Advances in Contact Angle, Wettability and Adhesion, Volume 1 E-Book

• Herausgeber: John Wiley & Sons
• Kategorie: Fachliteratur
• Serie: Adhesion and Adhesives - Fundamental and Applied Aspects
• Sprache: Englisch

Seitenzahl: 633

Veröffentlichungsjahr: 2013

Beschreibung

The topic of wettabilty is extremely important from both fundamental and applied aspects. The applications of wettability range from self-cleaning windows to micro- and nanofluidics. This book represents the cumulative wisdom of a contingent of world-class (researchers engaged in the domain of wettability. In the last few years there has been tremendous interest in the "Lotus Leaf Effect" and in understanding its mechanism and how to replicate this effect for myriad applications. The topics of superhydrophobicity, omniphobicity and superhydrophilicity are of much contemporary interest and these are covered in depth in this book.

Leseprobe

Contents

Cover

Half Title page

Title page

Copyright page

Preface

Acknowledgements

Part 1: Fundamental Aspects

Chapter 1: Correlation between Contact Line Pinning and Contact Angle Hysteresis on Heterogeneous Surfaces: A Review and Discussion

1.1 Introduction

1.2 Contact Line Pinning on Chemically Heterogeneous Flat Surfaces

1.3 Contact Line Pinning on Hydrophobic Structured Surfaces

1.4 Summary and Conclusion

References

Chapter 2: Computational and Experimental Study of Contact Angle Hysteresis in Multiphase Systems

2.1 Introduction

2.2 Origins of the CA Hysteresis

2.3 Modeling Wetting/Dewetting in Multiphase Systems

2.4 Experimental Observations

2.5 Numerical Modeling of CA Hysteresis

2.6 Conclusions

Acknowledgement

References

Chapter 3: Heterogeneous Nucleation on a Completely Wettable Substrate

3.1 Introduction

3.2 Interface-Displacement Model

3.3 Nucleation on a Completely-Wettable Flat Substrate

3.4 Nucleation on a Completely-Wettable Spherical Substrate

3.5 Conclusion

Acknowledgments

References

Chapter 4: Local Wetting at Contact Line on Textured Hydrophobic Surfaces

4.1 Introduction

4.2 Static Contact Angle

4.3 Wetting of Single Texture Element

4.4 Summary

References

Chapter 5: Fundamental Understanding of Drops Wettability Behavior Theoretically and Experimentally

5.1 Introduction

5.2 Discussion

5.3 Conclusion

References

Chapter 6: Hierarchical Structures Obtained by Breath Figures Self-Assembly and Chemical Etching and their Wetting Properties

6.1 Introduction

6.2 Materials and Methods

6.3 Results and Discussion

6.4 Conclusions

Acknowledgements

References

Chapter 7: Computational Aspects of Self-Cleaning Surface Mechanisms

7.1 Introduction

7.2 Droplet Membrane

7.3 Flow Model

7.4 Results

7.5 Summary

Acknowledgement

References

Chapter 8: Study of Material–Water Interactions Using the Wilhelmy Plate Method

8.1 Introduction

8.2 Upgrading Wetting Curves

8.3 Study of Surface-Oxidized Polyethylene

8.4 Study of Amphiphilic UV-Cured Coatings

8.5 Conclusion

Acknowledgements

References

Chapter 9: On the Utility of Imaginary Contact Angles in the Characterization of Wettability of Rough Medicinal Hydrophilic Titanium

9.1 Introduction

9.2 Theoretical Considerations

9.3 Materials and Methods

9.4 Results and Discussion

9.5 Conclusion

Acknowledgement

References

Chapter 10: Determination of Surface Free Energy at the Nanoscale via Atomic Force Microscopy without Altering the Original Morphology

10.1 Introduction

10.2 Materials and Methods

10.3 Results and Discussion

10.4 Conclusion

References

Part 2: Superhydrophobic Surfaces

Chapter 11: Assessment Criteria for Superhydrophobic Surfaces with Stochastic Roughness

11.1 Introduction

11.2 Model and Experiments

11.3 Results and Discussion

11.4 Summary

Acknowledgement

References

Chapter 12: Nanostructured Lubricated Silver Flake/Polymer Composites Exhibiting Robust Superhydrophobicity

12.1 Introduction

12.2 Experimental

12.3 Results and Discussion

12.4 Conclusions

References

Chapter 13: Local Wetting Modification on Carnauba Wax-Coated Hierarchical Surfaces by Infrared Laser Treatment

13.1 Introduction

13.2 Experimental

13.3 Results and Discussion

13.4 Conclusions

Acknowledgements

References

Part 3: Wettability Modification

Chapter 14: Cold Radiofrequency Plasma Treatment Modifies Wettability and Germination Rate of Plant Seeds

14.1 Introduction

14.2 Experimental

14.3 Results and Discussion

14.4 Conclusions

Acknowledgements

References

Chapter 15: Controlling the Wettability of Acrylate Coatings with Photo-Induced Micro-Folding

15.1 Introduction

15.2 The Process of Photo-induced Micro-folding

15.3 Experimental

15.4 Review of Results

15.5 Summary

Acknowledgment

References

Chapter 16: Influence of Surface Densification of Wood on its Dynamic Wettability and Surface Free Energy

16.1 Introduction

16.2 Experimental

16.3 Results and Discussion

16.4 Summary and Conclusions

Acknowledgments

References

Chapter 17: Contact Angle on Two Canadian Woods: Influence of Moisture Content and Plane of Section

17.1 Introduction

17.2 Materials and Experimental Procedures

17.3 Results and Discussion

17.4 Conclusions

Acknowledgement

References

Chapter 18: Plasma Deposition of ZnO Thin Film on Sugar Maple: The Effect on Contact Angle

18.1 Introduction

18.2 Materials and Experimental Procedures

18.3 Results and Discussion

18.4 Conclusion

Acknowledgements

References

Chapter 19: Effect of Relative Humidity on Contact Angle and its Hysteresis on Phospholipid DPPC Bilayer Deposited on Glass

19.1 Introduction

19.2 Experimental

19.3 Result and Discussion

19.4 Conclusion

Acknowledgments

References

Part 4: Wettability and Surface Free Energy

Chapter 20: Contact Angles and Surface Energy of Solids: Relevance and Limitations

20.1 Introduction

20.2 Thermodynamic Background

20.3 Determination of the Surface Energy of a Solid from Contact Angles

20.4 Wettability and Surface Composition of Polypropylene Modified by Oxidation

20.5 Wettability and Surface Cleanliness of Inorganic Materials

20.6 Conclusion

Acknowledgements

References

Chapter 21: Surface Free Energy and Wettability of Different Oil and Gas Reservoir Rocks

21.1 Introduction

21.2 Experimental

21.3 Results and Discussion

21.4 Conclusions

References

Chapter 22: Influence of Surface Free Energy and Wettability on Friction Coefficient between Tire and Road Surface in Wet Conditions

22.1 Introduction

22.2 Theoretical Basis of the New Model

22.3 Materials and Methods

22.4 Results and Discussion

22.5 Summary and Conclusions

Acknowledgement

References

Advances in Contact Angle, Wettability and Adhesion

Scrivener Publishing 100 Cummings Center, Suite 541J Beverly, MA 01915-6106

Adhesion and Adhesives: Fundamental and Applied Aspects

The topics to be covered include, but not limited to, basic and theoretical aspects of adhesion; modeling of adhesion phenomena; mechanisms of adhesion; surface and interfacial analysis and characterization; unraveling of events at interfaces; characterization of interphases; adhesion of thin films and coatings; adhesion aspects in reinforced composites; formation, characterization and durability of adhesive joints; surface preparation methods; polymer surface modification; biological adhesion; particle adhesion; adhesion of metallized plastics; adhesion of diamond-like films; adhesion promoters; contact angle, wettability· and adhesion; superhydrophobicity and superhydrophilicity. With regards to adhesives, the Series will include, but not limited to, green adhesives; novel and high-performance adhesives; and medical adhesive applications.

Series Editor: Dr. K.L. Mittal 1983 Route 52, P.O.1280, Hopewell Junction, NY 12533, USA Email: [email protected]

Publishers at Scrivener Martin Scrivener ([email protected]) Phillip Carmical ([email protected])

Copyright © 2013 by Scrivener Publishing LLC. All rights reserved.

Co-published by John Wiley & Sons, Inc. Hoboken, New Jersey, and Scrivener Publishing LLC, Salem, Massachusetts.Published simultaneously in Canada.

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ISBN 978-1-118-47292-7

Preface

The history of contact angle and wetting can be traced back to the early 17th century. The putative seminal paper on this topic was published in 1805 by Thomas Young [An essay on the cohesion of fluids, Phil. Trans. Roy. Soc., 95, 65–87(1805)]. In this paper he describes the balance of various forces (interfacial tensions) acting on a sessile liquid drop on a solid surface, which is popularly known today as the Young’s Equation. Apropos, there is no formal equation in this paper. Apparently, some brilliant individual transformed Young’s description into this equation. According to Prof. Robert J. Good [R.J. Good, Contact angle, wettability and adhesion, in: Contact Angle, Wettability and Adhesion, K.L. Mittal (Ed.) pp. 3–36, VSP, Utrecht 1993)] “Most surface and colloid chemists think of Thomas Young as the father of scientific research on contact angles and wetting. But probably the earliest direct recognition of wetting phenomena was given by Galileo [Galileo Galilei, Bodies that Stay Atop Water, or Move in it (1612)] who might be called the grandfather of the field.”

Another momentous event is this field occurred in 1997 when W. Barthlott and C. Neinhuis [W. Barthlott and C. Neinhuis, Purity of sacred lotus, or escape from contamination in biological surfaces, Planta, 202, 1–8(1997)] investigated the wetting properties of various plants and discovered extreme water-repellency (superhydropobicity) and self-cleaning mechanism of the sacred lotus (Nelumbo nucifera) and coined the term “Lotus Effect.” Since this discovery, there has been an explosive interest in the topic of superhydrophobicity and a legion of techniques have been described in the literature [see the book A. Carre’ and K.L. Mittal (Eds.) Superhydrophobic Surfaces, VSP/Brill, Leiden (2009)] to devise mechanically robust superhydrophobic surfaces of a variety of materials. The antonymous field of superhydrophilicity has also attracted fervent interest from the research community. These days there is an ardent interest (both from fundamental and applied views) in modifying surfaces to alter their wetting behavior to render them superhydrophobic, superhydrophilic, oleophobic, oleophilic, omniphobic, panphobic, amphiphobic. In other words, all kinds of “phobicities” and “philicities” are under intensive investigation.

Even a cursory look at the literature will evince that there is a brisk research activity regardingf contact angles and wetting/spreading from both fundamental and applied points of view. The wonderful world of wettability is very wide as it plays an extremely important role in many areas of human endeavor ranging from high-tech (microelectronics, micro-and nanofluidics, MEMS and NEMS, biomedical devices, for example) to the quite mundane (washing of clothes, spraying of insecticides/ pesticides on agricultural products). Researchers have also studied the wettability behavior of skins of people (both males and females) from different origins and backgrounds. I wonder if wettability can be correlated to beauty! I should also add that all signals indicate that the interest in wetting phenomena will continue unabated.

Now coming to this volume, which is essentially based on the written accounts of papers presented at the Eighth International Symposium on Contact Angle, Wettability and Adhesion held in Quebec City, Quebec, Canada during June 13–15, 2012 under the aegis of MST Conferences. It should be recorded for posterity that all manuscripts were rigorously peer-reviewed, suitably revised (some twice or thrice) and properly edited before inclusion in this book. So this book is not a mere collection of unreviewed and unedited papers, rather it represents articles which have passed the rigorous scrutiny. Thus, these articles are of archival value and their standard is as high as any journal or even higher than many journals.

This book containing 22 articles is divided into four Parts as follows. Part 1: Fundamental Aspects; Part 2: Superhydrophobic Surfaces; Part 3: Wettability Modification; and Part 4: Wettability and Surface Free Energy. The topics covered include: contact angle hysteresis on heterogeneous surfaces and in multiphase systems; fundamental understanding of drops wettability behavior; computational aspects of self-cleaning surface mechanisms; utility of imaginary contact angles in the characterization of wettability of rough surfaces; determination of surface free energy at the nanoscale via atomic force microscopy; superhydrophobicity and its assessment criteria; wettability modification techniques for different materials; effects of cold RF plasma treatment on germination rate of plant seeds; wettability of wood; wettability of DPPC bilayer; wettability, contact angles and surface free energy of solids; influence of surface free energy on friction coefficient between tire and road surface.

It is quite obvious from the above that this book comprising 22 articles written by world-renowned researchers covers many ramifications of contact angles and wettability. It represents a commentary on the contemporary research activity and reflects the cumulative wisdom of a number of key researchers in this arena.

Yours truly sincerely hopes that anyone interested in staying abreast of the latest developments and perspectives in the domain of contact angle, wettability and adhesion will find this compendium of great interest and value. Also I hope the information consolidated in this volume will serve as a fountainhead for new research ideas and applications.

Acknowledgements

Now comes the pleasant task of thanking those who were instrumental in the birth of this book. First and foremost, I would like to express my most sincere thanks to the authors for their interest, enthusiasm, cooperation and contribution, without which this book could not be materialized. Second, my heart-felt thanks go to the unsung heroes(reviewers) for their time and effort in providing invaluable comments which most certainly enhanced the quality of these articles. The comments from the peers are sine qua non for maintaining the highest standard of a publication. Last, but not least, I am appreciative of the earnest interest and unwavering help of Martin Scrivener (publisher) in bringing this book to fruition.

Kash Mittal P.O. Box 1280 Hopewell Jct., NY 12533 E-mail:[email protected] May 2, 2013

PART 1

FUNDAMENTAL ASPECTS

Chapter 1

Correlation between Contact Line Pinning and Contact Angle Hysteresis on Heterogeneous Surfaces: A Review and Discussion

Mohammad Amin Sarshar, Wei Xu, and Chang-Hwan Choi*

Department of Mechanical Engineering, Stevens Institute of Technology, Hoboken, New Jersey, USA

Abstract

Micro- or nano-textured hydrophobic surfaces have attracted considerable interest due to their highly water-repellent property, and are called superhydrophobic. Although such superhydrophobic surfaces typically exhibit high contact angles for water droplets, their adhesion and frictional properties such as contact angle hysteresis are significantly affected by the dynamics of contact line pinning at the droplet boundary. However, a clear correlation between the contact line pinning and the contact angle hysteresis has not been revealed yet. In this paper, we review the literature reporting on their correlation, both for chemically and physically patterned heterogeneous surfaces, including our recent discovery on superhydrophobic surfaces. Then, we propose and discuss an appropriate new physical parameter that shows close and consistent correlation between the dynamics of contact line pinning and the contact angle hysteresis.

Keywords: Contact angle hysteresis, contact line pinning, heterogeneous surfaces, superhydrophobic

1.1 Introduction

When hydrophobic surfaces are roughened or patterned in proper length scale and morphology, air can be entrapped between the surface structures (typically called as “Cassie state”) and the surfaces show highly non-wetting and slippery, so-called superhydrophobic property [1] that would be of great significance in many applications such as in self-cleaning [2], hydrodynamic friction reduction [3], anti-icing [4, 5], anti-corrosion [6], thermal/ energy system [7], biotechnology [8], and micro- and nano-devices [9]. Known as “lotus effect” [10], such superhydrophobic surfaces generally result in high contact angle and low contact angle hysteresis for water droplets so that water droplets can easily roll off from the surfaces. However, also known as “petal effect” [11], if water droplets wet the surfaces either partially or uniformly with no air void retained (typically called as “Wenzel state”), the surfaces exhibit high contact angle hysteresis despite high apparent contact angle. In such a case, water droplets get strongly pinned on the surfaces and do not roll off even when the surfaces are tiled even greater than 90°. Such sticky surfaces for droplets are also of great importance in many applications such as in spraying/coating [12], ink-jet printing [13], liquid transportation/analysis [14], and microfluidics [15]. Recently it has also been shown that superhydrophobic surfaces, even in Cassie state, can cause more significant contact line pinning and hence behave stickier than non-patterned planar hydrophobic surfaces, depending on the geometry and dimensions of surface patterns [16]. Such reports suggest that the pinning phenomena of droplets are affected in a complicate way by many surface parameters including physical morphology, chemical heterogeneity, and interfacial wetting states [17–21]. To date, a few different approaches have been applied to explain the direct correlation between the behaviors of contact line pinning and the adhesion or frictional properties such as contact angle hysteresis for moving droplets. One of them is based on the effective contact area between the droplet and the solid surface [22–27], while the other one is based on the effective contact length [16, 28–32]. In this paper, we review the literature and discuss which physical parameters would be more relevant to correlate the dynamics of contact line pinning and the adhesion properties of heterogeneous surfaces such as contact angle hysteresis of superhydrophobic surfaces. Based on these, we also propose a non-dimensional surface parameter that can be universally applied to determine their correlation. Despite being simple, the new physical parameter revealed in this paper should serve as a quick and efficient criterion for the design and engineering of heterogeneous or superhydrophobic surfaces with tailored adhesion properties.

1.2 Contact Line Pinning on Chemically Heterogeneous Flat Surfaces

(1.1)

When the contact line recedes or advances over the multiple defects with a small number density, the pinning force per unit length of the contact line can be reduced to [34]:

(1.2)

(1.3)

where WR and WA represent the dissipation energies per unit area (or pinning force per unit length) due to the deformation of contact line at a single defect in the receding (θR: receding contact angle) and the advancing (θA: advancing contact angle) motions of the droplet, respectively, and n is the total number of defects engaged in the contact line movement. By combining Equations 1.2 and 1.3, it leads to obtain an equation for contact angle hysteresis (cosθR − cosθA), such as:

(1.4)

Physically, WR and WA have the same meaning as the localized pinning force (F) described in Equation 1.1. Thus, if the localized pinning force (F) is known for each defect engaged in the contact line movement, the effect of key surface parameters determining the contact angle hysteresis can be understood, such as the diameter of the defect (d) shown in Equation 1.1.

Experimentally, Cubaud and Fermigier [35] also studied the pinning force of a contact line on chemically heterogeneous surfaces. In the case of a small number density of defects, they proposed that one of the useful parameters, which would be more relevant to define the pinning force than probing the mechanical deformation of the contact line (x, Figure 1.1), would be the angle which the two tangents to the contact lines at each side of the defect make (called depinning angle, Figure 1.1). In order to correlate with the depinning angle, they also introduced a new physical parameter fs for the defects, defined as:

(1.5)

where Δs is the difference in spreading coefficients between the substrate and the defect and h is the thickness (height) of the droplet. They regulated the value of fs by varying the diameter of the defect (from 100 μm to 1800 μm) and examined how the depinning angle would change for a single defect. Based on their experimental observation, they concluded that there should be a critical value for fs so if fs is less than the critical value there is only little change in the depinning angle, resulting in weak pinning. However, if fs is greater than the critical value, the depinning angle significantly decreases, resulting in strong pinning. In the case of the higher density of defects, an increase of fs also results in stronger pinning of the contact line, which consequently transitions the droplet shape from a circular drop to a faceted drop. For example, the droplet shape would be transitioned to a square shape with a square array of defects. They also reported that the roundness of the faceted shape, defined as P2r/4πψ where Pr is the perimeter of the droplet and ψ is the wetted area, tends to increase linearly with respect to fs. Cubaud and coworkers [36] also investigated the dynamics of contact line movement over the chemically patterned surfaces by fixing the defect diameter at 400 μm while varying the distance between them from 600 μm to 4000 μm. They observed that when the distance between two defects was less than twice the defect diameter, the deformation of the contact line by a single defect was not pronounced and the defects acted collectively as a cluster to deform the contact line globally.

Although Cubaud and coworkers [35, 36] showed how the number density of defects would affect the contact line morphology and the pinning force, it was not clearly discussed how the contact angle hysteresis would also be affected. In contrast, Di Meglio [37] directly measured the forces required for advancing and receding non-wetting liquids such as hexadecane and heptane on chemically heterogeneous surfaces by connecting a force measurement sensor to the surface samples while they were dipped into or pulled out of the liquids at a constant velocity. The surfaces of samples consisted of planar defects with two distinct diameters of 500 μm and 1500 μm at varying number densities with random distribution. In their experiment, hysteresis was defined as the difference between the advancing and receding forces. They found that the amount of hysteresis increased with the defect density in a non-linear manner.

1.3 Contact Line Pinning on Hydrophobic Structured Surfaces

Now we change our focus from chemically heterogeneous surfaces to physically patterned hydrophobic surfaces and the correlation between the dynamics of contact line pinning and the contact angle hysteresis on superhydrophobic surfaces. The fundamentals and overviews of the superhydrophobic wetting properties can be found in many review papers and references therein [1, 38–42]. In general, the concept used in the derivation of Equation 1.4 can still be applied to estimate how much force is necessary to make a droplet move on superhydrophobic surfaces [24, 43, 44] or roll off in inclination [21, 26, 31, 43]. In order to find out the key physical parameters associated with the depinning force and the contact angle hysteresis more specifically, the influence of surface morphology of superhydrophobic patterns on the droplet pinning has also been studied from the perspective of both contact area [22–24, 27, 43] and contact length [16, 28–30, 32, 45, 46].

McHale and coworkers [22, 23] have commented on the pinning phenomena and contact angle hysteresis as a consequence of the effective contact area between liquid and solid. They measured the contact angle hysteresis on systematically designed superhydrophobic surfaces (Figure 1.2), where the contact perimeter of the liquid-solid interface was varied but the effective contact area of the liquid-solid interface was held constant. Then, they observed that the contact angle hysteresis was invariant despite the differences in contact perimeters.

Figure 1.2 The superhydrophobic surfaces with different patterns tested in the work of McHale et al [22]. The fractions of the solid area (black squares) of the three tested surfaces are the same, while the perimeters are different.

Figure 1.3 Contact line deformation in a receding motion of a droplet over a superhydrophobic surface patterned with circular pillar structures.

(1.6)

(1.7)

where a is an empirical correction factor, b is the radius of the pillar, p is the pitch of the pillar array, and ϕ is the solid area fraction. Their experimental results showed good agreement with the analytical model (Equation 1.7), especially when the number density of the pillar structures was relatively small (i.e., the solid area fraction ϕ is small).

For a rolling droplet on inclined superhydrophobic surfaces, Lv et al. [43] proposed a theoretical model based on the total interfacial energy and derived an equation such as:

(1.8)

where is ρ the density of liquid, g is gravitational acceleration, V is the volume of the droplet, α is the roll-off (or sliding) angle, and R is the radius of the wetted area. On the other hand, by considering the force balance between the weight of the droplet and the pinning force associated with contact angle hysteresis, the following equation can also be derived [43]:

(1.9)

where it is assumed that a half of the droplet experiences an advancing motion and the other half experiences a receding motion as the droplet rolls (slides) down [24, 43]. Comparing Equations 1.8 and 1.9, the contact angle hysteresis can be related to the geometric parameters of the surface as follows:

(1.10)

Equation 1.10 suggests that the contact angle hysteresis is rather determined by the square root of the solid fraction (i.e., length scale such as a contact line) than the solid fraction (area) itself. If Equation 1.10 is plotted together with Equation 1.7 for comparison, they show a similar relationship between the contact angle hysteresis and the solid fraction. It further suggests that the length scale (e.g., contact line) is a more relevant parameter to determine the contact angle hysteresis than the contact area (e.g., solid fraction) itself.

The importance of the dynamics of contact line to the droplet pinning and the contact angle hysteresis was also discussed by McCarthy and coworkers [16, 28, 29]. They pointed out that what happens at the contact line during the advancing and receding motions of the droplet would be the key in determining the contact angle hysteresis. It is because only the events that occur at the contact line can contribute to the pinning phenomenon and the contact angle hysteresis (Figure 1.4). This suggests that the pinning force and the resultant contact angle hysteresis on superhydrophobic surfaces should significantly be dependent on the dynamics of contact line movement (e.g., deformation and shape) when the droplet advances or recedes. Dorrer and Rühe [46] numerically studied the deformation of contact line of a water droplet moving on square arrays of square post structures and reported a significant distortion of the contact line at the droplet boundary. They found the local contact angles to be different from apparent ones due to the local pinning effect at the surface structures. Especially, in an advancing motion, the contact line moves to the edges of the post structures and gets pinned at the edges until the local contact angle approaches 180°. Dorrer and Rühe [45] also experimentally observed that the advancing contact angle was not affected by the change in geometric parameters of the surface structures. In contrast, it was shown that the receding contact angle was strongly dependent on the geometric parameters of the surface structures. Mognetti and Yeomans [27] also numerically studied the morphology of contact line when the droplet moves on superhydrophobic surfaces with square arrays of post structures. They found that as the solid fraction decreased, the shape of the contact line in the receding motion would be of cosh form and the contact angle hysteresis would follow the same trend as shown in Equation 1.10.

Figure 1.4 The schematic of a droplet moving on a solid substrate. Only the liquid molecules near the contact line (unfilled circles) move during this process. No movement happens to the liquid molecules in the inner region of the interface between liquid and solid surface (filled circles) [28].

Recently, Xu and Choi [32] also proposed that the ratio of the actual contact line to the apparent contact line was a simple and efficient parameter to describe the pinning force and the contact angle hysteresis, instead of the solid fraction (area). They examined an evaporating droplet on superhydrophobic surfaces with square arrays of micropillar structures whose diameters were fixed at 5 μm while the inter-pillar distances were varied from 5 to 50 μm. By observing the contact interface between the droplet and the superhydrophobic surface directly using reflection interference contrast microscopy, they found that the actual contact line on a superhydrophobic surface comprised of both two-phase (liquid-air) and three-phase (liquid-solid-air) interfaces was significantly different from an apparent three-phase contact line as shown in Figure 1.5. Such multi-modal contact line state was dynamically altered when the droplet receded during evaporation (Figure 1.6), and the onset of the contact line depinning occurred when the three-phase contact line reached the maximum (i.e., covering the whole periphery of the circular pillar surface). Then, the depinning force (Fd) [47] defined as

Figure 1.5 The multi-modal droplet boundary on a pillar-patterned superhydrophobic surface, observed from the backside of a transparent superhydrophobic substrate using reflection interference contrast microscopy. The interference fringe, formed by the light reflected from the water-air interface and the solid substrate, indicates the location of the actual droplet boundary. This actual droplet boundary is different from the apparent boundary, and is constituted by the three-phase (liquid-solid-air) as well as the two-phase (liquid-air) interfaces [32].

Figure 1.6 The reflection interference contrast microscopy images show the evolution of the actual boundary of an evaporating droplet on a micropillar patterned superhydrophobic surface. The three-phase (liquid-solid-air) contact line and the two-phase (liquid-air) interface on the droplet boundary are shown by the solid and dashed lines, respectively. The depinning from pillars on the surface occurs when the three-phase contact line reaches the maximum (i.e., covering the whole periphery of the circular pillar top surface) [32].

(1.11)

was found to display a linear correlation with the normalized maximal three-phase contact line at the droplet boundary (i.e., the ratio of maximal actual three-phase contact line to apparent droplet boundary), called δ (Figure 1.7). The result shows that when δ is greater than unity (the value on a planar surface with no pattern), a higher depinning force is required even on superhydrophobic surfaces than that on a planar hydrophobic surface. Therefore, such superhydrophobic surfaces with δ > 1 behave as stickier surfaces for droplets than a planar hydrophobic surface. On the contrary, if δ is less than unity, a lower depinning force is required with the superhydrophobic surfaces, and hence a superhydrophobic surface with δ < 1 is slippery compared to a planar hydrophobic surface. The new non-dimensional parameter, δ, defined as the ratio of maximal actual three-phase contact line to apparent droplet boundary, is directly proportional to the square root of solid fraction, when the three-phase contact line covers the whole perimeter of surface structures as the droplet advances or recedes. Thus, this result also agrees with the general trend shown in Equation 1.10.

Figure 1.7 The linear dependence of the depinning force on the normalized maximal three-phase contact line (δ) at the droplet boundary. The superhydrophobic surfaces can behave as sticky or slippery surfaces depending on the surface parameter (δ). The result from Öner and McCarthy [16] was also analyzed with the new parameter (δ). In the experiments of Xu and Choi [32], the liquid-solid contact area fractions on the tested surfaces were systematically varied from 1.00, 0.20, 0.09, 0.03, to 0.01, denoted as Φ1.00, Φ0.20, Φ0.09, Φ0.03, and Φ0.01, respectively.

Xu and Choi [32] also analyzed the previous works reported by McHale and coworkers [22, 23] by using the parameter δ, and found that the normalized maximal three-phase contact lines (δ) of their tested surfaces (Figure 1.2) had the same value. Thus, according to the observation made by Xu and Choi [32], such surface morphologies with a constant δ value should result in the same depinning force and hence the same contact angle hysteresis, which was indeed observed by McHale and coworkers [22, 23]. Therefore, the experimental results of McHale and coworkers [22, 23] turn out to agree with the model proposed by Xu and Choi [32]. Xu and Choi [32] also compared their results with those of McCarthy and coworkers [16, 28, 29]. The three-phase contact line referred in the works of McCarthy and coworkers [16, 28, 29] represents a static and apparent one, instead of the dynamically altered actual three-phase contact line measured in the work of Xu and Choi [32]. Xu and Choi [32] pointed out that the static or apparent surface parameters would not be appropriate to understand and explain the dynamic behaviours of the contact line pinning and contact angle hysteresis on superhydrophobic surfaces. As commented by Xu and Choi [32], direct correlation between the surface morphology and contact angle hysteresis was not found in the work of McCarthy and coworkers [16, 28, 29] using the apparent three-phase contact line as a geometric parameter. Thus, Xu and Choi [32] reanalyzed the previous works of McCarthy and coworkers [16, 28, 29] by using their parameter δ, and found that their experimental results also agreed well with the model proposed by Xu and Choi [32] as shown in Figure 1.7.

Figure 1.8 Comparison of the depinning forces of superhydrophobic surfaces reported by Reyssat and Quéré [24] as well as Dorrer and and Rühe [45] with respect to the non-dimensional geometric parameter δ proposed by Xu and Choi [32].

1.4 Summary and Conclusion

To date, the correlation between surface parameters and contact angle hysteresis has been studied using many different approaches. Recently, due to the advancement of micro- and nanofabrication technologies, such studies have been extended to micro- or nanopatterned hydrophobic surfaces (typically called superhydrophobic surfaces) because of their highly non-wetting properties and their great potentials in many scientific and engineering applications. However, a unified model to correlate the surface parameters of superhydrophobic surfaces and the contact angle hysteresis has not been revealed yet. In this paper, we reviewed the literature which has reported such correlation both theoretically and experimentally. We first reviewed the droplet pinning and contact angle hysteresis on chemically heterogeneous surfaces with hydrophobic defects. Such studies showed that the deformation of contact line and its state (e.g., morphology) are critical in determining the pinning force and the contact angle hysteresis. Similar analysis can be applied to the physically heterogeneous superhydrophobic surfaces where a significant pinning occurs periodically on the array of hydrophobic structures. Most studies have used the solid wet-area fraction as the key surface parameter to interpret the pinning force/energy and the contact angle hysteresis. In contrast, a few recent studies proposed that the three-phase contact line should be a more relevant and direct parameter to correlate with the pinning force and contact angle hysteresis. Based on the new surface parameter proposed in recent studies, we revisited and analyzed the previous data. It shows that the depinning force of a receding droplet has overall linear correlation with a non-dimensional geometric parameter, defined as the ratio of the maximum length of the three-phase contact line configured at the droplet boundary to the circular perimeter of the apparent droplet boundary. It suggests that the morphology and pinning state of the contact line at the droplet boundary are more critical parameters than the effective contact area to determine the pinning force and the contact angle hysteresis on superhydrophobic surfaces. The morphology and pinning state of the contact line are significantly dependent on the morphology and surface chemistry of the patterned structures on superhydrophobic surfaces. Thus, more systematic and extensive studies are necessary to verify the linear model proposed by recent studies in order to use it as a universal and unified model to predict the pinning force and contact angle hysteresis for a variety of heterogeneous and superhydrophobic surfaces.

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*Corresponding author: [email protected]

Chapter 2

Computational and Experimental Study of Contact Angle Hysteresis in Multiphase Systems

Vahid Mortazavi, Vahid Hejazi, Roshan M D’Souza, and Michael Nosonovsky*

College of Engineering & Applied Science, University of Wisconsin-Milwaukee, Milwaukee, Wisconsin, USA

Abstract

Contact angle (CA) hysteresis exists due to the surface roughness and chemical heterogeneity. It is caused by a variety of factors, including adhesion hysteresis in the solid-water contact area (2D effect) and by pinning of the solid-water-air triple line (1D effect). In this study we show that CA hysteresis is present also in complex systems, such as an organic liquid (oil) in contact with a solid immersed in water. We study experimentally CA hysteresis in solid-water-air (droplet), solid-air-water (bubble), solid-water-oil and solid-water-air-oil systems. Then, we use the Cellular Potts Model (CPM) to discuss dependency of CA hysteresis on the surface structure and other parameters. This analysis allows decoupling of the 1D (pinning of the triple line) and 2D effects (adhesion hysteresis in the contact area) and provides new insights into the nature of the CA hysteresis.

Keywords: Contact angle hysteresis, hydrophobicity, oleophobicity, surface roughness, Cellular Potts model, multiphase system

2.1 Introduction

Contact angle (CA) is the main parameter in the study of wetting, which characterizes wetting of a solid surface by a liquid. It was introduced by Young [1] along with the concept of the interfacial tensions of the solid, liquid and vapor interfaces. Young related the CA to these interfacial tensions, using simple considerations of the equilibrium at the triple line, i.e., the line where the solid, liquid and vapor phases come in contact

(2.1)

where γSL, γSV, and γLV are the interfacial energies of the solid-liquid, solid-vapor and liquid-vapor interfaces, respectively (Figure 2.1). These interfacial energies can be thought of either as energies per unit area needed to create an interface or as generalized forces per unit length acting along the interfaces at the triple line in equilibrium. Note that unlike conventional mechanical forces, the tension forces are not applied to the triple line (which is a geometrical line and not a material object with mass) but rather constitute derivatives of the interfacial energies by the distance for which the triple line advances. These forces reflect the tendency of the system to reduce its energy (and increase entropy). The high solid-vapor energy of an interface causes wetting of the solid surface and spreading of liquid on it (low θ) while low energy produces non-wetting interfaces (high θ).

Figure 2.1 Three-phase interface of solid, water and vapor [28].

The molecules sitting at the free surface of materials have less binding with adjacent molecules than the molecules in the bulk, so they have potential to make new bindings. Materials with higher potential have higher wetting ability. The concept of interfacial free energy was introduced by J. W. Gibbs in the 1870s. Although the surface tension (measured in Nm−1) and interfacial energy (measured in Jm−2) are often assumed to be identical, they are not exactly the same. The surface tension or, more exactly, the surface stress is the reversible work per unit area needed to elastically stretch a pre-existing surface. The surface stress tensor is defined as

(2.2)

where εij is the elastic strain tensor and δij is the Kronecker delta. For a symmetric surface, the diagonal components of the surface stress can be calculated as

(2.3)

For liquids, the interfacial free energy does not change when the surface is stretched, however, for solids ∂γ/∂ε is not zero because the surface atomic structure of a solid is modified in elastic deformation [2].

Since the concept of the CA was introduced, it was realized that this single parameter cannot completely characterize wetting. Furthermore, there is no one single value of the CA, but it can have a range of values θrec ≤ θ ≤ θadv, where θrec and θadv denote the receding and advancing contact angles, respectively. The contact angle can be measured also on a tilted surface (Figure 2.2), although it is recognized that the values measured in this way do not always provide true values of the advancing and receding angles [3]. The difference between the advancing and receding CAs is called CA hysteresis. Originally, CA hysteresis was associated with surface contaminants. Lord Rayleigh [4] noted that for the contaminated glass surfaces the CA can vary significantly, since “if after the drop is deposited, some of the liquid is drown off, the angle may be diminished almost to zero.” This phenomenon was described in a letter from a German scientist Agnes Pockels, who had no formal education and made observation on dishes in a kitchen sink. She observed that water droplets behaved differently on clean and contaminated glass surfaces. She wrote a letter to Lord Rayleigh who published it in the journal Nature [4]:

Figure 2.2 Advancing and receding contact angles for a droplet on a tilted solid surface [28].

“The surface tension of a strongly contaminated water surface is variable; that is, it varies with the size of the surface. The minimum of the separating weight attained by diminishing the surface is to the maximum, according to my balance, in the ratio of 52: 100. If the surface is further extended, after the maximum tension is attained, the separating weight remains constant, as with oil, spirits of wine, and other normal liquids. It begins, however, to diminish again, directly the partition is pushed back to the point of the scale at which the increase of tension ceased. The water surface can thus exist in two sharply contrasted conditions; the normal condition, in which the displacement of the partition makes no impression on the tension, and the anomalous condition, in which every increase or decrease alters the tension”.

This phenomenon was later investigated by Pockels [5], Ablett [6], and Adam and Jessop [7] who wrote: “In the extreme cases, the angle when the liquid is advancing over the solid may be 60° greater than when it is receding. It is not necessary that there should be actual motion, for a force on the liquid tending to move it has the same effect. The phenomenon is obvious on inspection of a drop of water on slightly dirty glass plate; it appears to have been first described in detail by Pockels [5]. The cause of this dragging effect (often called “hysteresis” of the angle of contact) seems to us to lie, not in any absorption of the liquid by the solid, but in a simple friction of the liquid on the surface” [7].

Adam and Jessop [7] related CA hysteresis to the “friction force” per unit length of the triple line, F, acting upon the droplet in its motion as

(2.4)

Using similar models, Good [8] and Shepard and Bartell [9] investigated later the effect of surface roughness on the CA hysteresis, which is similar to the effect of surface contamination or chemical heterogeneity.

When a water droplet spreads along a solid surface with low velocity (so that the effect of viscosity is negligible), the CA hysteresis serves a measure of energy dissipation due to the wetting/dewetting cycle. The similarity of the CA hysteresis with the so-called adhesion hysteresis (the difference between the energy spent for the separation of two surfaces and gained by bringing them together) and with dry friction was discussed in the literature [10].

In the recent studies of superhydrophobicity it has been emphasized that a superhydrophobic surface should not only have a high CA above 150°, but in addition, it should possess small CA hysteresis [11]. Despite this, reports have appeared recently in the literature that a material can be superhydrophobic and simultaneously strongly adhesive to water [12]. This phenomenon is known as the “petal effect,” since it is typical for certain rose petals which are characterized by a high CA and large CA hysteresis [13]. The discovery of the petal effect caused a discussion in the literature as to whether superhydrophobicity is adequately characterized only by a high CA and whether a surface can have a high CA but at the same time strong water adhesion. The phenomenon of the large CA hysteresis and high water adhesion to rose petals (and similar surfaces), as opposed to small CA hysteresis and low adhesion to Lotus leaf, was observed by several research groups [14–15]. Bormashenko et al. [14] reported a transition between wetting regimes, e.g., the penetration of liquid into the micro/nanostructures.

Li and Amirfazli [16] argued that since “superhydrophobicity” means a strong fear of water or lacking affinity to water, “the claim that a superhydrophobic surface also has a high adhesive force to water is logically contradictory.” However, the experimental demonstration of the rose petal effect made it clear that the CA as a sole parameter is not sufficient to characterize the adhesion of a liquid to a solid, because such adhesion may be different depending on the condition (such as the normal or shear mode of loading). Gao and McCarthy [17] suggested several illustrative experiments showing that even Teflon (polytetrafluoroethylene), which is usually considered very hydrophobic, under certain conditions can behave in a hydrophilic manner, i.e., it can have affinity to water. They argued that the concepts of “shear and tensile hydrophobicity” should be used, which makes wetting (“solid-liquid friction”) similar to the friction force, as has been pointed out in the literature earlier [10].

Wang and Jiang [18] suggested five superhydrophobic states (Wenzel’s state, Cassie’s state, so-called “Lotus” and “Gecko” states, and a transitional state between Wenzel’s and Cassie’s states). It may be useful also to identify the transition between the Wenzel, Cassie, and dry states as a phase transition and to add the ability of a surface to bounce off water droplet to the definition of superhydrophobicity. In addition, there is an argument on how various definitions of the CA hysteresis are related to each other [3, 14, 15, 19, 20].

According to early Wenzel [21] and Cassie & Baxter [22] models, there are two regimes of wetting of a rough surface by water: a homogeneous regime with a two-phase solid-water interface and a non-homogeneous or composite regime with a three-phase solid-water-air interface (air pockets are trapped between the solid surface and water). Both models predict that surface roughness affects the water contact angle (CA) and can easily bring it to extreme values close to 180° (superhydrophobicity) or close to 0° (superhydrophilicity). The studies of wetting of microstructured surfaces have concentrated on the investigation of these two regimes and the factors which affect the transition between the regimes [19].

Recent experimental findings and theoretical analyses made it clear that the early Wenzel and Cassie-Baxter models do not explain the complexity of interactions during wetting of a rough surface which can follow several different scenarios [12, 17, 18, 20, 23, 24, 25]. Bhushan and Nosonovsky [25] pointed out that for a hierarchical surface (with nanoroughness superimposed on microroughness), there can exist nine modes of wetting depending on whether water penetrates in micro and nanopores. As a result, there are several modes of wetting of a rough surface, and, therefore, wetting cannot be characterized by a single number such as the CA (Figure 2.3). Bormashenko [26] argued that for materials with positive disjoining pressure, nano-cavities will be filled first and thus the states in the upper row of Figure 2.3 are unlikely.

Figure 2.3 Schematics of nine wetting regimes for a rough surface characterized by no penetration, partial penetration, and complete penetration of water into microroughness, nanoroughness and both micro and nanoroughnesses [25].

Furthermore, when oleophobicity is investigated, the standard Wenzel (solid-liquid) and Cassie-Baxter (solid-liquid-air) wetting states can be extended for general three-phase (solid-water-air, solid-oil-air, and solid-oil-water) and four-phase (solid-oil-water-air) interfaces [27]. In this chapter, the CA hysteresis is discussed in such complex systems and both experimental [28] and computational [29] studies are conducted. Furthermore, the Cellular Potts Model (CPM) is used for the numerical simulation of the CA hysteresis. The advantage of the CPM scheme over more traditional simulation techniques, such as the Molecular Dynamics (MD) simulation and the Computational Fluid Dynamics (CFD) method, is that it allows investigating the system at the mesoscale, i.e., at the typical length of micrometers where most important interactions occur.

2.2 Origins of the CA Hysteresis

Several theories explaining CA hysteresis due to surface roughness and chemical heterogeneity have been proposed. The simplest model attributes hysteresis to pinning of the triple line by sharp asperities at the surface. Two surfaces come together at a sharp edge (Figure 2.4a), so the value of the CA is not unique at the edge, being in the range of values from the minimum value (corresponding to the slope on the left of the edge) to the maximum value (corresponding to the slope on the right of the edge). When liquid front advances, the triple line will be pinned at the edge until the CA reaches its maximum value. Similarly, when liquid recedes, the triple line is pinned until the CA reaches its minimum value. Therefore, varying surface slope results in CA hysteresis [28].

Figure 2.4 Schematic of advancing and receding contact angles (a) due to surface slope and (b) heterogeneity; (c) water column suspended in a capillary due to CA hysteresis [28].