Liquid morphologies and capillary forces between three spherical beads

Equilibrium shapes of coalesced pendular bridges in a static assembly of spherical beads are computed by numerical minimization of the interfacial energy. Our present study focuses on generic bead configurations involving three beads, one of which is in contact to the two others while there is a gap of variable size between the latter. In agreement with previous experimental studies, we find interfacial `trimer' morphologies consisting of three coalesced pendular bridges, and `dimers' of two coalesced bridges. In a certain range of the gap opening we observe a bistability between the dimer and trimer morphology during shrinking and growth. The magnitude of the corresponding capillary forces in presence of a trimer or dimer depends, besides the gap opening only on the volume or Laplace pressure of liquid. For a given Laplace pressure, the capillary forces in presence of a trimer are slightly larger than the force of a single bridges at the same gap opening, which could explain the shallow maximum and plateau of the capillary cohesion of a wetting liquid for saturations in the funicular regime

The Role of Contact Angle Hysteresis for Fluid Transport in Wet Granular Matter

The stability of sand castles is determined by the structure of wet granulates. Experimental data about the size distribution of fluid pockets are ambiguous about their origin. We discovered that contact angle hysteresis plays a fundamental role in the equilibrium distribution of bridge volumes, and not geometrical disorder as commonly conjectured, which has substantial consequences on the mechanical properties of wet granular beds, including a history dependent rheology and lowered strength. Our findings are obtained using a novel model where the Laplace pressures, bridge volumes and contact angles are dynamical variables associated to the contact points. While accounting for contact line pinning, we track the temporal evolution of each bridge. We observe a cross-over to a power-law decay of the variance of capillary pressures at late times and a saturation of the variance of bridge volumes to a finite value connected to contact line pinning. Large scale simulations of liquid transport in the bridge network reveal that the equilibration dynamics at early times is well described by a mean field model. The spread of final bridge volumes can be directly related to the magnitude of contact angle hysteresis

Statics and dynamics of liquid barrels in wedge geometries

We present a theoretical study of the statics and dynamics of a partially wetting liquid droplet, of equilibrium contact angle , confined in a solid wedge geometry of opening angle . We focus on a mostly non-wetting regime, given by the condition , where the droplet forms a liquid barrel – a closed shape of positive mean curvature. Using a quasi-equilibrium assumption for the shape of the liquid–gas interface, we compute the changes to the surface energy and pressure distribution of the liquid upon a translation along the symmetry plane of the wedge. Our model is in good agreement with numerical calculations of the surface energy minimisation of static droplets deformed by gravity. Beyond the statics, we put forward a Lagrangian description of the droplet dynamics. We focus on the overdamped limit, where the driving capillary force is balanced by the frictional forces arising from the bulk hydrodynamics, the corner flow near the contact lines and the contact-line friction. Our results provide a theoretical framework to describe the motion of partially wetting liquids in confinement, and can be used to gain further understanding on the relative importance of dissipative processes that span from microscopic to macroscopic length scales

Wetting transitions on superhydrophobic auxetic metamaterials

Superhydrophobicity plays a pivotal role in numerous applications. Recently, we have demonstrated the potential of auxetic metamaterials in creating superhydrophobic materials with unique wetting properties. However, the superhydrophobic properties are lost when the liquid penetrates into the surface structure. Understanding the conditions for droplet penetration is crucial for advancing wetting control. Here, we experimentally identify the transition from droplet suspension to full-penetration on an auxetic bowtie/honeycomb lattice membrane. We develop a comprehensive physical model surface representing different states of strain, ranging from auxetic to conventional lattice membranes, and consider the wetting as the liquid surface tension is varied using water/ethanol mixtures. By examining the interplay between contact angle and lattice structure, we gain valuable insights into the conditions for droplet suspension and full-penetration. Additionally, we develop a simple touch test to discern whether a droplet has effectively fully penetrated the structure, providing a practical and efficient means of distinguishing the different wetting states (suspended or partially penetrating vs fully penetrating)

Transforming Auxetic Metamaterials into Superhydrophobic Surfaces

Superhydrophobic materials are often inspired by nature, whereas metamaterials are engineered to have properties not usually occurring naturally. In both, the key to their unique properties is structure. Here, it is shown that a negative Poisson's ratio (auxetic) mechanical metamaterial can transform into a unique superhydrophobic material. When stretched, its surface has the counterintuitive property that it also expands in the orthogonal lateral direction. The change in the solid surface fraction as strain is applied is modeled, and it is shown that it decreases as the space between solid elements of the auxetic lattice expands. This results in a unique dependence of the superhydrophobicity on strain. Experimental models are constructed to illustrate the relationship between different states of strain and superhydrophobicity as the lattice transitions from an auxetic to a conventional structure. The findings offer a new approach to designing superhydrophobic materials for self‐cleaning surfaces, droplet transportation, droplet encapsulation, and oil–water separation

Wetting on Anisotropically Patterned and Rough Surfaces

Since Young in 1805 described in words the trigonometric relations between the contact angle and the forces acting on a droplet in mechanical equilibrium on a sulid surface, many advances in the description of several aspects of wetting behavior have been done. Besides the recent years developements in the field of micropatterning allowed the production surfaces with chemical and geometrical regular patterns, which make possible a direct test of theoretical models. Beyond the patterns characterized by a global isotropic disposition if the surface asperities and heterogeneities, patterns constituted of series of parallel stripes or reliefs have been produced, introducing an anisotropic element in the substrate. Recently many works focused on the characterization of the anisotropic behavior of droplets on those surfaces. However there is not a complete theory describing the anisotropy of droplets in these conditions. Furthermore most part of previous works study the anisotropy on regular patterns made by micrometric channels. To give a general description of those aspects of the anisotropic behavior which are independent by the nature of the micrometric regular pattern, and to focus on the influence of different wettabilities, in this thesis we studied the anisotropic wetting of droplets sitting on the top of single posts, characterized by flat surfaces and sharp corners, and made with different materials. The anisotropy was quantified by measuring the contact angles and base elongations in the two principal symmetry axis. Measurements were obtained by a homemade apparatus, and the analysis software has been entirely developed in this thesis. The main finding is that the contact angle difference and the base eccentricity show the same relation within the experimental errors regardless of surface wettability. These measurements were complemented by numerical simulations with the Lattice Boltzmann method, which showed a good agreement with experimental results. We also developed a simple geometrical model, valid for small eccentricities which reproduces qualitatively experimental and numerical data. In addition, during this thesis I characterized the wetting properties of thin (isotropic) films of nanostructured titania, and related them to the morphological parameters of the substrates.Da quando Young nel 1805 descrisse a parole le relazioni trigonometriche tra l’angolo di contatto e le forze agenti su una goccia in equilibrio meccanico su una superficie solida sono stati ottenuti molti progressi nella descrizione di vari aspetti del wetting. Inoltre i progressi degli ultimi anni nel campo della microlavorazione hanno permesso di ottenere in modo semplice superfici con pattern chimici e geometrici assai regolari, su cui è stato possibile testare sperimentalmente le ipotesi dei vari modelli teorici. Oltre a tutti i pattern caratterizzati da una disposizione globalmente isotropa delle asperità, sono stati prodotti pattern costituiti da una serie di strisce e rilievi paralleli gli uni agli altri, introducendo così un elemento anisotropo nel substrato. Negli ultimi anni molti lavori sono stati rivolti alla caratterizzazione del comportamento anisotropo delle gocce su tali substrati. Tuttavia ad oggi non esiste una teoria completa che descriva l’anisotropia di gocce in queste condizioni. Inoltre la maggior parte dei lavori precedenti riguarda lo studio dell’anisotropia su pattern regolari costituiti da canali micrometrici. Per fornire una descrizione generale di quegli aspetti del comportamento anisotropo che sono indipendenti dai dettagli del pattern regolare su scala micrometrica, e per evidenziare l’influenza di diverse bagnabilità della superficie, in questa tesi abbiamo studiato il wetting anisotropo di gocce depositate su singoli rilievi, caratterizzati da una supervicie piana e spigoli vivi, e costruiti con diversi materiali. L’anisotropia è stata quantificata misurando gli angoli di contatto e le dimensioni della base delle gocce nei due principali assi di simetria. Le misure sono state ottenute con un apparato fatto in casa, e il software di analisi è stato interamente sviluppato durante questa tesi. Il risultato principale consiste nel fatto che la differenza tra gli angoli di contatto nelle due direzioni e l’eccentricità di base mostrano la stessa relazione all’interno degli errori sperimentali, indipendentemente dalla bagnabilità del substrato. Queste misure sono state completate tramite simulazioni numeriche per mezzo del metodo Lattice Boltzmann, e che hanno mostrato un buon accordo con i risultati sperimentali. Inoltre abbiamo formulato un semplice modello geometrico, valido per piccoli, che riproduce qualitativamente sia i risultati sperimentali che quelli numerici. Inoltre in questa tesi ho caratterizzato la bagnabilità di sottili film (isotropici) di titania nanostrutturata, mettendola in relazione con le proprietà morfologiche dei substrati stessi

Shape Evolution of Droplets Growing on Linear Microgrooves

Anisotropic spreading of liquids and elongated droplet shapes are often encountered on surfaces decorated with a periodic micropattern of linear surface topographies. Numerical calculations and wetting experiments show that the shape evolution of droplets that are slowly growing on a surface with parallel grooves can be grouped into two distinct morphological regimes. In the first regime, the liquid of the growing droplet spreads only into the direction parallel to the grooves. In the second regime, the three-phase contact line advances also perpendicular to the grooves, whereas the growing droplets approach a scale-invariant shape. Here, we demonstrate that shapes of droplets in contact with a large number of linear grooves are identical to the shapes of droplets confined to a plane chemical stripe, where this mapping of shapes is solely based on the knowledge of the cross section of the linear grooves and the material contact angle. The spectrum of interfacial shapes on the chemical stripe can be exploited to predict the particular growth mode and the asymptotic value of the base eccentricity in the limit of droplets covering a large number of grooves. The proposed model shows an excellent agreement with experimentally observed base eccentricities for droplets on grooves of various cross sections. The universality of the model is underlined by the accurate match with available literature data for droplet eccentricities on parallel chemical stripes