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Open-Channel Microfluidics Fundamentals and applications Open-Channel Microfluidics Fundamentals and applications Jean Berthier, Ashleigh B Theberge and Erwin Berthier University of Washington, Washington, USA Morgan & Claypool Publishers Copyrightª2019Morgan&ClaypoolPublishers Allrightsreserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystem ortransmittedinanyformorbyanymeans,electronic,mechanical,photocopying,recording orotherwise,withoutthepriorpermissionofthepublisher,orasexpresslypermittedbylawor undertermsagreedwiththeappropriaterightsorganization.Multiplecopyingispermittedin accordancewiththetermsoflicencesissuedbytheCopyrightLicensingAgency,theCopyright ClearanceCentreandotherreproductionrightsorganizations. Rights&Permissions Toobtainpermissiontore-usecopyrightedmaterialfromMorgan&ClaypoolPublishers,please [email protected]. ISBN 978-1-64327-664-9(ebook) ISBN 978-1-64327-661-8(print) ISBN 978-1-64327-662-5(mobi) DOI 10.1088/2053-2571/ab21ca Version:20190801 IOPConcisePhysics ISSN2053-2571(online) ISSN2054-7307(print) AMorgan&ClaypoolpublicationaspartofIOPConcisePhysics PublishedbyMorgan&ClaypoolPublishers,1210FifthAvenue,Suite250,SanRafael,CA, 94901,USA IOPPublishing,TempleCircus,TempleWay,BristolBS16HG,UK To Noam, Eden, Mila and Myron. Contents Foreword xi Acknowledgments xii Author biographies xiii Nomenclature xv Introduction: open-channel microfluidics and open microfluidics xvii 1 Capillarity theoretical basis 1-1 1.1 Liquid surface tension 1-1 1.2 Laplace pressure 1-2 1.3 Liquid–liquid surface tension 1-4 1.4 Contact with solid surface: Young’s law 1-5 1.5 Neumann’s construction 1-6 1.6 Work of adhesion, work of cohesion and the Young–Dupré equation 1-8 1.7 Solid surface energy: Zisman’s approach 1-9 1.7.1 Using Young’s law 1-9 1.7.2 Using Zisman’s plot 1-10 1.8 Wetting and pinning 1-14 1.8.1 Wetting 1-14 1.8.2 Pinning and canthotaxis 1-14 1.9 Wenzel law 1-17 1.10 Cassie–Baxter law 1-18 1.11 Capillary rise 1-20 1.12 Marangoni convection 1-21 References 1-22 2 Condition for capillary flow in open channels 2-1 2.1 Spontaneous capillary flow in a monolithic channel 2-1 2.2 Spontaneous capillary flow in composite open channels: 2-2 the generalized Cassie condition 2.3 Enhanced open capillary flows 2-3 2.3.1 Constant additional inlet pressure 2-3 2.3.2 Overfilled reservoir: initial additional Laplace pressure 2-6 Conclusions 2-10 References 2-10 vii Open-ChannelMicrofluidics 3 Flow dynamics in open channels 3-1 3.1 Background: spontaneous capillary flow in composite, 3-1 closed channels of arbitrary uniform cross section 3.2 Flow dynamics in open micro-channels of uniform cross section 3-9 3.3 Flow dynamics in open micro-channels of variable cross sections 3-12 3.3.1 Sudden constriction and enlargements 3-12 3.3.2 Sudden enlargement with pinning: open capillary valves 3-14 3.3.3 Progressive enlargements 3-15 3.3.4 Capillary pumps 3-16 3.3.5 Filters 3-18 3.3.6 One-way wicking 3-18 3.4 The capillary dynamics of non-Newtonian fluids 3-18 3.4.1 Shear-thinning fluids 3-20 3.4.2 The case of whole blood 3-21 References 3-23 4 Open-channel geometries 4-1 4.1 Rectangular channels 4-1 4.2 Rectangular channels with imperfect corners 4-7 4.3 Rounded channels 4-8 4.4 Semi-cylindrical channel 4-13 4.5 Suspended channels 4-13 4.6 Rails 4-16 4.7 Embossed channels 4-20 4.8 Fiber bundles and flow caging 4-21 4.9 Capillary rise and uphill open capillary flows 4-24 4.10 Capillary networks 4-27 4.10.1 Example #1 4-29 4.10.2 Example #2 4-31 4.10.3 Capillary flow after a bypass or a derivation 4-31 Conclusion 4-36 References 4-37 5 Capillary filaments 5-1 5.1 Capillary filaments: the Concus–Finn condition 5-1 5.2 The case of V-grooves 5-2 5.3 Capillary filaments in open-channel turns 5-3 viii Open-ChannelMicrofluidics 5.4 Capillary filaments in non-uniform channels 5-5 5.5 Detached capillary filaments 5-6 5.6 Metastable capillary filaments 5-8 5.7 Capillary filaments driving SCF 5-11 5.8 Dynamics of capillary filaments 5-12 5.9 Drying of capillary filaments 5-13 5.10 Capillary filaments stopped by rounded wedges 5-13 Conclusion 5-17 References 5-18 6 Two-phase open-channel capillary flows 6-1 6.1 Introduction 6-1 6.2 Plugs in uniform cross section open channels 6-1 6.2.1 Quasi steady state approach: SCF condition in 6-2 the presence of plugs 6.2.2 Plugs dynamics in open-channel capillary flow 6-5 6.2.3 Conclusions 6-10 6.2.4 Capillary wagons 6-11 6.3 Bypasses and bifurcations 6-11 6.3.1 Bifurcations 6-11 6.3.2 Bypasses 6-12 6.4 Plugs and capillary filaments 6-13 6.4.1 Plugs moved by capillary filaments 6-14 6.4.2 Plugs blocked by reverse capillary filaments 6-14 Conclusions 6-14 References 6-16 7 Applications 7-1 7.1 Materials and fabrication 7-1 7.2 Space: design of vanes 7-3 7.2.1 Space cup 7-3 7.2.2 Vanes 7-3 7.3 Microfluidics 7-4 7.3.1 Capillary channels on paper 7-4 7.3.2 Evaporation capillary pumping 7-5 7.4 Biology, biotechnology and medicine 7-6 ix