Microscopic Origin of Capillary Force Balance at Contact Line.

We investigate the underlying mechanism of capillary force balance at the contact line. In particular, we offer a novel approach to describe and quantify the capillary force on the liquid in coexistence with its vapor phase, which is crucial in wetting and spreading dynamics. Its relation with the interface tension is elucidated. The proposed model is verified by our molecular dynamics simulations over a wide contact angle range. Differences in capillary forces are observed in evaporating droplets on homogeneous and decorated surfaces. Our findings not only provide a theoretical insight into capillary forces at the contact line, but also validate Young's equation based on a mechanical interpretation.

How Wettability Controls Nanoprinting.

Using large scale molecular dynamics simulations, we study in detail the impact of nanometer droplets of low viscosity on flat substrates versus the wettability of the solid plate. The comparison between the molecular dynamics simulations and different macroscopic models reveals that most of these models do not correspond to the simulation results at the nanoscale, in particular for the maximal contact diameter during the nanodroplet impact (D_{max}). We have developed a new model for D_{max} that is in agreement with the simulation data and also takes into account the effects of the liquid-solid wettability. We also propose a new scaling for the time required to reach the maximal contact diameter t_{max} with respect to the impact velocity, which is also in agreement with the observations. With the new model for D_{max} plus the scaling found for t_{max}, we present a master curve collapsing the evolution of the nanometer drop contact diameter during impact for different wettabilities and different impact velocities. We believe our results may help in designing better nanoprinters since they provide an estimation of the maximum impact velocities required to obtain a smooth and homogenous coverage of the surfaces without dry spots.

Spreading Dynamics of Molten Polymer Drops on Glass Substrates.

Wetting dynamics drive numerous processes involving liquids in contact with solid substrates with a wide range of geometries. The spreading dynamics of organic liquids and liquid metals at, respectively, room temperature and >1000 °C have been studied extensively, both experimentally and numerically; however, almost no attention has been paid to the wetting behavior of molten drops of thermoplastic polymers, despite its importance, for example, in the processing of fiber-reinforced polymer composites. Indeed, the ability of classical theories of dynamic wetting, that is, the hydrodynamic and the molecular-kinetic theories, to model these complex liquids is unknown. We have therefore investigated the spreading dynamics on glass, over temperatures between 200 and 260 °C, of two thermoplastics: polypropylene (PP) and poly(vinylidene fluoride) (PVDF). PP and PVDF showed, respectively, the highest and lowest slip lengths due to their different interactions with the glass substrate. The jump lengths of PP and PVDF are comparable to their Kuhn segment lengths, suggesting that the wetting process of these polymers is mediated by segmental displacements. The present work not only provides evidence of the suitability of the classical models to model dynamic wetting of molten polymers but also advances our understanding of the wetting dynamics of molten thermoplastics at the liquid/solid interface.

Young's equation at the nanoscale.

In 1805, Thomas Young was the first to propose an equation to predict the value of the equilibrium contact angle of a liquid on a solid. Today, the force exerted by a liquid on a solid, such as a flat plate or fiber, is routinely used to assess this angle. Moreover, it has recently become possible to study wetting at the nanoscale using an atomic force microscope. Here, we report the use of molecular-dynamics simulations to investigate the force distribution along a 15 nm fiber dipped into a liquid meniscus. We find very good agreement between the measured force and that predicted by Young's equation.

Toward a predictive theory of wetting dynamics.

The molecular kinetic theory (MKT) of dynamic wetting, first proposed nearly 50 years ago, has since been refined to account explicitly for the effects of viscosity and solid-liquid interactions. The MKT asserts that the systematic deviation of the dynamic contact angle from its equilibrium value quantitatively reflects local energy dissipation (friction) at the moving contact line as it traverses sites of solid-liquid interaction. Specifically, it predicts that the coefficient of contact-line friction ζ will be proportional to the viscosity of the liquid ηL and exponentially dependent upon the strength of solid-liquid interactions as measured by the equilibrium work of adhesion Wa(0). Here, we analyze a very large set of dynamic wetting data drawn from more than 20 publications and representative of a very wide range of systems, from molecular-dynamics-simulated Lenard-Jones liquids and substrates, through conventional liquids and solids, to molten glasses and liquid metals on refractory solids. The combined set spans 9 decades of viscosity and 11 decades of contact-line friction. Our analysis confirms the predicted dependence of ζ upon ηL and Wa(0), although the data are scattered. In particular, a plot of ln(ζ/ηL) versus Wa(0)/n (i.e., the work of adhesion per solid-liquid interaction site) is broadly linear, with 85% of the data falling within a triangular envelope defined by Wa(0) and 0.25Wa(0). Various reasons for this divergence are explored, and a semi-empirical approach is proposed to predict ζ. We suggest that the broad agreement between the MKT and such a wide range of data is strong evidence that the local microscopic contact angle is directly dependent upon the velocity of the contact line.

Is superhydrophobicity robust with respect to disorder?

We consider theoretically the Cassie-Baxter and Wenzel states describing the wetting contact angles for rough substrates. More precisely, we consider different types of periodic geometries such as square protrusions and disks in 2D, grooves and nanoparticles in 3D and derive explicitly the contact angle formulas. We also show how to introduce the concept of surface disorder within the problem and, inspired by biomimetism, study its effect on superhydrophobicity. Our results, quite generally, prove that introducing disorder, at fixed given roughness, will lower the contact angle: a disordered substrate will have a lower contact angle than a corresponding periodic substrate. We also show that there are some choices of disorder for which the loss of superhydrophobicity can be made small, making superhydrophobicity robust.

Dynamic wetting of various liquids: Theoretical models, experiments, simulations and applications.

Dynamic wetting is a ubiquitous phenomenon and frequently observed in our daily life, as exemplified by the famous lotus effect. It is also an interfacial process of upmost importance involving many cutting-edge applications and has hence received significantly increasing academic and industrial attention for several decades. However, we are still far away to completely understand and predict wetting dynamics for a given system due to the complexity of this dynamic process. The physics of moving contact lines is mainly ascribed to the full coupling with the solid surface on which the liquids contact, the atmosphere surrounding the liquids, and the physico-chemical characteristics of the liquids involved (small-molecule liquids, metal liquids, polymer liquids, and simulated liquids). Therefore, to deepen the understanding and efficiently harness wetting dynamics, we propose to review the major advances in the available literature. After an introduction providing a concise and general background on dynamic wetting, the main theories are presented and critically compared. Next, the dynamic wetting of various liquids ranging from small-molecule liquids to simulated liquids are systematically summarized, in which the new physical concepts (such as surface segregation, contact line fluctuations, etc.) are particularly highlighted. Subsequently, the related emerging applications are briefly presented in this review. Finally, some tentative suggestions and challenges are proposed with the aim to guide future developments.

A nanoscale view of the origin of boiling and its dynamics.

In this work, we present a dynamical theory of boiling based on fluctuating hydrodynamics and the diffuse interface approach. The model is able to describe boiling from the stochastic nucleation up to the macroscopic bubble dynamics. It covers, with a modest computational cost, the mesoscale area from nano to micrometers, where most of the controversial observations related to the phenomenon originate. In particular, the role of wettability in the macroscopic observables of boiling is elucidated. In addition, by comparing the ideal case of boiling on ultra-smooth surfaces with a chemically heterogeneous wall, our results will definitively shed light on the puzzling low onset temperatures measured in experiments. Sporadic nanometric spots of hydrophobic wettability will be shown to be enough to trigger the nucleation at low superheat, significantly reducing the temperature of boiling onset, in line with experimental results. The proposed mesoscale approach constitutes the missing link between macroscopic approaches and molecular dynamics simulations and will open a breakthrough pathway toward accurate understanding and prediction.

Electrospinning of a functional perfluorinated block copolymer as a powerful route for imparting superhydrophobicity and corrosion resistance to aluminum substrates.

Superhydrophobic aluminum surfaces with excellent corrosion resistance were successfully prepared by electrospinning of a novel fluorinated diblock copolymer solution. Micro- and nanostructuration of the diblock copolymer coating was obtained by electrospinning which proved to be an easy and cheap electrospinning technology to fabricate superhydrophobic coating. The diblock copolymer is made of poly(heptadecafluorodecylacrylate-co-acrylic acid) (PFDA-co-AA) random copolymer as the first block and polyacrylonitrile (PAN) as the second one. The fluorinated block promotes hydrophobicity to the surface by reducing the surface tension, while its carboxylic acid functions anchor the polymer film onto the aluminum surface after annealing at 130 °C. The PAN block of this copolymer insures the stability of the structuration of the surface during annealing, thanks to the infusible character of PAN. It is also demonstrated that the so-formed superhydrophobic coating shows good adhesion to aluminum surfaces, resulting in excellent corrosion resistance.

A generalized examination of capillary force balance at contact line: On rough surfaces or in two-liquid systems.

We investigate the capillary force balance at the contact line on rough solid surfaces and in two-liquid systems. Our results confirm that solid-liquid interactions perpendicular to the interface have a significant influence on the lateral component of the capillary force exerted on the contact line. Surface roughness of the solid substrate reduces the mobility of liquid and alters how the perpendicular solid-liquid interactions transfer into a force acting parallel to the interface. A quantitative relation between surface roughness and the transfer strategy is proposed. Moreover, when a liquid is in coexistence with another immiscible liquid on a solid, the capillary forces exerted on liquids of both sides are involved in our theoretical model. The contact angle can be predicted by calculating three interfacial tensions. These arguments are then verified by molecular dynamics simulations. Our findings set up the generalized theoretical framework for the capillary force balance at the contact line and broaden its application in more realistic scenarios.

Correlation between superhydrophobicity and the power spectral density of randomly rough surfaces.

We show experimentally and analytically that for single-valued, isotropic, homogeneous, randomly rough surfaces consisting of bumps randomly protruding over a continuous background, superhydrophobicity is related to the power spectral density of the surface height, which can be derived from microscopy measurements. More precisely, superhydrophobicity correlates with the third moment of the power spectral density, which is directly related to the notion of Wenzel roughness (i.e., the ratio between the real area of the surface and its projected area). In addition, we explain why randomly rough surfaces with identical root-mean-square roughness values may behave differently with respect to water repellence and why roughness components with wavelength larger than 10 µm are not likely to be of importance or, stated otherwise, why superhydrophobicity often requires a contribution from submicrometer-scale components such as nanoparticles. The analysis developed here also shows that the simple thermodynamic arguments relating superhydrophobicity to an increase in the sample area are valid for this type of surface, and we hope that it will help researchers to fabricate efficient superhydrophobic surfaces based on the rational design of their power spectral density.

Drop impact on soft surfaces: beyond the static contact angles.

The wettability of cross-linked poly(dimethylsiloxane) elastomer films and of octadecyltrichlorosilane self-assembled monolayers with water has been measured and compared using various methods. Contact angle hysteresis values were compared with values reported in the literature. A new method to characterize advancing, receding contact angles, and hysteresis using drop impact have been tested and compared with usual methods. It has been found that for the rigid surfaces the drop impact method is comparable with other methods but that for elastomer surfaces the hysteresis is function of the drop impact velocity which influences the extent of the deformation of the soft surface at the triple line.

Superhydrophobic aluminum surfaces by deposition of micelles of fluorinated block copolymers.

Superhydrophobic surfaces are generated by chemisorption on aluminum substrates of fluorinated block copolymers synthesized by reversible addition-fragmentation chain transfer in supercritical carbon dioxide. In an appropriate solvent, those block copolymers can form micelles with a fluorinated corona, which are grafted on the aluminum substrate thanks to the presence of carboxylic acid groups in the corona. Water contact angle and drop impact analysis were used to characterize the wettability of the films at the macroscale, and atomic force microscopy measurements provided morphological information at the micro- and nanoscale. The simple solvent casting of the polymer solution on a hydroxylated aluminum surface results in a coating with multiscale roughness, which is fully superhydrophobic over areas up to 4 cm(2).

Superhydrophobicity of composite surfaces created from polymer blends.

HYPOTHESIS: When they are used alone, some polymers, such as polypropylene, Carnauba wax or polycarbonate allow the creation of superhydrophobic surfaces by spin coating or casting. On the other hand, some other polymers, such as polystyrene, polyvinylacetate or polychloroprene, are unable to render a superhydrophobic surface by these techniques. Using binary mixtures of these two types of polymers in a single common solvent, superhydrophobic composite surfaces can be created. We aim to show that superhydrophobicity is depending on the ratio between the two polymers in the initial blend and their intrinsic wettability. EXPERIMENTS: The transition towards superhydrophobicity is studied on composite surfaces made of various polymers. Surfaces are created with simple coating methods, such as casting or spin-coating, of polymer solutions and letting the solvent evaporate at ambient conditions. FINDINGS: Transitions are sharp and the amount of polypropylene in the blend to achieve superhydrophobicity decreases with the hydrophobicity of the second polymer. Topographic and wettability measurements are performed that show that both effects, topographical and chemical, interplay in the property of superhydrophobicity.

Bulk and Surface Wettability Characteristics of Probiotic Powders in Their Compressed Disc and Packed-Bed Column Forms.

Most probiotic-based products are available in powder particles under different solid-state forms. Such diversity can affect the probiotic stability, viability, and performance at different stages of processing, storage, and use. Here, we apply complementary physical chemistry techniques to characterize the bulk and surface properties of probiotic powder particles under different forms and report quantitative results of a highly concentrated multistrain reference product. The solid particle morphology, size/shape distribution, and the powder surface wettability in the compressed disc and porous packed bed forms are successively measured by sessile drop and capillary rise techniques. A complete wettability of the disc surface is observed through equilibrium contact angle measurements for various solvents, whereas the associated capillary rise data exhibit two regimes: a power law regime for the first few moments followed by a second regime, which can be described using Darcy's law. The use of this modeling approach shows the possibility of assessing the particle-packed bed permeability and porosity. These results open a new route of the structure-activity relationship study on the impact of probiotic solid particles on their functionalities and performance in promoting health benefits, related particularly to the human and animal gut permeability. This statement also strengthens the idea of using the compressed disc technique for easily performing probiotic wettability measurements.

Vibrational analysis of amino acids and short peptides in aqueous media. V. The effect of the disulfide bridge on the structural features of the peptide hormone somatostatin-14.

To emphasize the role played by the S-S bridge in the structural features of somatostatin-14 (SST-14), newly recorded CD and Raman spectra of this cyclic peptide and its open analogue obtained by Cys-->Ser substitution are presented. CD spectra of both peptides recorded in aqueous solutions in the 100-500 microM concentration range are strikingly similar. They reveal principally that random conformers constitute the major population in both peptides. Consequently, the S-S bridge has no structuring effect at submillimolar concentrations. In methanol, the CD spectrum of somatostatin-14 keeps globally the same spectral shape as that observed in water, whereas its open analogue presents a major population of helical conformers. Raman spectra recorded as a function of peptide concentration (5-20 mM) and also in the presence of 150 mM NaCl provide valuable conformational information. All Raman spectra present a mixture of random and beta-hairpin structures for both cyclic and open peptides. More importantly, the presence or the absence of the disulfide bridge does not seem to influence considerably different populations of secondary structures within this range of concentrations. CD and Raman data obtained in the submillimolar and millimolar ranges of concentrations, respectively, lead us to accept the idea that SST-14 monomers aggregate upon increasing concentration, thus stabilizing beta-hairpin conformations in solution. However, even at high concentrations, random conformers do not disappear. Raman spectra of SST-14 also reveal a concentration effect on the flexibility of the S-S linkage and consequently on that of its cyclic part. In conclusion, although the disulfide linkage does not seem to markedly influence the SST-14 conformational features in aqueous solutions, its presence seems to be necessary to ensure the flexibility of the cyclic part of this peptide and to maintain its closed structure in lower dielectric constant environments.

Capillary rise of polydimethylsiloxane around a poly(ethylene terephthalate) fiber versus viscosity: Existence of a sharp transition in the dynamic wetting behavior.

HYPOTHESIS: Since the emergence of the molecular-kinetic theory and the hydrodynamic approach, it is generally accepted that the displacement of the contact line is controlled by the viscous or frictional channel of energy dissipation for respectively high-viscosity and low-viscosity liquids. However, how the dissipation switches from one channel to another is still unknown. We therefore hypothesized that, by progressively changing the viscosity of a liquid, a better understanding of the underlying mechanism driving this wetting dynamic transition would be obtained. EXPERIMENTS: Performing capillary rise experiments of polydimethylsiloxane on a poly(ethylene terephthalate) fiber at different temperatures, i.e. at different liquid viscosities, we characterized the transition between the viscous and frictional regimes. The fiber surface topography was also characterized and its effect on the wetting dynamics was quantified. FINDINGS: The wetting dynamics switched from one regime to the other in a very short viscosity interval. Besides, the wetting behavior in the transition region is sensitive to the fiber surface topography. The presence or the absence of a liquid rim ahead of the contact line actually determines the dominant channel of dissipation.

A new model to predict the influence of surface temperature on contact angle.

The measurement of the equilibrium contact angle (ECA) of a weakly evaporating sessile drop becomes very challenging when the temperatures are higher than ambient temperature. Since the ECA is a critical input parameter for numerical simulations of diabatic processes, it is relevant to know the variation of the ECA with the fluid and wall temperatures. Several research groups have studied the effect of temperature on ECA either experimentally, with direct measures, or numerically, using molecular dynamic simulations. However, there is some disagreement between the authors. In this paper two possible theoretical models are presented, describing how the ECA varies with the surface temperature. These two models (called Decreasing Trend Model and Unsymmetrical Trend Model, respectively) are compared with experimental measurements. Within the experimental errors, the equilibrium contact angle shows a decrease with increasing surface temperatures on the hydrophilic surface. Conversely the ECA appears approximately constant on hydrophobic surfaces for increasing wall temperatures. The two conclusions for practical applications for weakly evaporating conditions are that (i) the higher the ECA, the smaller is the effect of the surface temperature, (ii) a good evaluation of the decrease of the ECA with the surface temperature can be obtained by the proposed DTM approach.

Wetting dynamics of polydimethylsiloxane mixtures on a poly(ethylene terephthalate) fiber.

HYPOTHESIS: The wetting dynamics of liquids with identical surface tensions are mostly controlled by their viscosities. We therefore hypothesized that the wetting dynamics of one- (pure liquid) and two-component (mixture) polydimethylsiloxane (PDMS) on a poly(ethylene terephthalate) (PET) fiber with similar surface tensions and viscosities should be controlled by the same underlying physical mechanisms. EXPERIMENTS: We studied the capillary rise of PDMS liquids on a PET fiber. We compared the different contact angle relaxations and characterized the transitions between the molecular-kinetic theory (MKT) and hydrodynamic approach (HD) for the PDMS mixtures and the pure liquids as a function of their viscosities. FINDINGS: Compared to the pure PDMS liquid with a viscosity of 20 mm2/s that presents a contact angle relaxation following a t-1/2 scale law in agreement with HD, the PDMS mixture with a higher viscosity (27.4 mm2/s) shows a t-1 behavior predicted by the MKT. Moreover, the transition between MKT and HD appears in a regime with higher viscosities for PDMS mixtures than for pure liquids. Surface segregation of shorter PDMS chains or precursor film may be responsible for this shift.

Contact angles of a drop pinned on an incline.

For a drop on an incline with small tilt angle α, when the contact line is a circle of radius r, we derive the relation mgsinα=γrπ/2(cosθ^{min}-cosθ^{max}) at first order in α, where θ^{min} and θ^{max} are the contact angles at the back and at the front, m is the mass of the drop and γ the surface tension of the liquid. We revisit in this way the Furmidge model for a large range of contact angles. We also derive the same relation at first order in the Bond number B=ρgR^{2}/γ, where R is the radius of the spherical cap at zero gravity. The drop profile is computed exactly in the same approximation. Results are compared with surface evolver simulations, showing a surprisingly large range of contact angles for applicability of first-order approximations.