Wetting and spreading Daniel Bonn1, Jens Eggers2, Joseph Indekeu3, Jacques Meunier1, and Etienne Rolley1 1Laboratoire de Physique Statistique, Ecole Normale Sup´erieure, 24, rue Lhomond, 75005 Paris, France 2School of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, United Kingdom 3Instituut voor Theoretische Fysica, Katholieke Universiteit Leuven, 3001 Leuven, Belgium 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, we first consider the surface forces that lead to wetting, 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; we show that recent progress allows to relate the critical exponents directly to the nature of 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, or 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 micro- and nanofluidics applications. The second part of the paper deals with the dynamics of wetting. A drop placed on a substrate which it wets, spreads out to form a film. Conversely, a non-wetted substrate previously covered by a film dewets upon an appropriate change of system parameters. The hydrodynamics of both wetting and dewetting is influenced profoundly by the presence of the three-phase contact line separating “wet” regions from those which are either dry or covered by a microscopic film only. We review recent theoretical, experimental, and numerical progress in the description of moving contact line dynamics, and explore its relation to the thermodynamics of wetting. In addition we survey recent progress on rough surfaces. We explore in detail the anchoring of contact lines and contact angle hysteresis, resulting from surface inhomogeneities. Further, we discuss new ways to mold wetting characteristics according to technological constraints, e.g., the use of patterned surfaces, surfactants or complex fluids. PACS numbers: Contents 2. Finite equilibrium contact angle 32 D. Contact line dissipation and microscopic contact angles33 I. Introduction 2 1. Free energy balance 33 A. How, What and Why? 2 2. Sources of dissipation 34 B. Statics 3 3. Precursor films 34 1. Basic surface thermodynamics 3 E. Matching to the contact line 35 C. Drop spreading: basic concepts 4 1. Sharp interface 35 1. Huh and Scriven’s paradox 6 2. Diffuse interface 35 2. Apparent and “microscopic” contact angles 7 F. Molecular dynamics 36 3. Spreading laws 8 G. Receding contact line 38 D. Real solid surfaces: contact line hysteresis 8 H. Dewetting 39 I. Linear instabilities of driven contact lines 40 II. Equilibrium wetting phenomena 10 J. Hot topics 42 A. Equilibrium wetting behavior in relation to the 1. Corners and air pockets 42 intermolecular interactions 10 2. Spreading of complex fluids: polymers and 1. Long-range forces: the Hamaker constant 11 surfactants 43 2. Short-range forces: the phenomenological 3. Evaporating drops 45 Cahn-Landau theory of wetting 13 B. Real systems: three scenarios for wetting transitions 14 IV. Disordered solid surfaces 46 1. First-order and critical wetting 14 A. How to model a real solid surface? 46 2. Long-range critical wetting 15 B. The single defect case 47 C. Fluctuation effects and short-range critical wetting 18 1. Pinning on a single defect 47 D. Hot topics 19 2. Dilute defects 48 1. Wetting in colloid-polymer mixtures 19 3. Dynamics 48 2. Wetting on structured surfaces 21 C. Substrates with interacting defects 49 3. Wedge filling transitions 23 1. The shape of the contact line at equilibrium 50 4. Incomplete wetting by crystalline phases 25 2. Hysteresis 50 5. Electrowetting 25 3. Predictions and measurement of the critical behavior 51 III. Dynamics 26 D. Thermal noise 52 A. Contact line region 26 E. Hot topics 54 B. Matching to a macroscopic flow 28 1. Hysteresis again! 54 1. Numerical simulations 29 2. Prewetting transition on disordered substrates 54 C. Experiment 30 1. Zero equilibrium contact angle 30 References 54 2 I. INTRODUCTION A. How, What and Why? Wetting phenomena are a playground where chemistry, physics and engineering intersect. Surface chemistry is of key importance in determining wetting behavior, and a large research effort has been put into modifying the sur- face chemistry of various solids in order to obtain specific wetting properties (Durian and Franck, 1987). More or less standard chemical means to do this are for instance, FIG. 1 Plant leaves after the rain. plasma treatment (Wu, 1982) or silanization (Brzoska et al., 1992). By such treatments, one modifies the chem- ical properties of the surface of the materials, and hence the contact energy of the surface with liquids, vapors or other solids. As these “chemical” interactions act over a scale of may pass from one wetting state to another. These so- molecules, one often refers to them as short-ranged in- called wetting transitions have perhaps been the most teractions. In addition to the surface chemistry, surface active sub-discipline in the field of phase transitions over forces such as van der Waals or electrostatic forces are the past two decades. In particular, a number of recent paramount for determining whether a fluid will wet a experiments have reinvigorated interest and challenged given surface or not. These forces have been studied in some long-held theoretical views. detail by physicists and physical chemists. As we will see below, van der Waals surface forces can still be important Next we describe the dynamic problems involved in over distances corresponding to a few tens of molecules, reaching an equilibrium state, and their relation to the because their algebraic decay is rather slow; we hence surface chemistry. This is a subtle problem, as a classi- call them “long-ranged”. The van der Waals forces are cal hydrodynamic description breaks down at the moving responsible for the equilibrium thickness of wetting films, contact line at the edge of a spreading droplet, and micro- and are believed to be important for the way fluids spread scopic features have to be invoked. As a result, both large over a solid surface. Both van der Waals and electrostatic scale (hydrodynamic) features and short scale (molecu- forces determine the stability of soap films (Vrij, 1966). lar) dynamics are inextricably linked into a truly multi Indeed, wetting and spreading are of key importance scale problem. for many applications. At large scales, wetting or non- wetting plays an important role in oil recovery (Bertrand, Finally, wetting is a subject in which disorder plays a 2002), the efficient deposition of pesticides on plant leaves very important role in practice, and even under idealized (Bergeron et al., 2000), but also in the drainage of water laboratory conditions, for both statics and dynamics. On from highways (Shahidzadeh et al., 2003) and the cool- the one hand, impurities may lead to frustration, such ing of industrial reactors. On a smaller scale, wetting so- that the true equilibrium state is never reached: a small lutions have been proposed to solve technological prob- droplet is often observed to rest on an inclined surface, lems in microfluidics and nanoprinting, inkjet printing see Fig. 1. On the other hand, the resulting roughness of etc. (Tabeling, 2004). All these phenomena are governed the contact line leads to very complicated dynamics, still by the surface and interfacial interactions, acting usually poorly understood. The close connection to other dy- at small (a few nm for van der Waals or electrostatic in- namical problems involving many length scales, such as teractions) or very small (molecular) distances. These domain walls, imbibition fronts, or vortex lattices, have length scales are now being probed with relatively new made this an extremely active field. experimental techniques such as atomic force microscopy and the surface force apparatus or theoretical tools, such Some or all of the ground covered in this review has as molecular dynamics etc., allowing new insights into been treated in a number of previous books and articles. the old problems of surface forces. In addition, new con- For older work, see the classical review by de Gennes cepts are being introduced to influence both the statics (1985), as well as L´eger and Joanny (1992) and the col- and dynamics of wetting, such as patterned surfaces, sur- lection of articles in J. C. Berg (1993). More recent factants, non-Newtonian flow, in order to solve some of work has been reviewed by Voinov (2002), Blake (2006), the technological problems mentioned above. and in the books by de Gennes et al. (2003) and Starov In this review, we first study the equilibrium state of et al. (2007). Equilibrium phenomena are covered by liquids deposited on a solid or another liquid, and how Fisher (1986), Sullivan and Telo da Gama (1986), Diet- this state is determined by both short-range and long- rich (1988), Schick (1990), Evans (1990), Indekeu (1994), range molecular interactions. As a thermodynamic pa- and more recently by Bonn and Ross (2001) and in the rameter, such as the temperature, is varied, the system book by Safran (2003). 3 B. Statics 1. Basic surface thermodynamics If we consider a liquid drop on a solid substrate, there are three different phases present, see Fig.2. Therefore there are three surface tensions that need to be consid- ered: solid-liquid, liquid-gas and solid-gas. Young’s equa- tion (Young, 1805) gives the relation between the equilib- FIG. 2 Young’s equation can also be interpreted as a mechan- ical force balance on the three-phase contact line; the surface rium contact angle θeq the drop makes with the surface and the three surface tensions as: tension is an energy per unit area, equivalent to a force per unit length acting on the contact line.