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Wetting and Spreading REVIEWS OF MODERN PHYSICS, VOLUME 81, APRIL–JUNE 2009 Wetting and spreading Daniel Bonn Laboratoire de Physique Statistique, Ecole Normale Supérieure, 24 rue Lhomond, 75005 Paris, France and van der Waals-Zeeman Institute, University of Amsterdam, Valckenierstraat 65, 1018 XE, Amsterdam, The Netherlands Jens Eggers School of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, United Kingdom Joseph Indekeu Instituut voor Theoretische Fysica, Katholieke Universiteit Leuven, 3001 Leuven, Belgium Jacques Meunier and Etienne Rolley Laboratoire de Physique Statistique, Ecole Normale Supérieure, 24 rue Lhomond, 75005 Paris, France ͑Published 27 May 2009͒ Wetting phenomena are ubiquitous in nature and technology. A solid substrate exposed to the environment is almost invariably covered by a layer of fluid material. In this review, the surface forces that lead to wetting are considered, and the equilibrium surface coverage of a substrate in contact with a drop of liquid. Depending on the nature of the surface forces involved, different scenarios for wetting phase transitions are possible; recent progress allows us to relate the critical exponents directly to the nature of the surface forces which lead to the different wetting scenarios. Thermal fluctuation effects, which can be greatly enhanced for wetting of geometrically or chemically structured substrates, and are much stronger in colloidal suspensions, modify the adsorption singularities. Macroscopic descriptions and microscopic theories have been developed to understand and predict wetting behavior relevant to microfluidics and nanofluidics applications. Then the dynamics of wetting is examined. A drop, placed on a substrate which it wets, spreads out to form a film. Conversely, a nonwetted substrate previously covered by a film dewets upon an appropriate change of system parameters. The hydrodynamics of both wetting and dewetting is influenced by the presence of the three-phase contact line separating “wet” regions from those that are either dry or covered by a microscopic film only. Recent theoretical, experimental, and numerical progress in the description of moving contact line dynamics are reviewed, and its relation to the thermodynamics of wetting is explored. In addition, recent progress on rough surfaces is surveyed. The anchoring of contact lines and contact angle hysteresis are explored resulting from surface inhomogeneities. Further, new ways to mold wetting characteristics according to technological constraints are discussed, for example, the use of patterned surfaces, surfactants, or complex fluids. DOI: 10.1103/RevModPhys.81.739 PACS number͑s͒: 68.08.Bc, 47.55.np, 47.15.gm, 68.35.Dv CONTENTS 1. First-order and critical wetting 753 2. Long-range critical wetting 754 C. Fluctuation effects and short-range critical wetting 756 I. Introduction 740 D. Hot topics 757 A. How, what, and why? 740 1. Wetting in colloid-polymer mixtures 757 B. Statics 741 1. Basic surface thermodynamics 741 2. Wetting on structured surfaces 759 C. Drop spreading: Basic concepts 743 3. Wedge filling transitions 761 1. Huh and Scriven’s paradox 744 4. Incomplete wetting by crystalline phases 763 2. Apparent and microscopic contact angles 745 5. Electrowetting 763 3. Spreading laws 746 III. Dynamics 764 D. Real solid surfaces: Contact line hysteresis 746 A. Contact line region 765 II. Equilibrium Wetting Phenomena 748 B. Matching to a macroscopic flow 766 A. Equilibrium wetting behavior in relation 1. Numerical simulations 767 to the intermolecular interactions 748 C. Experiment 768 1. Long-range forces: The Hamaker constant 749 1. Zero equilibrium contact angle 769 2. Short-range forces: The phenomenological 2. Finite equilibrium contact angle 770 Cahn-Landau theory of wetting 751 D. Contact line dissipation and microscopic contact B. Real systems: Three scenarios for wetting transitions 752 angles 771 0034-6861/2009/81͑2͒/739͑67͒ 739 ©2009 The American Physical Society 740 Bonn et al.: Wetting and spreading 1. Free energy balance 771 surface forces can still be important over distances cor- 2. Sources of dissipation 772 responding to a few tens of molecules, because their al- 3. Precursor films 773 gebraic decay is rather slow; we hence call them “long E. Matching to the contact line 773 ranged.” The van der Waals forces are responsible for 1. Sharp interface 773 the equilibrium thickness of wetting films, and are be- 2. Diffuse interface 774 lieved to be important for the way fluids spread over a F. Molecular dynamics 775 solid surface. Both van der Waals and electrostatic G. Receding contact line 776 forces determine the stability of soap films ͑Vrij, 1966͒. H. Dewetting 777 Indeed, wetting and spreading are of key importance I. Linear instabilities of driven contact lines 779 for many applications. At large scales, wetting or non- J. Hot topics 780 wetting plays an important role in oil recovery ͑Ber- 1. Corners and air pockets 780 trand, Bonn, Broseta, Shahidzadeh, et al., 2002͒ and the 2. Spreading of complex fluids: Polymers and efficient deposition of pesticides on plant leaves ͑Berg- surfactants 782 eron et al., 2000͒, and also in the drainage of water from 3. Evaporating drops 783 highways ͑Shahidzadeh et al., 2003͒ and the cooling of IV. Disordered Solid Surfaces 784 industrial reactors. On a smaller scale, wetting solutions A. How to model a real solid surface? 784 have been proposed to solve technological problems in B. The single defect case 785 microfluidics and nanoprinting, inkjet printing, etc. 1. Pinning on a single defect 785 ͑Tabeling, 2004͒. All these phenomena are governed by 2. Dilute defects 786 the surface and interfacial interactions, acting usually at 3. Dynamics 787 small ͑a few nanometers for van der Waals or electro- C. Substrates with interacting defects 788 static interactions͒ or very small ͑molecular͒ distances. 1. The shape of the contact line at equilibrium 788 These length scales are now being probed with relatively 2. Hysteresis 789 new experimental techniques, such as atomic force mi- 3. Predictions and measurement of the critical croscopy and surface force apparatus, or theoretical behavior 789 tools, such as molecular dynamics, etc., allowing new in- a. Equation of motion 789 sights into the old problems of surface forces. In addi- b. Critical behavior 790 tion, new concepts are being introduced to influence c. Beyond the harmonic approximation 791 both the statics and dynamics of wetting, such as pat- D. Thermal noise 791 terned surfaces, surfactants, and non-Newtonian flow, in E. Hot topics 792 order to solve some of the technological problems men- 1. Hysteresis again 792 tioned above. 2. Prewetting transition on disordered In this review, we first study the equilibrium state of substrates 792 liquids deposited on a solid or another liquid, and how Acknowledgments 793 this state is determined by both short-range and long- References 793 range molecular interactions. As a thermodynamic pa- rameter, such as the temperature, is varied, the system may pass from one wetting state to another. These so- I. INTRODUCTION called wetting transitions have perhaps been the most A. How, what, and why? active subdiscipline in the field of phase transitions over the past two decades. In particular, a number of recent Wetting phenomena are an area where chemistry, experiments have reinvigorated interest and challenged physics, and engineering intersect. Surface chemistry is some long-held theoretical views. of key importance in determining wetting behavior, and Next we describe the dynamic problems involved in much research has been devoted to modifying the sur- reaching an equilibrium state, and their relation to the face chemistry of various solids in order to obtain spe- surface chemistry. This is a subtle problem, as a classical cific wetting properties ͑Durian and Franck, 1987͒. More hydrodynamic description breaks down at the moving or less standard chemical means to do this is, for in- contact line at the edge of a spreading droplet, and mi- stance, plasma treatment ͑Wu, 1982͒ or silanization croscopic features have to be invoked. As a result, both ͑Brzoska et al., 1992͒. By such treatments, one modifies large-scale ͑hydrodynamic͒ features and short-scale ͑mo- the chemical properties of the surface of the material, lecular͒ dynamics are inextricably linked into a truly and hence the contact energy of the surface with liquids, multiscale problem. vapors, or other solids. Finally, wetting is a subject in which disorder plays an As these “chemical’’ interactions act over the scale of important role in practice, and even under idealized molecules, one often refers to them as short-ranged in- laboratory conditions, for both statics and dynamics. On teractions. In addition to the surface chemistry, surface the one hand, impurities may lead to frustration, so that forces such as van der Waals or electrostatic forces are the true equilibrium state is never reached: a small drop- paramount for determining whether or not a fluid will let is often observed to rest on an inclined surface; see wet a given surface. These forces have been studied in Fig. 1. On the other hand, the resulting roughness of the detail by physicists and physical chemists. van der Waals contact line leads to complicated dynamics, still poorly Rev. Mod. Phys., Vol. 81, No. 2, April–June 2009 Bonn et al.: Wetting and spreading 741 FIG. 3. ͑Color online͒ The three different possible wetting states according to Young’s equation. ␥ ␥ ␥ ␪ ͑ ͒ SV = SL + cos eq, 1 where throughout ␥ϵ␥ denotes the liquid-vapor sur- ͑ ͒ LV FIG. 1. Color online Plant leaves after rain. face tension. Here the surface tensions are defined when the three phases, solid, liquid, and gas, are at least in mechanical equilibrium ͑force balance͒ with each other. understood. The close connections to other dynamical In addition, we consider chemical equilibrium ͑chemical problems involving many length scales, such as domain potential matching for each component present͒ and walls, imbibition fronts, or vortex lattices, have made thermal equilibrium ͑temperature matching͒ between this an extremely active field.
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