Table of contents

The discovery of wetting as a topic of physical science dates back two hundred years, to one of the many achievements of the eminent British scholar Thomas Young. He suggested a simple equation relating the contact angle between a liquid surface and a solid substrate to the interfacial tensions involved [1],

γ_lg cos θ = γ_sg - γ_sl (1)

In modern terms, γ denotes the excess free energy per unit area of the interface indicated by its indices, with l, g and s corresponding to the liquid, gas and solid, respectively [2]. After that, wetting seems to have been largely ignored by physicists for a long time. The discovery by Gabriel Lippmann that θ may be tuned over a wide range by electrochemical means [3], and some important papers about modifications of equation~(1) due to substrate inhomogeneities [4,5] are among the rare exceptions.

This changed completely during the seventies, when condensed matter physics had become enthusiastic about critical phenomena, and was vividly inspired by the development of the renormalization group by Kenneth Wilson [6]. This had solved the long standing problem of how to treat fluctuations, and to understand the universal values of bulk critical exponents. By inspection of the critical exponents of the quantities involved in equation~(1), John W Cahn discovered what he called critical point wetting: for any liquid, there should be a well-defined transition to complete wetting (i.e., θ = 0) as the critical point of the liquid is approached along the coexistence curve [7]. His paper inspired an enormous amount of further work, and may be legitimately viewed as the entrance of wetting into the realm of modern physics.

Most of the publications directly following Cahn's work were theoretical papers which elaborated on wetting in relation to critical phenomena. A vast amount of interesting, and in part quite unexpected, ramifications were discovered, such as the breakdown of universality in thin film systems [8]. Simultaneously, a number of very specific and quantitative predictions were put forward which were aimed at direct experimental tests of the developed concepts [9].

Experimentally, wetting phenomena proved to be a rather difficult field of research. While contact angles seem quite easy to measure, deeper insight can only be gained by assessing the physical properties of minute amounts of material, as provided by the molecularly thin wetting layers. At the same time, the variations in the chemical potential relevant for studying wetting transitions are very small, such that system stability sometimes poses hard to solve practical problems. As a consequence, layering transitions in cryogenic systems were among the first to be thoroughly studied [10] experimentally, since they require comparably moderate stability. First-order wetting transitions were not observed experimentally before the early nineties, either in (cryogenic) quantum systems [11,12] or in binary liquid mixtures [13,14]. The first observation of critical wetting, a continuous wetting transition, in 1996 [15] was a major breakthrough [16].

In the meantime, a detailed seminal paper by Pierre Gilles de Gennes published in 1985 [17] had spurred a large number of new research projects which were directed to wetting phenomena other than those related to phase transitions. More attention was paid to non-equilibrium physics, as it is at work when oil spreads over a surface, or a liquid coating beads off (`dewets') from its support and forms a pattern of many individual droplets. This turned out to be an extremely fruitful field of research, and was more readily complemented by experimental efforts than was the case with wetting transitions. It was encouraging to find effects analogous to layering (as mentioned above) in more common systems such as oil films spreading on a solid support [18,19]. Long standing riddles such as the divergence of dissipation at a moving contact line were now addressed both theoretically and experimentally [20,21].

However, the requirements concerning resolution of the measurements, as well as the stability and cleanliness of the systems, were immense for the reasons mentioned above. The pronounced impact of impurities was already well-known from contact angle measurements, where one invariably observes quite significant hysteresis effects and history dependence of the measured angle due to minute substrate inhomogeneity. This is why pioneering work on characteristic patterns emerging upon dewetting of thin liquid films [22] opened a long lasting, and eventually very fruitful, controversy on the question whether the underlying mechanism was unstable surface waves [24] (which was unambiguously observed for the first time in 1996 [23]) or `just' nucleation from defects.

By the mid-nineties, the physics of wetting had made its way into the canon of physical science topics in its full breadth. The number of fruitful aspects addressed by that time is far too widespread to be covered here with any ambition to completeness. The number of researchers turning to this field was continuously growing, and many problems had already been successfully resolved, and many questions answered. However, quite a number of fundamental problems remained, which obstinately resisted solution. Only a few shall be mentioned:

• There was no satisfactory explanation for triple point wetting [25], in particular for its ubiquity.

• The numerical values of contact line tensions in both theory and (very reproducible) experiments [26] were many orders of magnitude apart.

• In the particularly interesting field of structure formation, i.e., dewetting, there was no clear interpretation of many experimental results, and no possibility to distinguish with certainty between the different possible mechanisms. Furthermore, the impact of the rather strong non-linearities of the involved van der Waals forces was entirely unclear.

• In the more remote field of bionics, it was not clear how some plants manage to make liquids bead off so perfectly from their leaves.

This list, which is of course far from complete, serves to illustrate the wide scope of open questions. At that time, research groups in Germany concerned with wetting phenomena gathered and finally applied for a priority programme on wetting and structure formation at interfaces, which obtained funding from the German Science Foundation [27]. This special issue is dedicated to the research carried out within this programme. It spans the period starting from spring 1998 until summer 2004, and is presented as a combination of review over that period and original presentation of the state-of-the-art at its end.

Although only a very limited number of problems could be tackled within the programme, a few significant achievements could be attained. Some of these shall be highlighted:

• It could be shown that triple point wetting is a direct consequence of topographic substrate imperfection. By taking the bending energy of a solid slab on a rough substrate into account, accordance between theory [28] and experiment [29] was finally achieved.

• By applying scanning force microscopy to three phase contact lines, it could be shown that the `real' contact line tension is indeed much smaller than `observed' on macroscopic scale [39], and comes close to what is theoretically expected.

• In the field of structure formation by dewetting, unprecedented agreement between experiment [31], theory [32], and particularly careful simulations [33] was achieved. The underlying mechanisms could be clearly distinguished by means of Minkowski functionals.

• It could be shown both theoretically [34,35] and experimentally [36,37] that chemically patterned substrates give rise not only to a large variety of liquid morphologies, but that the latter can be manipulated and controlled in a precise manner.

• It was demonstrated that spherical (colloidal) beads may not only be used like surfactants as in Pickering emulsions, but that the resulting interface configurations may be applied to generate an amazing variety of well-controlled porous membranes, with a lot of potential applications [39].

This gives a flavour of the variety of topics addressed in the papers making up this issue. They are organized in five sections, each of which is opened with a short introduction explaining their mutual relation. For further access to the pertinent literature, the reader is referred to the references given in each article separately.

References

[1] Young T 1805 Philos. Trans. R. Soc. London 95 65

[2] Equation (1) is readily derived by demanding force balance at the contact line, where all three phases meet.

[3] Lippmann G 1886 Anal. Chim. 48 776

[4] Cassie A B D and Baxter S 1944 Trans. Faraday Soc. 40 546

[5] Wenzel R N 1949 J. Phys. Chem. 531466

[6] Wilson K G 1971 Phys. Rev. B 4 3174 and 3184

[7] Cahn J W 1977 J. Chem. Phys. 66 3667

[8] See, for example

Dietrich S and Schick M 1986 Phys. Rev. B 33 4952

[9] See, for example

Cheng E et al 1991 Phys. Rev. Lett. 67 1007

[10] Dash J G and Ruvalds J (ed) 1980 Phase Transitions in Surface Films (NATO advanced study series vol B51) (New York: Plenum)

[11] Nacher P J and Dupont-Roc J 1991 Phys. Rev. Lett. 67 2966

[12] Rutledge J E and Taborek P 1992 Phys. Rev. Lett. 69 937

[13] Bonn D, Kellay H and Wegdam G H 1992 Phys. Rev. Lett. 69 1975

[14] Bonn D, Kellay H and Wegdam G H 1993 J. Chem. Phys. 99 7115

[15] Ragil K et al 1996 Phys. Rev. Lett. 771532

[16] Findenegg G H and Herminghaus S 1997 Curr. Opin. Colloid Interface Sci. 2 301

[17] de Gennes P G 1985 Rev. Mod. Phys. 57 827

[18] Heslot F, Fraysse N and Cazabat A M 1989 Nature 338 1289

[19] Fraysse N et al 1993 J. Colloid Int. Sci. 158 27

[20] Huh C and Scriven L E 1971 J. Colloid Int. Sci. 35 85

[21] Brochard F et al 1994 Langmuir 10 1566

[22] Reiter G 1992 Phys. Rev. Lett. 68 75

[23] Bischof J et al 1996 Phys. Rev. Lett. 77 1536

[24] Ruckenstein E and Jain R K 1974 J. Chem. Soc. Faraday Trans. II 70 132

[25] Herminghaus S et al 1997 Annal. Phys. 6 425

[26] Li D and Neumann A W 1990 Colloids Surf. 43 195

[27] Deutsche Forschungsgemeinschaft, Schwerpunktprogramm 1052, `Benetzung und Strukturbildung an Grenzflächen'

[28] Esztermann A and Löwen H 2005 J. Phys.: Condens. Matter 17 S429

[29] Sohaili M et al 2005 J. Phys.: Condens. Matter 17 S415

[30] Pompe T and Herminghaus S 2000 Phys. Rev. Lett. 85 1930

[31] Seemann R et al 2005 J. Phys.: Condens. Matter 17 S267

[32] Herminghaus S et al 1998 Science 282 916

[33] Becker J and Gr\"un G 2005 J. Phys.: Condens. Matter 17 S291

[34] Lipowsky R \etal 2005 J. Phys.: Condens. Matter 17 S537

[35] Dietrich S et al 2005 J. Phys.: Condens. Matter 17 S577

[36] Gau H et al 19999 Science 283 46

[37] Mugele F \etal 2005 J. Phys.: Condens. Matter 17 S559

[38] Pfohl T et al 2003 Chem. Phys. Chem. 4 1291

[39 Xu H et al 2005 J. Phys.: Condens. Matter 17 S465

This first section deals with symmetry breaking and structure formation phenomena in thin films dewetting from solid substrates. In general, the system is prepared as a homogeneous film on a smooth substrate, and may thus be considered translationally invariant in the two dimensions of the film surface. Dewetting breaks this symmetry and leads to the formation of liquid topologies meant to minimize the total interfacial energy. For kinetic reasons, the `ground state' consisting of a single drop on an elsewhere dry substrate, forming the equilibrium contact angle with the latter, is never attained. Depending on the details of the system under study, a huge variety of different morphologies may form. A major unsolved problem, among others, was the experimental distinction between two important mechanisms: heterogeneous nucleation of dry patches, as by dust particles or other defects, and dewetting via dynamically unstable surface waves, also called spinodal dewetting.

The first two papers (Seemann et al, Becker and Grün) review recent advances concerning these topics from the experimental as well as the theoretical point of view. It is shown how samples must be prepared in order to observe spinodal dewetting, and how this may be assessed quite unambiguously by means of integral geometry methods. The so-called Minkowski functionals are successfully applied to the emerging structures to identify the dewetting scenario. All analysis is performed in the capillary wave picture, and hence by means of the thin-film equation. It is demonstrated that a simple linear inclusion of viscoelastic effects may explain all generic types of dewetting fronts observed experimentally, and it is shown that careful simulation of the thin film equation leads to quantitative agreement with experimentally observed liquid structures.

The third and fourth papers (Münch, Becker and Mugele) concentrate on effects of the boundary condition of the liquid at the substrate. It is first shown that the amount of friction at that interface may strongly affect the dewetting morphology discussed in the preceding papers, and it is then shown how this friction can be directly measured by means of the surface--force balance. The latter allows us to distinguish the friction between the liquid and the substrate from friction within the liquid itself. It is shown that proper preparation of the substrates (after-cleaving) may be crucial to prevent unwanted side effects, which have sometimes before been interpreted as solidification of the liquid.

The last two papers (Müller and Binder, Müller-Buschbaum et al) deal with the interplay of wetting, dewetting and phase separation. Comprehensive Monte Carlo simulations of polymer melts in various geometries are presented, with a strong focus on critical phenomena. Furthermore, the interplay of dewetting and phase separation in polymer blend films is investigated experimentally with a number of different methods, demonstrating the wealth of different structures which emerge.

The stability of thin liquid coatings plays a fundamental role in everyday life. We studied the stability conditions of thin (3 to 300 nm) liquid polymer films on various substrates. The key role is played by the effective interface potential ϕ of the system air/film/substrate, which determines the dewetting scenario in case the film is not stable. We describe in this study how to distinguish a spinodal dewetting scenario from heterogeneous and homogeneous dewetting by analysing the emerging structures of the film surface by e.g. Minkowski measures. We also include line tension studies of tiny droplets, showing that the long-range part of ϕ does affect the drop profile, but only very close to the three phase boundary line. The dynamic properties of the films are characterized via various experimental methods: the form of the dewetting front, for example, was recorded by scanning probe microscopy and gives insight into the boundary condition between the liquid and the substrate. We further report experiments probing the viscosity and the glass transition temperature of nm-thick films using e.g. ellipsometry. Here we find that even short-chained polymer melts exhibit a significant reduction of the glass transition temperature as the film thickness is reduced below 100 nm.

This paper is concerned with mathematical aspects of lubrication equations. In the first part, we discuss recent analytical achievements for various types of thin-film equations. Of interest are issues like (non-)uniqueness, wetting behaviour and contact line motion, in particular optimal propagation rates and waiting time or dead core phenomena. In the second part, we shall present novel numerical results for thin-film flow on heterogeneous substrates based on entropy consistent schemes. Finally, we will be concerned with new algorithmic concepts for the simulation of thin-film flow of shear-thinning liquids.

We investigate the dewetting rates of thin liquid films using a lubrication model that describes the dewetting process of polymer melts on hydrophobized substrates. We study the effect of different boundary conditions at the liquid/solid interface, in particular, of the no-slip and the Navier slip boundary condition, and compare our numerical solutions for the no-slip and the slip-dominated cases to available results that originate from scaling arguments, simplified flow assumptions and energy balances. We furthermore consider these issues for an extended lubrication model that includes nonlinear curvature.

We present a new experimental set-up and experimental strategies designed for investigating dynamic processes in molecularly thin lubricant layers. The experimental set-up is an extension of a conventional surface forces apparatus, which allows for two-dimensional imaging of the thickness of liquid layers confined between two atomically smooth mica surfaces. We present details of a mica surface preparation technique that eliminates otherwise frequently encountered contamination of the surfaces with nanoparticles, which were recently shown to affect surface forces measurements. Multiple-beam interferometry results in a thickness resolution of approximately 0.2 nm. The data analysis relies on fitting of numerically calculated optical transmission spectra of asymmetric multilayer Fabry–Perot interferometers. The lateral resolution and time resolution are determined by the optical resolution of the video microscopy and the frame rate of the digital CCD camera, respectively. Furthermore, we summarize several results and new insights into the collapse dynamics of thin lubricant layers that were obtained with this technique.

By confining a binary mixture, one can profoundly alter its miscibility behaviour. The qualitative features of miscibility in confined geometry are rather universal and are shared by polymer mixtures as well as small molecules, but the unmixing transition in the bulk and the wetting transition are typically well separated in polymer blends. We study the interplay between wetting and miscibility of a symmetric polymer mixture via large scale Monte Carlo simulations in the framework of the bond fluctuation model and via numerical self-consistent field calculations. The film surfaces interact with the monomers via short-ranged potentials, and the wetting transition of the semi-infinite system is of first order. It can be accurately located in the simulations by measuring the surface and interface tensions and using Young's equation.

If both surfaces in a film attract the same component, capillary condensation occurs and the critical point is close to the critical point of the bulk. If surfaces attract different components, an interface localization/delocalization occurs which gives rise to phase diagrams with two critical points in the vicinity of the pre-wetting critical point of the semi-infinite system. The crossover between these two types of phase diagrams as a function of the surface field asymmetry is studied.

We investigate the dependence of the phase diagram on the film width Δ for antisymmetric surface fields. Upon decreasing the film width the two critical points approach the symmetry axis of the phase diagram, and below a certain width, Δ_tri, there remains only a single critical point at symmetric composition. This corresponds to a second order interface localization/delocalization transition even though the wetting transition is of first order. At a specific film width, Δ_tri, tricritical behaviour is found.

The behaviour of antisymmetric films is compared with the phase behaviour in an antisymmetric double wedge. While the former is the analogy of the wetting transition of a planar surface, the latter is the analogy of the filling behaviour of a single wedge. We present evidence for a second order interface localization/delocalization transition in an antisymmetric double wedge and relate its unconventional critical behaviour to the predictions of Parry et al (1999 Phys. Rev. Lett.83 5535) for wedge filling. The critical behaviour differs from the Ising universality class and is characterized by strong anisotropic fluctuations. We present evidence that the transition in large double wedges can be of second order although there is a first order wetting transition on a planar substrate.

In thin film geometry, the interplay between dewetting and phase separation or microphase separation controls the morphology of the polymeric structures resulting on a solid support. For the model system of polystyrene, polyparamethylstyrene and the diblock copolymer of the two homopolymers, the regime of ultrathin films is addressed experimentally. Evolving structures are probed with real and reciprocal space analysis techniques such as the optical microscopy, phase measuring interference microscopy, scanning force microscopy, neutron or x-ray reflectivity and grazing incidence small angle neutron or x-ray scattering approaches. The effective interface potential of the solid support is tuned by means of a change of the silicon substrate coating. Coating layers of silicon oxide, polyamide and polyimide are under investigation. A power law behaviour describing the most prominent in-plane length as a function of the initially prepared film thickness is observed. All reported structures have been prepared on large scale surfaces, such as typical Si wafers with 100 mm diameter.

Up to this point, we have only dealt with perfectly smooth substrates, at least conceptually. In reality, however, substrates are never really smooth. At least on the minute length scale at which wetting forces play their part, there is almost always considerable roughness. As is well-known, this gives rise even to macroscopically noticeable effects, such as the almost ubiquitous contact angle hysteresis.

At the outset, Geoghegan et al show the dramatic effect of substrate structure on polymer film dewetting, resorting to the type of systems considered in the preceding section. Both chemical and topographical structuring of the substrate give rise to dewetting morphologies dramatically different from those observed on a smooth support. As expected from the symmetry breaking mechanisms that are active in dewetting, only minute deviations from the perfectly plane surface bring about large changes in liquid morphology.

The next two papers (Reineltet al), Sohaili et al) demonstrate that this is not unique to polymer films, but also holds for systems as fundamental as liquid helium. While the first of them (Reinelt et al) concentrates on dynamic phenomena of superfluid helium films on rough cesium substrates, the second (Sohaili et al) provides a careful study of triple point wetting, exemplified with solid hydrogen films on various moderately rough substrates. Together with the last (theoretical) paper (Esztermann and Löwen), the long standing question as to the origin of this ubiquitous phenomenon is solved: it is the roughness itself which gives rise to triple point wetting, by means of the huge energy required to accommodate a solid film to the topography of a wavy support.

We study the effect of a chemical pattern on the wetting and dewetting behaviour of thin polystyrene (PS) films on regularly corrugated silicon substrates. Our results reveal that the film preparation, annealing method, and confinement play a critical role in the final film structure. On evaporating gold on both sides of the facets (such that it covered the crests of the facets, and not the troughs), we observed dewetting, which proceeded to the gold, demonstrating an enthalpic effect contrary to the outcome previously observed when gold was only evaporated on one side of the facet. We also coated the substrate with octadecyltrichlorosilane (OTS); this led to a gold and OTS striped structure. PS films several nanometres thick dewet such substrates, with a preferential direction for dewetting in the direction of the stripes forming droplets of a considerably larger size than the stripes.

Liquid ⁴He shows a dewetting phase on Cs and Rb at low temperatures. These are the only substrates which are not wetted by ⁴He. On Cs the wetting temperature, T_w, is about 2 K. Usually one observes a thick metastable helium film remaining on the Cs substrate when either the surface is cooled below T_w (so starting from a wet film) or when bulk helium (in the form of a drop or an advancing film) is deposited on the Cs. The contact line of this film is generally very stable and so there is no dewetting. However, we have observed that spontaneous drying of helium on Cs can occur and that contact lines can recede for temperatures close to T_w. This exceptional behaviour is analysed and the dependence of substrate roughness is discussed. Furthermore, we have studied the non-wetting 'thin-film' of liquid ⁴He on Cs. Far away from coexistence this film grows as a two-dimensional (2D) gas until about one monolayer is obtained, then remains nearly constant for a certain range of chemical potential and, close to coexistence, rapidly forms a thicker 2D-liquid-like film as stable thermodynamical solution.

Triple-point wetting is a well-known phenomenon of simple adsorbates on solid substrates, which involves, in the liquid phase above the triple-point temperature, T₃, complete wetting with the formation of arbitrary thick films being observed, whereas below T₃ only a few monolayers of the solid phase are adsorbed at saturated vapour pressure. This effect is usually ascribed to the substrate-induced strain in the solid film, which occurs due to the lattice mismatch and the strong van der Waals pressure in the first few monolayers. Molecular hydrogen is a suitable system in which to investigate this phenomenon, in particular by tailoring the adsorbate–substrate interaction by means of thin preplating layers of other adsorbates, and by introducing disorder into the system by using not only the pure systems H₂ and D₂, but also mixtures thereof. The experiments show that triple-point wetting is a rather dominant effect which, in contrast to expectations, persists even if the system parameters are widely varied. This indicates that the present understanding of this effect is incomplete. We present an investigation of the influence of the roughness of the substrate which is expected to be responsible for the dewetting of the solid phase.

The physics of wetting phenomena at structured surfaces by crystalline layers as investigated by theory, computer simulation and experiments is reviewed. Both realizations on the molecular scale and more mesoscopic realizations in colloidal models systems are included. We explore how a crystalline wall pattern affects the wetting by a crystalline phase in the context of a simple hard sphere model relevant for sterically stabilized colloids. We further discuss decoration lattices generated by adsorption of colloidal particles on stripe-patterned substrates. For molecular systems, the influence of a rough and preplated surface on triple-point wetting of hydrogen is calculated. Finally, we present data for fluid layering in primitive model simulations of charged colloids near neutral walls.

In most situations of practical relevance, the morphology of the substrate is much more complex than what was discussed in the previous section. The behaviour of wet granular materials, the phreatic rise, or the dynamics of tertiary oil recovery from porous rock are all concerned with formidably complex interface topologies, and transformations among them. The next four papers lead us gradually into this vast universe of phenomena.

The first three papers (Gillies et al, Xu et al, Fournier et al) all consider the wetting of spherical particles, but with strongly different focuses, and with increasing system complexity. Gillies et al introduce us to the subject by considering wetting and adhesion to single small spheres, and show that this rather simple system already poses enough interesting questions to necessitate the novel method of measurement the authors put forward.

The next two papers discuss the wetting and other physical properties of large ensembles of such spheres. Xu et al show that spherical particles may not only behave similarly to surfactants (as in Pickering emulsions), but that these systems may be used to generate a variety of completely novel micro- and nano\/structures by simple self-assembly processes. Fournier et al discuss the physical properties of a model wet granulate, consisting of a dense pile of many spherical particles and some liquid. They demonstrate that despite the enormous complexity of this system, many of its physical properties may be understood on the basis of rather perspicuous concepts.

Finally, Mecke and Arns display the full power of Minkowski functionals, which have been exemplarily applied to dewetting morphologies in the first section (Seemann et al). It is shown that not only wetting, but also mechanical properties of structures as complex as samples of natural soil, may be successfully predicted. Finally, direct relations between Minkowski functionals and thermodynamic potentials are established.

A 'particle interaction apparatus' based on the technique of atomic force microscopy was constructed that allows us to measure the interaction between single micron-sized particles and the air–water interface. From the force versus distance profiles ('force curves') the contact angle of single microspheres could be determined. This new method for microsphere tensiometry was validated using a variety of materials with contact angles between 20° and 90°. Contact angles measured on single microspheres correlated well with those measured on flat substrates of the same materials.

The interaction of single silica microspheres with an air bubble in the presence of surfactants (SDS and DTAB) was investigated. Depending on surfactant type and concentration, adhesion or repulsion could be induced. Adhesion forces were found to depend on the applied load, indicating possible adsorption/desorption processes at the particle–bubble interface.

We have built a new set-up that combines a particle interaction apparatus with a Langmuir trough and a fluorescence microscope. This will allow study of interactions at the air–water interface in more detail, especially in the presence of a definite surface density of amphiphilic molecules.

The interaction of single ZnS spheres with a bubble (modelling flotation of ZnS) was studied at different pH values. The results suggest that the isoelectric point of these spheres exists between pH 7 and 8.

Wetting of a solid surface by a liquid is dramatically impeded if either the solid or the liquid is decorated by particles. Here it is shown that in the case of contact between two liquids the opposite effect may occur; mixtures of a hydrophobic liquid and suitable particles form wetting layers on a water surface though the liquid alone is non-wetting. In these wetting layers, the particles adsorb to, and partially penetrate through, the liquid/air and/or the liquid/water interface. This formation of wetting layers can be explained by the reduction in total interfacial energy due to the replacement of part of the fluid/fluid interfaces by the particles. It is most prominent if the contact angles at the fluid/fluid/particle contact lines are close to 90°.

We elaborate on the impact of liquids upon the mechanical properties of granular materials. We find that most of the experimental and simulation results may be accounted for by a simple model assuming frictionless, spherical grains, with a hysteretic attractive interaction between neighbouring grains due to capillary forces.

Predicting the relationship between the morphology of porous media and their physical properties, e.g, the conductivity, elasticity and permeability, is a long-standing problem and important to a range of applications from geophysics to materials science. Here, a set of four morphological measures, so-called Minkowski functionals, is defined which allows one to quantitatively characterize the shape of spatial structures, to optimally reconstruct porous media, and to accurately predict material properties. The method is based on integral geometry and Kac's theorem which relates the spectrum of the Laplace operator to the four Minkowski functionals. Analytic expressions for mean values of Minkowski functionals in Boolean models allow the definition of an effective shape of a grain in a system made up of a distribution of arbitrarily shaped constituents. Reconstructing the microstructure using this effective grain shape leads to an excellent match to the percolation thresholds and to the mechanical and transport properties across all phase fractions. Additionally, the use of the effective shape in effective medium formulations leads to good explicit predictions of bulk moduli. The method is verified for several model systems and sedimentary rock samples, demonstrating that a single tomographic image is sufficient to estimate the morphology and physical properties such as permeabilities and elastic moduli for a range of porosities.

Also the thermodynamic behaviour of fluids in porous media, i.e., the shape dependence of the grand canonical potential and of surface energies of a fluid bounded by an arbitrarily shaped convex pore, can be calculated in the thermodynamic limit fully from the knowledge of the Minkowski functionals, i.e., of only four morphometric measures. This remarkable result is based on Hadwiger's theorem on the completeness of the additive Minkowski functionals and the assumption that a thermodynamic potential is an 'additive' functional which can be understood as a more precise definition for the conventional term 'extensive'. As a consequence, the surface energy and other thermodynamic quantities contain in the thermodynamic limit, beside a constant term, only contributions linear in the mean and Gaussian curvature of the pore and not an infinite number of curvature terms. Finally, starting from a microscopic density functional for an inhomogeneous fluid in a porous medium the phase coexistence (capillary condensation) and the critical point of the fluid is determined in terms of structure functions and morphological measures of the pore space and calculated explicitly for specific random porous structures using results from integral geometry.

After having explored some of the many ways in which topographic features of the substrate may affect the statics and dynamics of wetting, let us now turn to something more subtle. Instead of sculpturing the solid support into topographic shapes, we may as well keep it geometrically smooth (as far as this is experimentally possible), and only pattern its chemical surface properties. Many technical methods of preparing such surfaces are meanwhile well-known, micro-contact printing probably being the most popular. As the contribution by Geoghegan et al has demonstrated, the impact on wetting and dewetting may be tremendous. Will it be possible to use chemical substrate patterning to stabilize and control liquid morphologies?

The first two papers tackle this question mainly from a static point of view. Lipowsky et al explore theoretically the interaction of a liquid interface with a substrate bearing a stripe pattern of wettability. Minimiziation of the total energy, which in the case of vesicular interfaces includes bending rigidity, yields a large variety of different morphologies. In the experimental work by Mugele et al, it is shown that by continuously varying the effective wettability of such stripes by means of the electro-wetting effect, one may not only form the various shapes predicted by theory, but also deliberately, and reversibly, switch between them.

We then cross over to dynamics. Dietrich et al consider the dynamics of wetting on chemical (wettability) patterns, with particular emphasis on nanoscopic effects. It is shown that down-scaling patterns like those discussed in the previous papers leads to qualitative changes in both the static and the dynamic aspects of wetting. The two consecutive papers (Mock et al, Michel et al) do not dwell on the nanoscopic aspects, but strongly on dynamics, investigating the behaviour of a liquid drop impacting on a chemically patterned solid surface. It is demonstrated that chemical patterns may even tame, and position, a drop approaching at high speed.

The last paper (Meyer and Braun) draws the attention to a completely different aspect of chemically patterned substrates. Depending on the chemical composition of the solid support, the coating deposited upon it may exhibit strikingly different phase transformation properties. The crystallization of thin polyethylene oxide films is guided (almost) at will by virtue of the underlying chemical pattern.

Liquid droplets, gas bubbles, and membrane vesicles which are in contact with chemically structured substrate surfaces can undergo morphological transitions or shape transformations. The structured surfaces considered here consist of two types of surface domains, γ and δ, which attract and repel the droplets, bubbles, and vesicles, respectively. For droplets on a striped γ domain, one has to distinguish droplets with fixed end caps from those with freely moving end caps. Both types of channels undergo morphological wetting transitions. For vesicles, one has a strong adhesion regime in which the vesicle shapes have constant mean curvature and exhibit effective contact angles. One can then map the shape bifurcation diagram for vesicles onto the one for droplets if one includes the constraint of fixed membrane area. We also report preliminary experimental observations of the adhesion of vesicles to chemically structured surfaces.

Electrowetting is a versatile tool to reduce the apparent contact angle of partially wetting conductive liquids by several tens of degrees via an externally applied voltage. We studied various fundamental and applied aspects of equilibrium liquid surface morphologies both theoretically and experimentally. Our theoretical analysis showed that surface profiles on homogeneous surfaces display a diverging curvature in the vicinity of the three phase contact line. The asymptotic contact angle at the contact line is equal to Young's angle, independent of the applied voltage. With respect to the morphology of the liquid surface, contact angle variations achieved by electrowetting are equivalent to those achieved by varying the chemical nature of the substrates, except for electric field-induced distortions in a region close to the contact line. Experimentally, we studied the (global) morphology of liquid microstructure substrates with stripe-shaped electrodes. As the local contact angle is reduced by increasing the applied voltage, liquid droplets elongate along the stripe axis as expected. For droplets on a single surface with a stripe electrode, there is a discontinuous morphological transition where elongated droplets transform into translationally invariant cylinder segments with the contact line pinned along the stripe edge and vice versa. If the liquid is confined between two parallel surfaces with parallel stripe electrodes, the elongation of the droplet and its transformation into a translationally invariant morphology with pinned contact lines is continuous. Experimental results are compared to analytical and numerical models.

Chemically patterned surfaces are of significant interest in the context of microfluidic applications, and miniaturization of such devices aims at generating structures on the nano-scale. Whereas on the micron scale purely macroscopic descriptions of liquid flow are valid, on the nanometre scale long-ranged inter-molecular interactions, thermal fluctuations such as capillary waves, and finally the molecular structure of the liquid become important. We discuss the most important conceptual differences between flow on chemically patterned substrates on the micron scale and on the nanometre scale, and formulate four design issues for nanofluidics related to channel width, channel separation, and channel bending radius. As a specific example of nano-scale transport we present a microscopic model for the dynamics of spreading of monolayers on homogeneous substrates. Kinetic Monte Carlo simulations of this model on a homogeneous substrate reveal a complex spatio-temporal structure of the extracted monolayer, which includes the emergence of interfaces and of scaling properties of density profiles. These features are discussed and rationalized within the corresponding continuum limit derived from the microscopic dynamics. The corresponding spreading behaviour on a patterned substrate is briefly addressed.

We describe recent investigations on the impact behaviour of liquid drops onto chemically structured surfaces. The surface patterns were prepared via photochemical attachment of polymer molecules with different hydrophilicities using self-assembled monolayers of benzophenone bearing silanes. Immobilization of the polymer monolayers was followed by an ablation process to generate a chemical surface pattern. Impact experiments on systems consisting of very hydrophobic poly(perfluoroalkylethyl)acrylate coatings and hydrophilic areas show that within certain limitations the water drop has a strong tendency to reach the hydrophilic spots, even for inclined substrates. Impact experiments of drops on arrays of hydrophilic spots on the background of a perfluorinated polymer show that the drops spontaneously self-centre on the lithographically generated pattern. The obtained results suggest that the process can be used to circumvent some of the current problems in micro-array fabrication.

The normal and inclined impact of liquid drops onto chemically structured surfaces has been studied experimentally and theoretically. The surface functionalization comprised a self-assembly process of a covalently bound monochlorosilane on a silicon substrate, followed by a photochemical attachment of a polymer of defined hydrophilicity and a subsequent deep UV ablation step to create a local spot of high wettability in a region of low wettability so that a self-centring effect of the impacting liquid could be achieved.

Experimentally the impact is observed using a high-speed camera, changing the impact velocity, the impact displacement from the wettable spot and the inclination of the surface. The temporal spread of the drop was recorded, yielding also the macroscopic dynamic contact angle as a function of time. A theoretical model of the drop impact is developed, based on a mass balance and on a momentum balance which includes capillary forces and viscous drag, and which accounts for the inertial and wettability effects. The theoretical predictions for the time evolution of the drop edges agree well with the experimental data.

Dewetting and crystallization of thin polyethyleneoxide (PEO) films obtained by dip-coating on microheterogeneous surfaces are investigated. Formation of thin polymer films and crystallization are characterized as sequential processes. Film topography and morphology are influenced by surface pattern geometry and polymer solution properties. Under appropriate experimental conditions in which heterogeneous nucleation is avoided, ultrathin non-crystalline PEO films can be prepared which are stable with respect to crystallization over a long time. The experimental procedure established generates films by dewetting on microheterogenous surfaces in which isolated amorphous micrometre-sized areas surrounded from non-wetting barriers are formed. Within these amorphous PEO areas, crystallization can be initiated on request with respect to starting time and location. The crystallization in ultrathin PEO films results in highly branched lamella morphology arising from a diffusion limited aggregation processes (DLA). As time and location for onset of diffusion limited crystallization can be chosen, the morphological features characteristic for DLA growth processes such as correlation width and growth direction of branches can be tuned. In addition, influences of limited material reservoirs in confined areas on film morphology are discussed.

Research on such genuinely soft-matter related phenomena as wetting and dewetting would not be complete without reminiscence to biological systems. The recent stir around what has been known as the lotus effect, the amazing ultra-hydrophobic properties of many plants, has highlighted the interconnections of wetting with bio-systems. In the first paper of this section (Mock et al), a `biomimetic' system is conceived which imitates the properties of plant leaves with elastic hairs. The synthesis of such a system turns out to be tricky, but the progress is encouraging.

The next three papers deal with surfactant layers, as they occur in many biological systems, such as the plasma membrane. Various experimental techniques, such as fluorescence microscopy (Tanaka et al), neutron reflectivity (Steitz et al), and x-ray scattering (Ahrens et al), are demonstrated as powerful tools for their investigation.

The last paper (Heim et al) takes us back to where we started: the morphologies emerging upon dewetting of a liquid. This time, the full diversity of patterns is shown which appears in the deposited solute, once the liquid has evaporated. The motivation of this work is the morphology of deposition of DNA on bio-chips, which may affect the readout results of such devices. It is shown that although much can already be understood, a lot of work has still to be done, and many beautiful mechanisms may still be discovered.

We report on efforts to mimic the wetting behaviour of surfaces or leaves of certain plants, which are rendered ultrahydrophobic through a dense layer of hairs grown on top of the leaf. We use a simple moulding approach to obtain elastic hydrophilic hydrogel networks with pillar structures that may serve as model systems for such hairy surfaces. In order to generate such structures, we first generate either a steel master or directly use a lady's mantle leaf. Second, the master is moulded against a silicone to yield an elastomer, which is a negative of the hairy surface. A subsequent radical polymerization in the negative leads to the formation of an elastic hydrogel even for the very high aspect ratios characteristic of the natural system. The results of some preliminary contact angle measurements on the obtained structures are discussed.

In this paper, we study wetting and dewetting of hydrated biopolymer layers mediating cell–cell and cell–tissue contacts, called the extracellular matrix and cell surface glycocalix, by the combination of various physical techniques. Here, the sum of the net effects of the various interfacial forces, which is referred to as the disjoining pressure, is used as a semi-quantitative measure to describe the thermodynamics of hydrated interlayers. The disjoining pressure can be measured by applying external forces to maintain the equilibrium distance between two parallel surfaces (in biology, two neighbouring plasma membranes). Using artificial models of the extracellular matrix and glycocalix, we describe stable cell–cell contacts in terms of the wetting (or spreading) of complex fluids on polymer surfaces. In fact, the adjustment of the wetting interaction via thin hydrating layers enables us to transform three-dimensional cell membranes into quasi-two-dimensional films on macroscopically large surfaces. Fine-tuning of local wetting conditions at the interface further allows for the selective wetting of native cell membranes on microstructured polysaccharide films, which has a large potential for individual detection of biological functions in confined geometries.

The boundary layer of aqueous surfactants and amphiphilic triblock copolymers against flat solid surfaces of different degrees of hydrophobicity was investigated by neutron reflectometry (NR), grazing incidence small angle neutron scattering (GISANS) and atomic force microscopy (AFM). Solid substrates of different hydrophobicities were prepared by appropriate surface treatment or by coating silicon wafers with polymer films of different chemical natures. For substrates coated with thin films (20–30 nm) of deuterated poly(styrene) (water contact angle ), neutron reflectivity measurements on the polymer/water interface revealed a water depleted liquid boundary layer of 2–3 nm thickness and a density about 90% of the bulk water density. No pronounced depletion layer was found at the interface of water against a less hydrophobic polyelectrolyte coating (). It is believed that the observed depletion layer at the hydrophobic polymer/water interface is a precursor of the nanobubbles which have been observed by AFM at this interface.

Decoration of the polymer coatings by adsorbed layers of nonionic C_mE_n surfactants improves their wettability by the aqueous phase at surfactant concentrations well below the critical micellar concentration (CMC) of the surfactant. Here, GISANS experiments conducted on the system SiO₂/C₈E₄/D₂O reveal that there is no preferred lateral organization of the C₈E₄ adsorption layers.

For amphiphilic triblock copolymers (PEO–PPO–PEO) it is found that under equilibrium conditions they form solvent-swollen brushes both at the air/water and the solid/water interface. In the latter case, the brushes transform to uniform, dense layers after extensive rinsing with water and subsequent solvent evaporation. The primary adsorption layers maintain properties of the precursor brushes. In particular, their thickness scales with the number of ethylene oxide units (EO) of the block copolymer. In the case of dip-coating without subsequent rinsing, surface patterns of the presumably crystalline polymer on top of the primary adsorption layer develop upon drying under controlled conditions. The morphology depends mainly on the nominal surface coverage with the triblock copolymer. Similar morphologies are found on bare and polystyrene-coated silicon substrates, indicating that the surface patterning is mainly driven by segregation forces within the polymer layers and not by interactions with the substrate.

Langmuir monolayers of polymacromonomers (cylindrical brushes) with poly(vinyl)pyridine side chains of different length, polyPV P_20.8 and polyPV P_46.7, are studied at the air–water interface by means of x-ray diffraction and reflectivity. The advantages of measurements on an aqueous subphase, which contains NaI, are demonstrated. This subphase does not affect the structure of an uncharged monolayer, although NaI is incorporated into the side chains, it provides an enhanced contrast for the x-ray investigations. A structural transition from aligned single molecules to a homogeneous monolayer is found, which is attributed to intra- and intermolecular interactions.

We have studied the morphologies of unspecifically bound DNA on solid substrates that arise when it is deposited from a liquid drop. Depending on the mode of removal of the liquid from the surface, and on the properties of the solvent and substrate, the observed single-molecule morphologies range from elongated to condensed conformations. Further, we have examined the amount of unspecifically bound DNA on microarrays deposited from drying droplets, for which we have employed test systems based on gene fragments of E. coli and oligonucleotides.