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.

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.

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.

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.

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 kBT (where kB 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 kBT, 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.

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)'.

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.

Scaling in Colloidal and Biological Networks.

Scaling and dimensional analysis is applied to networks that describe various physical systems. Some of these networks possess fractal, scale-free, and small-world properties. The amount of information contained in a network is found by calculating its Shannon entropy. First, we consider networks arising from granular and colloidal systems (small colloidal and droplet clusters) due to pairwise interaction between the particles. Many networks found in colloidal science possess self-organizing properties due to the effect of percolation and/or self-organized criticality. Then, we discuss the allometric laws in branching vascular networks, artificial neural networks, cortical neural networks, as well as immune networks, which serve as a source of inspiration for both surface engineering and information technology. Scaling relationships in complex networks of neurons, which are organized in the neocortex in a hierarchical manner, suggest that the characteristic time constant is independent of brain size when interspecies comparison is conducted. The information content, scaling, dimensional, and topological properties of these networks are discussed.

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).

Einstein's Viscosity Equation for Nanolubricated Friction.

The generalized Einstein equation for the viscosity of a dispersion/suspension, µ = (1 + αfϕ)µ0, where µ0 is the liquid viscosity, ϕ is the solid volume fraction, and αf 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.

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.

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.

We study the correlation of wetting properties and corrosion rates on hydrophobized cast iron. Samples of different surface roughnesses (abraded by sandpaper) are studied without coating and with two types of hydrophobic coatings (stearic acid and a liquid repelling spray). The contact angles and contact angle hysteresis are measured using a goniometer while corrosion rates are measured by a potentiodynamic polarization test. The data show a decrease in corrosion current density and an increase in corrosion potential after superhydrophobization. A similar trend is also found in the recent literature data. We conclude that a decrease in the corrosion rate can be attributed to the changing open circuit potential of a coated surface and increased surface area making the non-homogeneous (Cassie-Baxter) state possible. We interpret these results in light of the idea that the inherent surface energy is coupled with the electric potential in accordance with the Lippmann law of electrowetting and Le Châtelier's principle and, therefore, hydrophobization leads to a decrease in the corrosion potential. This approach can be used for novel anti-corrosive coatings.

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.