Inversion of Stabilized Large Droplet Clusters

We investigate the spontaneous rearrangement of microdroplets in a self-assembled droplet cluster levitating over a thin locally heated water layer. The center-to-periphery droplet diameter ratio (the "inversion coefficient") controls the onset of the inversion. Larger droplets can squeeze between smaller ones due to increased drag force on them from the air-vapor flow. In smaller clusters, the rotation of the droplets plays an important role since larger droplets rotating with the same angular velocity (dependent on the rotor of the airflow field) have higher viscous friction force with the liquid layer. It is desirable to avoid cluster inversion in experiments where individual droplet positions should be traced.

Ergodicity Breaking and Self-Destruction of Cancer Cells by Induced Genome Chaos

During the progression of some cancer cells, the degree of genome instability may increase, leading to genome chaos in populations of malignant cells. While normally chaos is associated with ergodicity, i.e., the state when the time averages of relevant parameters are equal to their phase space averages, the situation with cancer propagation is more complex. Chromothripsis, a catastrophic massive genomic rearrangement, is observed in many types of cancer, leading to increased mutation rates. We present an entropic model of genome chaos and ergodicity and experimental evidence that increasing the degree of chaos beyond the non-ergodic threshold may lead to the self-destruction of some tumor cells. We study time and population averages of chromothripsis frequency in cloned rhabdomyosarcomas from rat stem cells. Clones with frequency above 10% result in cell apoptosis, possibly due to mutations in the BCL2 gene. Potentially, this can be used for suppressing cancer cells by shifting them into a non-ergodic proliferation regime.

Deposition of Nanostructured Tungsten Oxide Layers by a New Method: Periodic Modulation of the Deposition Angle

Periodic modulation of the deposition angle (PMDA) is a new method to deposit nanostructured and continuous layers with controllable periodic density fluctuation. The method is used for the magnetron sputtering of a WO3 layer for an electrochromic device (ECD). An experimental study indicates that the electrochromic coloration-bleaching rate nearly doubles and the electrochromic efficiency grows by about 25% in comparison with the traditional method. The ECD efficiency rises with the increasing degree of nanostructure ordering, surface roughness, and homogeneity of the WO3 layer. The method is promising for coating deposition techniques needed to produce versatile devices with specific requirements for ion transport in surface layers, coatings, and interfaces, such as fuel cells, batteries, and supercapacitors.

Fluorescence profiles of water droplets in stable levitating droplet clusters

Clusters of nearly identical water microdroplets levitating over a locally heated water layer are considered. The high-resolution and high-speed fluorescence microscopy showed that there is a universal brightness profile of single droplets, and this profile does not depend on the droplet temperature and size. We explain this universal profile using the theory of light scattering and propose a new method for determining the parameters of possible optical inhomogeneity of a droplet from its fluorescent image. In particular, we report for the first time and explain the anomalous fluorescence of some large droplets with initially high brightness at the periphery of the droplet. The disappearance of this effect after a few seconds is related to the diffusion of the fluorescent substance in water. Understanding the fluorescence profiles paves the way for the application of droplet clusters to the laboratory study of biochemical processes in individual microdroplets.

Folding-unfolding asymmetry and a RetroFold computational algorithm

We treat protein folding as molecular self-assembly, while unfolding is viewed as disassembly. Fracture is typically a much faster process than self-assembly. Self-assembly is often an exponentially decaying process, since energy relaxes due to dissipation, while fracture is a constant-rate process as the driving force is opposed by damping. Protein folding takes two orders of magnitude longer than unfolding. We suggest a mathematical transformation of variables, which makes it possible to view self-assembly as time-reversed disassembly, thus folding can be studied as reversed unfolding. We investigate the molecular dynamics modelling of folding and unfolding of the short Trp-cage protein. Folding time constitutes about 800 ns, while unfolding (denaturation) takes only about 5.0 ns and, therefore, fewer computational resources are needed for its simulation. This RetroFold approach can be used for the design of a novel computation algorithm, which, while approximate, is less time-consuming than traditional folding algorithms.

Reaction-Diffusion Pathways for a Programmable Nanoscale Texture of the Diamond-SiC Composite

The diamond-SiC composite has a low density and the highest possible speed of sound among existing materials except for diamond. The composite is synthesized by a complex exothermic chemical reaction between diamond powder and liquid Si. This makes it an ideal material for protection against impact loading. Experiments show that a system of patterns is formed at the diamond-SiC interface. Modeling of reaction-diffusion processes of composite synthesis proves a formation of ceramic materials with a regular (periodic) interconnected microstructure in a given system. The composite material with interconnected structures at the interface has very high mechanical properties and resistance to impact since its fractioning is intercrystallite.

Topological bio-scaling analysis as a universal measure of protein folding

Scaling relationships for polymeric molecules establish power law dependencies between the number of molecular segments and linear dimensions, such as the radius of gyration. They also establish spatial topological properties of the chains, such as their dimensionality. In the spatial domain, power exponents α = 1 (linear stretched molecule), α = 0.5 (the ideal chain) and α = 0.333 (compact globule) are significant. During folding, the molecule undergoes the transition from the one-dimensional linear to the three-dimensional globular state within a very short time. However, intermediate states with fractional dimensions can be stabilized by modifying the solubility (e.g. by changing the solution temperature). Topological properties, such as dimension, correlate with the interaction energy, and thus by tuning the solubility one can control molecular interaction. We investigate these correlations using the example of a well-studied short model of Trp-cage protein. The radius of gyration is used to estimate the fractal dimension of the chain at different stages of folding. It is expected that the same principle is applicable to much larger molecules and that topological (dimensional) characteristics can provide insights into molecular folding and interactions.

Branched droplet clusters and the Kramers theorem

Scaling laws inherent for polymer molecules are checked for the linear and branched chains constituting two-dimensional (2D) levitating microdroplet clusters condensed above the locally heated layer of water. We demonstrate that the dimensionless averaged end-to-end distance of the droplet chain r[over ¯] normalized by the averaged distance between centers of the adjacent droplets l[over ¯] scales as r[over ¯]/l[over ¯]∼n^{0.76}, where n is the number of links in the chain, which is close to the power exponent ¾, predicted for 2D polymer chains with excluded volume in the dilution limit. The values of the dimensionless Kuhn length b[over ̃]≅2.12±0.015 and of the averaged absolute value of the bond angle of the droplet chains |θ|[over ¯]=22.0±0.5^{0} are determined. Using these values we demonstrate that the predictions of the Kramers theorem for the gyration radius of branched polymers are valid also for the branched droplets' chains. We discuss physical interactions that explain both the high value of the power exponent and the applicability of the Kramers theorem including the effects of the excluded volume, surrounding droplet monomers, and the prohibition of extreme values of the bond angle.

When Bubbles Are Not Spherical: Artificial Intelligence Analysis of Ultrasonic Cavitation Bubbles in Solutions of Varying Concentrations

Ultrasonic irradiation of liquids, such as water-alcohol solutions, results in cavitation or the formation of small bubbles. Cavitation bubbles are generated in real solutions without the use of optical traps making our system as close to real conditions as possible. Under the action of the ultrasound, bubbles can grow, oscillate, and eventually collapse or decompose. We apply the mathematical method of separation of motions to interpret the acoustic effect on the bubbles. While in most situations, the spherical shape of a bubble is the most energetically profitable as it minimizes the surface energy, when the acoustic frequency is in resonance with the natural frequency of the bubble, shapes with the dihedral symmetry emerge. Some of these resonance shapes turn unstable, so the bubble decomposes. It turns out that bubbles in the solutions of different concentrations (with different surface energies and densities) attain different evolution paths. While it is difficult to obtain a deterministic description of how the solution concentration affects bubble dynamics, it is possible to separate images with different concentrations by applying the artificial neural network (ANN) algorithm. An ANN was trained to detect the concentration of alcohol in a water solution based on the bubble images. This indicates that artificial intelligence (AI) methods can complement deterministic analysis in nonequilibrium, near-unstable situations.

Topological Data Analysis of Nanoscale Roughness in Brass Samples

Rough surfaces possess complex topographies, which cannot be characterized by a single parameter. The selection of appropriate roughness parameters depends on a particular application. Large datasets representing surface topography possess orderliness, which can be expressed in terms of topological features in high-dimensional dataspaces reflecting properties such as anisotropy and the number of lay directions. The features are scale-dependent because both sampling length and resolution affect them. We study nanoscale surface roughness using 3 × 3, 4 × 4, and 5 × 5 pixel patches obtained from atomic force microscopy (AFM) images of brass (Cu Zn alloy) samples roughened by a sonochemical treatment. We calculate roughness parameters, correlation length, extremum point distribution, persistence diagrams, and barcodes. These parameters of interest are discussed and compared.

Separation of motions and vibrational separation of fractions for biocide brass

The mathematical method of separation of motions represents the effect of fast high-frequency oscillations by an effective averaged force or potential. Ultrasound acoustic vibrations are an example of such rapid oscillations leading to cavitation in water due to the gas phase formation (bubbles). Ultrasound cavitation is used to treat the surface of brass microparticles submerged in water. The formation of bubbles and their collapse triggers the modification of surface roughness and chemical composition. Consequently, the suspension separates into various fractions related to demonstrating biocide properties. While the exact mechanism of this process is complex, it can be explained phenomenologically by using the Onsager reciprocal relations for coupling the copper ion diffusion with the gas phase separation in water as a result of the action of the effective average vibrational force.

Predictive Analysis of Wettability of Al-Si Based Multiphase Alloys and Aluminum Matrix Composites by Machine Learning and Physical Modeling

Wetting of multiphase alloys and their composites depends on multiple parameters, and these relationships are difficult to predict from first principles only. We study correlations between the composition, surface finish, and microstructure of Al-Si alloys (Si content 7-50%) and Al metal matrix composites (MMCs) with graphite (Gr), NiAl₃, and SiC and the water contact angle (CA) experimentally, theoretically, and with machine learning (ML) techniques. Their surface properties were modified by mechanical abrasion, etching, and addition of alloying elements. An ML approach was developed to investigate correlations between the predictor variables (properties of the materials) and the CA. Theoretical models of wetting of rough surfaces (Wenzel, Cassie-Baxter, and their modifications) do not fully capture the CA, while ML models follow the experimental values. A full factorial design is utilized with combinations of all levels of the predictor factors (grit size, silicon percentage, droplet size, elapsed time, etching, reinforcing particles). To map the predictor variables to the response variables, 409 experimental data points were applied to train and test various supervised ML models, namely, regression, artificial neural network (ANN), chi-square automatic interaction detection (CHAID), extreme gradient boosting (XGBoost), and random forest. The correlations between the most significant factors and CA are explored through visualization techniques. The most accurately trained model shows a strong positive linear correlation (r > 0.9) between predicted and observed CA values in the test set, indicating the robustness of the model. The experimental measurements and artificial intelligence results demonstrate that CA increases following mechanically abrading the surface, etching, and adding Gr to the surface. The ML methods are promising to predict wetting properties and to provide a deeper understanding of the physical phenomena associated with the wettability of metallic alloys and their metal matrix composites.

Survival of Virus Particles in Water Droplets: Hydrophobic Forces and Landauer's Principle

Many small biological objects, such as viruses, survive in a water environment and cannot remain active in dry air without condensation of water vapor. From a physical point of view, these objects belong to the mesoscale, where small thermal fluctuations with the characteristic kinetic energy of k_BT (where k_B is the Boltzmann’s constant and T is the absolute temperature) play a significant role. The self-assembly of viruses, including protein folding and the formation of a protein capsid and lipid bilayer membrane, is controlled by hydrophobic forces (i.e., the repulsing forces between hydrophobic particles and regions of molecules) in a water environment. Hydrophobic forces are entropic, and they are driven by a system’s tendency to attain the maximum disordered state. On the other hand, in information systems, entropic forces are responsible for erasing information, if the energy barrier between two states of a switch is on the order of k_BT, which is referred to as Landauer’s principle. We treated hydrophobic interactions responsible for the self-assembly of viruses as an information-processing mechanism. We further showed a similarity of these submicron-scale processes with the self-assembly in colloidal crystals, droplet clusters, and liquid marbles.

Impact of Surfactants on the Formation and Properties of Droplet Clusters

A levitating cluster of condensed microdroplets can form over the heated area of a water layer. The thermocapillary (TC) flow at the surface of the water layer combined with the convective flow in the layer often prevents a cluster's stability due to disturbances that it creates in the gas flow over the water surface. The TC flow can be suppressed by introducing small amounts of surfactants into the water layer. We conduct a systematic study of the effect of a surfactant on the cluster. We show experimentally that the introduction of the surfactant sodium laureth sulfate with concentrations of 0.05-0.5 g/L can suppress the TC convection. It is shown that the amount of surfactant does not affect the condensational growth of droplets and the structure of the cluster. In the absence of the surfactant, a ring-shaped cluster is formed, which is reported in this paper for the first time.

Symmetry of small clusters of levitating water droplets

Self-assembled clusters of condensed water microdroplets can levitate over a locally heated layer of water. Large clusters form hexagonally ordered (honeycomb) structures similar to colloidal crystals, while small (from one to several dozens of droplets) clusters possess special symmetry properties. Small clusters may demonstrate 4-fold, 5-fold, and 7-fold symmetry which is absent from large clusters and crystals. The symmetry properties of small cluster configurations are universal, i.e., they do not depend on the size of the droplets and details of the interactions between the droplets. The small cluster configurations may be compared with other types of symmetric objects in geometry.

Clustering and self-organization in small-scale natural and artificial systems

Physical properties of clusters, i.e. systems composed of a 'small' number of particles, are qualitatively different from those of infinite systems. The general approach to the problem of clustering is suggested. Clusters, as they are seen in the graphs theory, are discussed. Various physical mechanisms of clustering are reviewed. Dimensional properties of clusters are addressed. The dimensionality of clusters governs to a great extent their properties. Weakly and strongly coupled clusters are discussed. Hydrodynamic and capillary interactions giving rise to clusters formation are surveyed. Levitating droplet clusters, turbulent clusters and droplet clusters responsible for the breath-figures self-assembly are considered. Entropy factors influencing clustering are considered. Clustering in biological systems results in non-equilibrium multi-scale assembly, where at each scale, self-driven components come together by consuming energy in order to form the hierarchical structure. This article is part of the theme issue 'Bioinspired materials and surfaces for green science and technology (part 3)'.

Effect of Microstructure on Contact Angle and Corrosion of Ductile Iron: Iron-Graphite Composite

Ductile iron samples with similar compositions and varying microstructures were uniformly abraded, and the effects of phase fractions (ferrite, pearlite, and graphite) on the apparent contact angle (with water) and corrosion characteristics of ductile iron were investigated. We also investigated the effect of droplet volume on the apparent contact angle of ductile iron. Irrespective of the droplet size, the ductile iron system followed the Wenzel model of wetting, and the contact angle increased with increasing droplet volume. The Wenzel and Cassie-Baxter contact angles were calculated, and the calculated results agreed well with the experimental results. It was experimentally proven that pearlite is more susceptible to corrosion than ferrite and graphite, and a higher portion of pearlite in the microstructure can be detrimental to the corrosion resistance of the material. Understanding the relationship between the microstructure, contact angle, and corrosion can be used to develop materials with higher contact angle and corrosion-resistant microstructures. Using metal pipes that have high contact angles is desirable because artificial coatings on metal pipes can degrade over time leading to high cost of replacement and contamination to water systems.

Self-Arranged Levitating Droplet Clusters: A Reversible Transition from Hexagonal to Chain Structure

Water microdroplets condense over locally heated water-vapor interfaces and levitate in an ascending vapor-air flow forming self-assembled ordered monolayer clusters. The droplets do not coalesce due to complex aerodynamic interactions between them. The droplet cluster formation is governed by the condensation/evaporation balance and by coupling of heat flux and vapor flow with aerodynamic forces. Here, we report the observations of a reversible structural transition from the ordered hexagonal-structure cluster to the chain-like structure and provide an explanation of its mechanism and conditions under which the transition occurs. The phenomenon provides new insights on the fundamental physical and chemical processes with microdroplets including their role in reaction catalysis in nature and their potential for aerosol and microfluidic applications.

Droplet clusters: nature-inspired biological reactors and aerosols

Condensed microdroplets play a prominent role in living nature, participating in various phenomena, from water harvesting by plants and insects to microorganism migration in bioaerosols. Microdroplets may also form regular self-organized patterns, such as the hexagonally ordered breath figures on a solid surface or levitating monolayer droplet clusters over a locally heated water layer. While the breath figures have been studied since the nineteenth century, they have found a recent application in polymer surface micropatterning (e.g. for superhydrophobicity). Droplet clusters were discovered in 2004, and they are the subject of active research. Methods to control and stabilize droplet clusters make them suitable for the in situ analysis of bioaerosols. Studying life in bioaerosols is important for understanding microorganism origins and migration; however, direct observation with traditional methods has not been possible. We report preliminary results on direct in situ observation of microorganisms in droplet clusters. We also present a newly observed transition between the hexagonally ordered and chain-like states of a droplet cluster. This article is part of the theme issue 'Bioinspired materials and surfaces for green science and technology (part 2)'.

Ternary Logic of Motion to Resolve Kinematic Frictional Paradoxes

Paradoxes of dry friction were discovered by Painlevé in 1895 and caused a controversy on whether the Coulomb–Amontons laws of dry friction are compatible with the Newtonian mechanics of the rigid bodies. Various resolutions of the paradoxes have been suggested including the abandonment of the model of rigid bodies and modifications of the law of friction. For compliant (elastic) bodies, the Painlevé paradoxes may correspond to the friction-induced instabilities. Here we investigate another possibility to resolve the paradoxes: the introduction of the three-value logic. We interpret the three states of a frictional system as either rest-motion-paradox or as rest-stable motion-unstable motion depending on whether a rigid or compliant system is investigated. We further relate the ternary logic approach with the entropic stability criteria for a frictional system and with the study of ultraslow sliding friction (intermediate between the rest and motion or between stick and slip).

Characterization of Self-Assembled 2D Patterns with Voronoi Entropy

The Voronoi entropy is a mathematical tool for quantitative characterization of the orderliness of points distributed on a surface. The tool is useful to study various surface self-assembly processes. We provide the historical background, from Kepler and Descartes to our days, and discuss topological properties of the Voronoi tessellation, upon which the entropy concept is based, and its scaling properties, known as the Lewis and Aboav–Weaire laws. The Voronoi entropy has been successfully applied to recently discovered self-assembled structures, such as patterned microporous polymer surfaces obtained by the breath figure method and levitating ordered water microdroplet clusters.

Einstein's Viscosity Equation for Nanolubricated Friction

The generalized Einstein equation for the viscosity of a dispersion/suspension, μ = (1 + α_fϕ)μ₀, where μ₀ is the liquid viscosity, ϕ is the solid volume fraction, and α_f is a coefficient, is applied to the viscosity of a nanofluid lubricant. The coefficient of lubricated friction in the hydrodynamic regime is proportional to the viscosity of the lubricant. Therefore, an equation for the coefficient of friction with nanofluid lubrication can be formulated. We present such an equation and show its validity for common types of bearings (journal, rolling, and ball bearings). The equation, which may be viewed as one of nanofriction laws, is compared with experimental results for WS₂ nanoparticle-enhanced oil lubrication, showing agreement within 7% accuracy.

Langevin Approach to Modeling of Small Levitating Ordered Droplet Clusters

A self-assembled cluster of microdroplets levitating over a heated water surface is a fascinating phenomenon with potential applications for microreactors and for chemical and biological analysis of small volumes of liquids. Recently, we suggested a method to synthesize a cluster with an arbitrary number of small monodisperse droplets. However, the interactions, which control the structure of the cluster, are still not well understood. Here we propose a Langevin computational model considering the aerodynamic forces between the droplets and random diffusion-like fluctuations. Characteristic length and time scales and scaling relationships of interactions are discussed. The model shows excellent agreement with experimental observations for a small number of droplets.

Small Levitating Ordered Droplet Clusters: Stability, Symmetry, and Voronoi Entropy

A method to generate levitating monodisperse microdroplet clusters with an arbitrary number of identical droplets is presented. Clusters with 1-28 droplets levitate over a locally heated water layer in an ascending vapor-air jet. Due to the attraction to the center of the heated area combined with aerodynamic repulsion between the droplets, the clusters form structures that are quite diverse and different from densest packing of hard spheres. The clusters self-organize into stable and reproducible configurations dependent on the number of droplets while independent of the droplets' size. The central parts of larger clusters reproduce the shape of smaller clusters. The ability to synthesize stable clusters with a given number of droplets is important for tracing droplets, which is crucial for potential applications such as microreactors and for chemical analysis of small volumes of liquid.

Vibrations and spatial patterns in biomimetic surfaces: using the shark-skin effect to control blood clotting

We study the effect of small-amplitude fast vibrations and small-amplitude spatial patterns on various systems involving wetting and liquid flow, such as superhydrophobic surfaces, membranes and flow pipes. First, we introduce a mathematical method of averaging the effect of small spatial and temporal patterns and substituting them with an effective force. Such an effective force can change the equilibrium state of a system as well as a phase state, leading to surface texture-induced and vibration-induced phase control. Vibration and patterns can effectively jam holes in vessels with liquid, separate multi-phase flow, change membrane properties, result in propulsion and locomotion and lead to many other multi-scale, nonlinear effects including the shark-skin effect. We discuss the application of such effects to blood flow for novel biomedical 'haemophobic' applications which can prevent blood clotting and thrombosis by controlling the surface pattern at a wall of a vessel (e.g. a catheter or stent).This article is part of the themed issue 'Bioinspired hierarchically structured surfaces for green science'.

Why re-entrant surface topography is needed for robust oleophobicity

Surface patterns affect wetting properties of solid materials allowing manipulation of the phase state of an adjacent fluid. The best known example of this effect is the superhydrophobic composite (Cassie-Baxter) interface with vapour/air pockets between the solid and liquid. Mathematically, the effect of surface micropatterns can be studied by an averaging technique similarly to the method of separation of motions in dynamics. However, averaged parameters are insufficient for robust superhydrophobic and superoleophobic surfaces because additional topography features are important: hierarchical organization and re-entrant roughness. The latter is crucial for the oleophobicity because it enhances the stability of a composite interface. The re-entrant topography can be achieved by various methods. Understanding the role of re-entrant surface topography gives us new insights on the multitude of wetting scenarios beyond the standard Wenzel and Cassie-Baxter models.This article is part of the themed issue 'Bioinspired hierarchically structured surfaces for green science'.

Vibrations and Spatial Patterns Change Effective Wetting Properties of Superhydrophobic and Regular Membranes

Small-amplitude fast vibrations and small surface micropatterns affect properties of various systems involving wetting, such as superhydrophobic surfaces and membranes. We review a mathematical method of averaging the effect of small spatial and temporal patterns. For small fast vibrations, this method is known as the method of separation of motions. The vibrations are substituted by effective force or energy terms, leading to vibration-induced phase control. A similar averaging method can be applied to surface micropatterns leading surface texture-induced phase control. We argue that the method provides a framework that allows studying such effects typical to biomimetic surfaces, such as superhydrophobicity, membrane penetration and others. Patterns and vibration can effectively jam holes and pores in vessels with liquid, separate multi-phase flow, change membrane properties, result in propulsion, and lead to many other multiscale, non-linear effects. Here, we discuss the potential application of these effects to novel superhydrophobic membranes.

Dynamics of droplet impact on hydrophobic/icephobic concrete with the potential for superhydrophobicity

The ability of superhydrophobic surfaces to resist wetting and repel impinging water droplets is not less important for practical applications than the contact angle and contact angle hysteresis. Here we study novel hydrophobic concrete (with the potential for superhydrophobicity) and its ability to repel incoming droplets (e.g., rain). It is found that the onset of the pinning mode can be delayed by changing the surface topography. Also, the pinning or breakup of droplets of higher velocities depends on the incoming angle. Hydrophobic concrete with better pinning resistance showed less tendency for ice accretion.

Coupling of surface energy with electric potential makes superhydrophobic surfaces corrosion-resistant

The superhydrophobicity makes metallic surfaces corrosion-resistant. Hydrophobization leads to a decrease in the corrosion potential.

Surface micro/nanotopography, wetting properties and the potential for biomimetic icephobicity of skunk cabbage Symplocarpus foetidus

Lotus (Nelumbo nucifera) is known for its two remarkable properties: superhydrophobicity and thermogenesis; however, the relationship between these two properties remains obscure. Most botanists agree that thermogenesis helps to attract pollinators, while non-wetting helps to catch pollinators and prevents contamination. Here we investigate the surface micro- and nanotopography and wetting properties of eastern skunk cabbage (Symplocarpus foetidus), another thermogenic plant, which is known for its ability to melt snow. The skunk cabbage leaves are hydrophobic but not superhydrophobic, and they have high contact angle hysteresis (similar to the rose petal effect). We develop a heat transfer model to relate icephobicity with heat transfer and discuss the biomimetic potential that both thermogenic and superhydrophobic plants may have for icephobicity in soft materials.

Beyond Wenzel and Cassie-Baxter: second-order effects on the wetting of rough surfaces

The Wenzel and Cassie-Baxter models are almost exclusively used to explain the contact angle dependence of the structure of rough and patterned solid surfaces. However, these two classical models do not always accurately predict the wetting properties of surfaces since they fail to capture the effect of many interactions occurring during wetting, including, for example, the effect of the disjoining pressure and of crystal microstructure, grains, and defects. We call such effects the second-order effects and present here a model showing how the disjoining pressure isotherm can affect wettability due to the formation of thin liquid films. We measure water contact angles on pairs of metallic surfaces with nominally the same Wenzel roughness obtained by abrasion and by chemical etching. These two methods of surface roughening result in different rough surface structure, thus leading to different values of the contact angle, which cannot be captured by the Wenzel- and Cassie-type models. The chemical and physical changes that occur on the stainless steel and aluminum alloy surfaces as a result of intergranular corrosion, along with selective intermetallic dissolution, lead to a surface roughness generated on the nano- and microscales.

Vibro-levitation and inverted pendulum: parametric resonance in vibrating droplets and soft materials

The phenomenon of liquid droplets "levitating" or bouncing off a liquid vibrating surface has attracted attention of scientists due to its possible application in microfluidics and novel nanostructured superhydrophobic materials. Several models have been suggested in the literature, and the effect is usually attributed to non-linear viscosity. Here we suggest a simple model relating the effect to the parametric resonance as described by the Mathieu equation, which explains stabilization of an inverted pendulum with vibration foundation. Small fast vibrations can be substituted by an effective "levitation" force. We present modeling and experimental results for oil droplets and discuss how the mathematical separation of the slow and fast motion provides insights on the relation of vibro-levitation of oil droplets and soft materials with the vibro-stabilization of an inverted pendulum, and the "Indian rope" and "Cornstarch monster" tricks.

Self-assembling particle-siloxane coatings for superhydrophobic concrete

We report here, for the first time in the literature, a method to synthesize hydrophobic and superhydrophobic concrete. Concrete is normally a hydrophilic material, which significantly reduces the durability of concrete structures and pavements. To synthesize water-repellent concrete, hydrophobic emulsions were fabricated and applied on portland cement mortar tiles. The emulsion was enriched with the polymethyl-hydrogen siloxane oil hydrophobic agent as well as metakaolin (MK) or silica fume (SF) to induce the microroughness and polyvinyl alcohol (PVA) fibers to create hierarchical surfaces. Various emulsion types were investigated by using different mixing procedures, and single- and double-layer hydrophobic coatings were applied. The emulsions and coatings were characterized with optical microscope and scanning electron microscope (SEM), and their wetting properties, including the water contact angle (CA) and roll-off angle, were measured. A theoretical model for coated and non-coated concrete, which can be generalized for other types of materials, was developed to predict the effect of surface roughness and composition on the CA. An optimized distance between the aggregates was found where the CA has the highest value. The maximal CA measured was 156° for the specimen with PVA fibers treated with MK based emulsion. Since water penetration is the main factor leading to concrete deterioration, hydrophobic water-repellent concretes have much longer durability then regular concretes and can have a broad range of applications in civil and materials engineering.

Wetting transitions in underwater oleophobic surface of brass

An oil droplet in water can be in the Cassie state (with water and/or air trapped between the solid and oil) with a high contact angle (top left) or in the Wenzel state (top right). Depending on the roughness of the brass substrate, both states with high (bottom left) and low (bottom right) contact angle are observed.

Why superhydrophobic surfaces are not always icephobic

We discuss mechanical forces that act upon a water droplet and a piece of ice on a rough solid surface and the difference between dewetting and ice fracture. The force needed to detach a water droplet depends on contact angle (CA) hysteresis and can be reduced significantly in the case of a superhydrophobic surface. The force needed to detach a piece of ice depends on the receding CA and the initial size of interfacial cracks. Therefore, even surfaces with very high receding CA may have strong adhesion to ice if the size of the cracks is small.

Wetting transitions in two-, three-, and four-phase systems

We discuss wetting of rough surfaces with two-phase (solid-liquid), three-phase (solid-water-air and solid-oil-water), and four-phase (solid-oil-water-air) interfaces mimicking fish scales. We extend the traditional Wenzel and Cassie-Baxter models to these cases. We further present experimental observations of two-, three-, and four-phase systems in the case of metal-matrix composite solid surfaces immersed in water and in contact with oil. Experimental observations show that wetting transitions can occur in underwater oleophobic systems. We also discuss wetting transitions as phase transitions using the phase-field approach and show that a phenomenological gradient coefficient is responsible for wetting transition, energy barriers, and wetting/dewetting asymmetry (hysteresis).

Metal matrix composites for sustainable lotus-effect surfaces

The lotus effect involving roughness-induced superhydrophobicity is a way to design nonwetting, self-cleaning, omniphobic, icephobic, and antifouling surfaces. However, such surfaces require micropatterning, which is extremely vulnerable to even small wear rates. This limits the applicability of the lotus effects to situations when wear is practically absent. To design sustainable superhydrophobic surfaces, we suggest using metal matrix composites (MMCs) with hydrophobic reinforcement in the bulk of the material, rather than only at its surface. Such surfaces, if properly designed, provide roughness and heterogeneity needed for superhydrophobicity. In addition, they are sustainable, since when the surface layer is deteriorated and removed due to wear, hydrophobic reinforcement and roughness remains. We present a model and experimental data on wetting of MMCs. We also conducted selected experiments with graphite-reinforced MMCs and showed that the contact angle can be determined from the model. In order to decouple the effects of reinforcement and roughness, the experiments were conducted for initially smooth and etched matrix and composite materials.

Friction-induced pattern formation and Turing systems

We investigate the possibility of Turing-type pattern formation during friction. Turing or reaction-diffusion systems describe variations of spatial concentrations of chemical components with time due to local chemical reactions coupled with diffusion. Turing systems can lead to a variety of complex spatial patterns evolving with time. During friction, the patterns can form at the sliding interface due to the mass transfer (diffusion), heat transfer, various tribochemical reactions, and wear. We present simulation data showing the possibility of such pattern formation. On the other hand, existing experimental data suggest that in situ tribofilms can form at the frictional interface due to a variety of friction-induced chemical reactions (oxidation, the selective transfer of Cu ions, etc.). These tribofilms as well as other frictional "secondary structures" can form various patterns (islands or honeycomb domains). This mechanism of pattern formation can be attributed to the Turing systems.

Green tribology: principles, research areas and challenges

In this introductory paper for the Theme Issue on green tribology, we discuss the concept of green tribology and its relation to other areas of tribology as well as other 'green' disciplines, namely, green engineering and green chemistry. We formulate the 12 principles of green tribology: the minimization of (i) friction and (ii) wear, (iii) the reduction or complete elimination of lubrication, including self-lubrication, (iv) natural and (v) biodegradable lubrication, (vi) using sustainable chemistry and engineering principles, (vii) biomimetic approaches, (viii) surface texturing, (ix) environmental implications of coatings, (x) real-time monitoring, (xi) design for degradation, and (xii) sustainable energy applications. We further define three areas of green tribology: (i) biomimetics for tribological applications, (ii) environment-friendly lubrication, and (iii) the tribology of renewable-energy application. The integration of these areas remains a primary challenge for this novel area of research. We also discuss the challenges of green tribology and future directions of research.

The rose petal effect and the modes of superhydrophobicity

The wetting of rough surfaces remains a subject of active investigation by scientists. The contact angle (CA) is a traditional parameter used to characterize the hydrophobicity/philicity of a solid surface. However, it was found recently that high CAs can coexist with strong adhesion between water and a solid surface in the case of the so-called 'rose petal effect'. Several additional parameters have been proposed to characterize the interaction of water with a rough solid surface, including the CA hysteresis, the ability of water droplets to bounce off a solid surface, the tilt angle needed to initiate the flow of a droplet, and the normal and shear adhesion. It is clear now that wetting is not characterized by a single parameter, since several modes or regimes of wetting of a rough surface can exist, including the Wenzel, Cassie, lotus and petal. Understanding the wetting of rough surfaces is important in order to design non-adhesive surfaces for various applications.

Self-organization at the frictional interface for green tribology

Despite the fact that self-organization during friction has received relatively little attention from tribologists so far, it has the potential for the creation of self-healing and self-lubricating materials, which are important for green or environment-friendly tribology. The principles of the thermodynamics of irreversible processes and of the nonlinear theory of dynamical systems are used to investigate the formation of spatial and temporal structures during friction. The transition to the self-organized state with low friction and wear occurs through destabilization of steady-state (stationary) sliding. The criterion for destabilization is formulated and several examples are discussed: the formation of a protective film, microtopography evolution and slip waves. The pattern formation may involve self-organized criticality and reaction-diffusion systems. A special self-healing mechanism may be embedded into the material by coupling the corresponding required forces. The analysis provides the structure-property relationship, which can be applied for the design optimization of composite self-lubricating and self-healing materials for various ecologically friendly applications and green tribology.

Multiscale effects and capillary interactions in functional biomimetic surfaces for energy conversion and green engineering

Biological surfaces (plant leaves, lizard and insect attachment pads, fish scales, etc.) have remarkable properties due to their hierarchical structure. This structure is a consequence of the hierarchical organization of biological tissues. The hierarchical organization of the surfaces allows plants and creatures to adapt to energy dissipation and transition mechanisms with various characteristic scale lengths. At the same time, an addition of a micro-/nanoscale hierarchical level, for example of surface roughness, can change qualitatively the properties of a system and introduce multiple equilibriums, instability and dissipation. Thus, small roughness has a large effect. In particular, a small change of surface roughness can lead to a large change in the capillary force. The capillary effects are crucial for small-scale applications. Multiscale organization of the biomimetic surfaces and their adaptation to capillary effects make them suitable for applications using new principles of energy transition (e.g. capillary engines) and environment-friendly technologies (e.g. self-cleaning oleophobic surfaces).

Thermodynamics of surface degradation, self-organization and self-healing for biomimetic surfaces

Friction is a dissipative irreversible process; therefore, entropy is produced during frictional contact. The rate of entropy production can serve as a measure of degradation (e.g. wear). However, in many cases friction leads to self-organization at the surface. This is because the excess entropy is either driven away from the surface, or it is released at the nanoscale, while the mesoscale entropy decreases. As a result, the orderliness at the surface grows. Self-organization leads to surface secondary structures either due to the mutual adjustment of the contacting surfaces (e.g. by wear) or due to the formation of regular deformation patterns, such as friction-induced slip waves caused by dynamic instabilities. The effect has practical applications, since self-organization is usually beneficial because it leads to friction and wear reduction (minimum entropy production rate at the self-organized state). Self-organization is common in biological systems, including self-healing and self-cleaning surfaces. Therefore, designing a successful biomimetic surface requires an understanding of the thermodynamics of frictional self-organization. We suggest a multiscale decomposition of entropy and formulate a thermodynamic framework for irreversible degradation and for self-organization during friction. The criteria for self-organization due to dynamic instabilities are discussed, as well as the principles of biomimetic self-cleaning, self-lubricating and self-repairing surfaces by encapsulation and micro/nanopatterning.