Wetting and Spreading Dynamics, Second Edition

495 Pages·2019·25.851 MB·\495

by  Victor M. Starov (Author), Manuel G. Velarde (Author)

Wetting and Spreading Dynamics
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Wetting and Spreading Dynamics, Second Edition
Victor M. Starov and Manuel G. Velarde
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Wetting and Spreading Dynamics
Second Edition
Victor M. Starov
Department of Chemical Engineering, Loughborough  University
Loughborough, UK
Manuel G. Velarde
Instituto Pluridisciplinar, Universidad Complutense
Madrid, Spain
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Library of Congress Cataloging-in-Publication Data
Names: Starov, V. M., author. | Velarde, Manuel G. (Manuel Garcâia), author.
Title: Wetting and spreading dynamics / Victor M. Starov, Manuel G. Velarde.
Description: Second edition. | Boca Raton : CRC Press, Taylor & Francis
Group, 2019. | Includes bibliographical references.
Identifiers: LCCN 2019007787 | ISBN 9781138584075 (hardback : alk. paper)
Subjects: LCSH: Wetting. | Surface chemistry. | Surface tension. | Interfaces
(Physical sciences) | Solid-liquid interfaces.
Classification: LCC QD506 .S7835 2019 | DDC 541/.33--dc23
LC record available at https://lccn.loc.gov/2019007787
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Contents
Preface to the First Edition ....................................................................................................................xiii
Acknowledgments ....................................................................................................................................xv
Preface to the Second Edition ................................................................................................................xvii
Acknowledgments ...................................................................................................................................xix
About the Authors ...................................................................................................................................xxi
1. Surface Forces and Equilibrium of Liquids on Solid Substrates ................................................1
Introduction ........................................................................................................................................1
1.1 Wetting and Neumann–Young’s Equation ..............................................................................2
1.2 Surface Forces and Derjaguin’s Pressure ...............................................................................8
Components of the Derjaguin’s Pressure ..............................................................................10
Molecular or Dispersion Component ......................................................................10
Electrical Double Layers .........................................................................................12
Electrokinetic Phenomena .......................................................................................13
The Electrostatic Component of the Derjaguin’s Pressure .....................................13
Structural Component of the Derjaguin’s Pressure .................................................15
1.3 Static Hysteresis of Contact Angle ........................................................................................17
Static Hysteresis of Contact Angles from the Microscopic Point of View: Surface Forces ........20
References ........................................................................................................................................22
2. Equilibrium Wetting Phenomena .................................................................................................25
Introduction ......................................................................................................................................25
2.1 Thin Liquid Films on Flat Solid Substrates ..........................................................................25
Equilibrium Droplets on the Solid Substrate under Oversaturation (Pe < 0) ........................29
Flat Films at the Equilibrium with Menisci (Pe > 0) ...............................................30
2.2 Non-flat Equilibrium Liquid Shapes on Flat Solid Surfaces ................................................32
General Consideration ..........................................................................................................33
Microdrops: The Case Where Pe > 0 (The Case of Under-Saturation) .................................36
Microscopic Quasi-equilibrium Periodic Films ....................................................................37
Microscopic Equilibrium Depressions on β-Films ................................................................41
2.3 Equilibrium Contact Angle of Menisci and Drops: Liquid Shape in the Transition
Zone from the Bulk Liquid to the Flat Films in Front .........................................................42
Equilibrium of Liquid in a Flat Capillary: Partial Wetting Case...........................................43
Meniscus in a Flat Capillary .................................................................................................44
Meniscus in a Flat Capillary: Profile of the Transition Zone ................................................47
Partial Wetting: Macroscopic Liquid Drops ..........................................................................48
Profile of the Transition Zone in the Case of Droplets ..........................................................51
Axisymmetric Drops ...............................................................................................52
Meniscus in a Cylindrical Capillary ........................................................................53
Appendix 1 .......................................................................................................................................53
2.4 Profile of the Transition Zone between a Wetting Film and the Meniscus of the Bulk
Liquid in the Case of Complete Wetting ..............................................................................54
2.5 Thickness of Equilibrium Wetting Films on Rough Solid Substrates..................................59
2.6 Equilibrium Films on Locally Heterogeneous Surfaces: Hydrophilic Surface with
Hydrophobic Inclusions ........................................................................................................66
v
vi Contents
2.7 Equilibrium of Droplets on a Deformable Substrate: Influence of the Derjaguin’s
Pressure .......................................................................................................................72
Introduction ...........................................................................................................................73
Derjaguin’s Pressure and Deformation of Soft Substrates ....................................................73
Mathematical Model and Derivation ....................................................................................75
Spherical Region: h−hs >t1 ..................................................................................................78
Transitional Region: h−hs≤t1 ..............................................................................................78
Equilibrium Contact Angle ...................................................................................................82
Jacobi’s Condition .................................................................................................................83
2.8 Deformation of Fluid Particles in the Contact Zone ............................................................85
Two Identical Cylindrical Drops/Bubbles .............................................................................86
Interaction of Cylindrical Droplets of Different Radii ..........................................................89
Shape of a Liquid Interlayer between Interacting Droplets: Critical Radius ........................92
2.9 Liquid Profiles on Curved Interfaces, Effective Derjaguin’s Pressure. Equilibrium
Contact Angles of Droplets on Outer/Inner Cylindrical Surfaces and Menisci inside
Cylindrical Capillaries ..........................................................................................................97
Liquid Profiles on Curved Surface: Derivation of Governing Equations .............................98
Equilibrium Contact Angle of a Droplet on an Outer Surface of Cylindrical
Capillaries .............................................................................................................100
Equilibrium Contact Angle of a Meniscus inside Cylindrical Capillaries ..........................102
Derjaguin’s Pressure of Uniform Films in Cylindrical Capillaries .....................................103
2.10 Line Tension ........................................................................................................................104
The Comparison with the Experimental Data and Discussion ............................................113
2.11 Capillary Interaction between Solid Bodies ........................................................................114
Appendix 2 ......................................................................................................................................119
References .......................................................................................................................................121
3. Hysteresis of Contact Angles Based on Derjaguin’s Pressure .................................................125
Introduction ....................................................................................................................................125
3.1 Hysteresis of Contact Angle of a Meniscus inside a Capillary with Smooth
Homogeneous Non-deformable Walls ................................................................................125
The Derjaguin’s Pressure Components ...............................................................................127
The Derjaguin’s Pressure and Wetting Phenomena ............................................................128
Hysteresis of Contact Angle in Capillaries .........................................................................129
Calculation Procedure .........................................................................................................134
Conclusions .........................................................................................................................137
3.2 Hysteresis of Contact Angle of Sessile Droplets on Non-deformable Substrates ..............137
Introduction .........................................................................................................................137
Equilibrium Contact Angle and Derjaguin’s Pressure for Sessile Droplets ........................139
Static Hysteresis of the Contact Angle of Sessile Droplets on Smooth Homogeneous
Substrates .............................................................................................................................141
Expressions for the Advancing Contact Angle ....................................................................142
Expressions for the Receding Contact Angle .......................................................................145
Conclusions .........................................................................................................................146
3.3 Hysteresis of Contact Angle of Sessile Droplets on Deformable Substrates ......................146
Introduction ..........................................................................................................................147
Equilibrium Contact Angle of Droplet on Deformable Substrates and the Surface
Forces Action: A Simplified Model Adopted in this Section ...............................................147
Theory and Model for Hysteresis of Contact Angle on a Deformable Substrate ................149
Results and Discussions .......................................................................................................153
Conclusions ..........................................................................................................................155
Appendix: Advancing Contact Angle ..............................................................................................155
References ......................................................................................................................................157
Contents vii
4. Kinetics of Wetting ........................................................................................................................161
Introduction .....................................................................................................................................161
4.1 Spreading of Nonvolatile Liquid Drops over Flat Solid Substrates:
Qualitative Analysis ....................................................................................................168
Capillary Regime of Spreading ............................................................................................172
Gravitational Spreading as a Continuation of the Capillary Spreading Regime ..................177
Similarity Solution ...............................................................................................................178
Spreading of Very Thin Droplets ........................................................................................180
4.2 Spreading of Nonvolatile Liquid Drops over Dry Surfaces: Influence of
Surface Forces ................................................................................................................185
n = 2 Case ............................................................................................................................191
n = 3 Case ............................................................................................................................191
Comparison with Experiments ............................................................................................194
Conclusions .........................................................................................................................196
Appendix 1 .....................................................................................................................................196
Appendix 2 .....................................................................................................................................197
Appendix 3 .....................................................................................................................................198
Appendix 4 .....................................................................................................................................199
4.3 Spreading of Drops over a Surface Covered with a Thin Layer of the Same Liquid .........200
4.4 Quasi-Steady-State Approach in the Kinetics of Spreading ..............................................206
4.5 Dynamic Advancing Contact Angle and the Form of the Moving Meniscus in Flat
Capillaries in the Case of Complete Wetting ......................................................................213
Appendix 5 ......................................................................................................................................217
Asymptotic Behavior of Solution of y3d3y =y−1 at y→∞ ..................................217
dx3
4.6 Motion of Long Drops in Thin Capillaries in the Case of Complete Wetting ...................220
Appendix 6 .....................................................................................................................................228
4.7 Liquid Film Coating of a Moving Thin Cylindrical Fiber ..................................................231
Statement of the Problem ....................................................................................................232
Derivation of the Equation for the Liquid–Liquid Interface Profile ...................................232
Equilibrium Configuration ..................................................................................................234
Matching of Asymptotic Solutions in Zones I and II ..........................................................234
Equilibrium Case (Ca = 0) .................................................................................................236
Numerical Results ...............................................................................................................237
4.8 Blow-off Method for Investigating Boundary Viscosity of Volatile Liquids .....................238
Boundary Viscosity .............................................................................................................238
Theory of the Method .........................................................................................................239
Experimental Part ..................................................................................................249
Conclusions ..........................................................................................................................251
4.9 Combined Heat and Mass Transfer in Tapered Capillaries with Bubbles under the
Action of a Temperature Gradient ......................................................................................252
Cylindrical Capillaries ........................................................................................................255
Tapered Capillaries .............................................................................................................256
4.10 Spreading of Non-Newtonian Liquids over Solid Substrates .............................................258
Governing Equation for the Evolution of the Profile of the Spreading Drop .....................258
Gravitational Regime of Spreading .....................................................................................262
Capillary Regime of Spreading ...........................................................................................265
Conclusions .........................................................................................................................268
References ......................................................................................................................................269
viii Contents
5. Spreading over Porous Substrates ..............................................................................................271
Introduction ....................................................................................................................................271
5.1 Spreading of Liquid Drops over Saturated Porous Layers .................................................272
Theory .................................................................................................................................272
Liquid inside the Drop (0 < z < h(t, r)) ................................................................272
Inside the Porous Layer beneath the Drop (−Δ < z < 0, 0 < r < L) .......................273
Materials and Methods ..........................................................................................278
Results and Discussion. Experimental Determination of the “Effective
Lubrication Coefficient” ω ....................................................................................279
5.2 Spreading of Liquid Drops over a Thin Dry Porous Layer: Complete Wetting Case ........282
Theory .................................................................................................................................282
Inside the Porous Layer outside the Drop (−Δ < z < 0, L < r < l) ......................287
Experimental Part ..................................................................................................290
Independent Determination of K p .....................................................................290
p c
Results and Discussion ...........................................................................................291
Appendix 1 .....................................................................................................................................295
5.3 Spreading of Liquid Drops over Thick Porous Substrates: Complete Wetting Case .........297
Theory .................................................................................................................................298
Inside the Porous Substrate ...................................................................................300
Experimental Part ..................................................................................................300
Results and Discussion ..........................................................................................301
Spreading of Silicone Oil Drops of Different Viscosity over Identical
Glass Filters ...........................................................................................................303
Spreading of Silicone Oil Drops over Filters with Similar Properties but
Made of Different Materials ..................................................................................304
Spreading of Silicone Oil Drops with the Same Viscosity (η = 5 P) over
Glass Filters with Different Porosity and Average Pore Size ................................305
Conclusions ...........................................................................................................308
5.4 Spreading of Liquid Drops from a Liquid Source ..............................................................308
Theory .................................................................................................................................309
Experimental Setup and Results ..........................................................................................312
Materials and Methods ...........................................................................................312
Results and Discussion ...........................................................................................313
Conclusions ..........................................................................................................................315
Appendix 2 ......................................................................................................................................316
Capillary Regime, Complete Wetting ....................................................................316
Gravitational Regime, Complete Wetting ..............................................................319
Partial Wetting ........................................................................................................321
5.5 Spreading of Non-Newtonian Liquids over Dry Porous Layer: Complete and Partial
Wetting Cases ......................................................................................................................321
Partial and Complete Wetting Cases ...................................................................................322
5.5.1 Complete Wetting Case ...........................................................................................323
Introduction .........................................................................................................................323
Theory .................................................................................................................................324
Droplet Profile .......................................................................................................325
Spreading above Porous Substrate ........................................................................326
Inside the Porous Layer outside the Drop (−Δ < z < 0, L < r < l) ......................328
Experimental Data ..................................................................................................331
Numerical Solution of Eqs. (5.132) and (5.133) ....................................................332
Results and Discussion ...........................................................................................333
Conclusions on Section “Complete Wetting Case” ...............................................336
5.5.2 Partial Wetting Case .............................................................................................337
Contents ix
Theory .................................................................................................................................337
Droplet Profile .......................................................................................................338
Pores of the Porous Substrate Are Large Enough and Red Blood Cells
Penetrate into the Substrate with Plasma Flow .....................................................339
The Second Stage of the Process ..........................................................................339
Pores inside the Porous Substrate Are Small and Red Blood Cells Do
Not Penetrate into the Porous Substrate ................................................................340
Conclusions on Section “Partial Wetting Case” ....................................................342
Appendix 3 .....................................................................................................................................343
Capillary Imbibition of Non-Newtonian Liquid into a Thin Capillary .................343
One-Dimensional Penetration of a Non-Newtonian Liquid into a
Porous Medium .....................................................................................................344
Appendix 4 .....................................................................................................................................344
References ......................................................................................................................................345
6. Wetting of Wetting/Spreading in the Presence of Surfactants ................................................349
Introduction ....................................................................................................................................349
6.1 Spreading of Aqueous Surfactant Solutions over Porous Layers .......................................349
Experimental Methods and Materials .................................................................................350
Spreading on Porous Substrates ............................................................................350
Measurement of Static Advancing and Receding Contact Angles on
Nonporous Substrates ............................................................................................351
Results and Discussion ...........................................................................................352
Advancing and Hydrodynamic Receding Contact Angles on Porous
Nitrocellulose Membranes .....................................................................................355
Static Hysteresis of the Contact Angle of SDS Solution Drops on Smooth
Nonporous Nitrocellulose Substrate .....................................................................357
Conclusions .........................................................................................................................359
6.2 Spontaneous Capillary Imbibition of Surfactant Solutions into Hydrophobic
Capillaries ......................................................................................................................360
Theory .................................................................................................................................362
Concentration below the CMC ...........................................................................................365
Concentration above the CMC ............................................................................................367
Spontaneous Capillary Rise in Hydrophobic Capillaries ....................................................370
Appendix 1 .....................................................................................................................................372
Excess Free Energy of an Aqueous Surfactant Droplet on a
Hydrophobic Substrate ..........................................................................................372
Appendix 2 ......................................................................................................................................374
6.3 Capillary Imbibition of Surfactant Solutions in Porous Media and Thin Capillaries:
The Partial Wetting Case ....................................................................................................376
Theory .................................................................................................................................376
Concentration below the CMC ...........................................................................................377
Concentration above the CMC ............................................................................................383
Experimental Part ................................................................................................................384
Results and Discussions ......................................................................................................385
6.4 Spreading of Surfactant Solutions over Hydrophobic Substrates .......................................386
Theory .................................................................................................................................387
Experiment: Materials .........................................................................................................390
Monitoring Method .............................................................................................................390
Results and Discussion .......................................................................................................390
6.5 Spreading of Insoluble Surfactants over Thin Viscous Liquid Layers ...............................393
Theory and Relation to Experiment ....................................................................................394
Experimental Results ..........................................................................................................400