecewise Varying Width 2367.3.4 Filtration and Separation 2377.3.5 Mixing 2387.3.6 Y-junctions 2407.3.7 Hydrodynamic Focusing 2417.3.8 H-filters: Separation and Extraction 2427.3.9 Valves 2437.3.10 Architecture for Time Sequencing 2447.3.11 3D paths – Fluidic Origamis 2447.3.12 Electrokinetics on Paper 2447.4 Paper-based Systems Fabrication and Detection 2457.4.1 Fabrication Techniques of Paper Strips 2467.4.2 Fabrication Techniques of μPADs 2477.4.2.1 Hydrophobic Barrier 2477.4.2.2 Hydrophobization of the Substrate 2477.4.3 Functionalization and Loading of Reagents 2497.4.4 Detection 2497.4.4.1 Colorimetry 2497.4.4.2 Electrochemistry(EC) 2507.4.4.3 Chemiluminescence 2518 Fiber-based Microfluidics 2578.1 Introduction 2578.2 Droplet on Fibers 2598.2.1 Droplet on a Horizontal Fiber 2598.2.2 Small Droplet 2608.2.2.1 Effect of Gravity on Small Droplets 2618.2.2.2 Large Droplet 2618.2.3 Droplet Between Fibers 2638.2.3.1 Droplet Between Two Parallel Fibers 2638.2.3.2 Non-parallel Fibers in the Same Plane 2648.2.3.3 Drop Between Two Fibers – General Case 2658.2.3.4 Droplet Sliding Down a Fiber 2668.3 SCF Guided by Fibers 2688.3.1 Approximate General Condition for Spontaneous Capillary Flow in a Fiber Bundle 2688.3.2 Geometrical Study: SCF Guided by Fibers 2708.3.2.1 Homogeneous Bundle 2718.3.2.2 Inhomogeneous Bundles 2738.3.2.3 Numerical Example 2798.3.2.4 Packed Bundle 2818.3.2.5 Generalization to Large Bundles 2828.3.2.6 Influence of the Parameter C=R 2828.3.2.7 Conclusion 2828.4 Examples of Microfluidics on Fibers 2848.5 Electrochemical Detection on Fibers 2848.6 Applications in Biology 2858.6.1 Blood Typing Diagnostics 2858.6.2 Woven Fibers 2868.6.3 Smart Bandages 2868.6.4 Smart Textiles 2888.7 Capillary Rise in Fibers 2888.7.1 Cylindrical Tubes: Jurin’s law 2888.7.2 Capillary Rise Between Pillars 2918.7.2.1 Capillary Rise in a Bundle of Four Vertical Square Pillars 2918.7.2.2 Comparison of Capillary Rise Between a Wilhelmy Plate and Pillars 2928.7.2.3 Comparison of Capillary Rise Between a Single Rod and a Bundle of Packed Rods 2948.8 Conclusions 2958.9 References 296Appendix 8.1 Calculation of the Laplace Pressure for a Droplet on aHorizontal Cylindrical Wire 298Appendix 8.2 Perimeters 299Appendix 8.3 Wonky Corners SCF 300Appendix 8.4 Transition Between “All Wetted” and “All But Corners” Cases 3019 Epilog 3039.1 Open Microfluidics 3039.2 References 305Index 307