On the cohesion of fluids and their adhesion to solids: Young's equation at the atomic scale

Effect of molecular branching and surface wettability on solid-liquid surface tension and line-tension of liquid alkane surface nanodroplets

HYPOTHESIS

Surface nanodroplets have important technological applications. Previous experiments and simulations have shown that their contact angle deviates from Young's equation. A modified version of Young's equation considering the three-phase line tension (τ) has been widely used in literature, and a wide range of values for τ are reported. We have recently shown that molecular branching affects the liquid-vapour surface tension γlv of liquid alkanes. Therefore, the wetting behaviour of surface nanodroplets should be affected by molecular branching. This study conducted molecular dynamics (MD) simulations to gain insight into the wetting behaviour of linear and branched alkane nanodroplets on oleophilic and oleophobic surfaces. We aim to examine the Young equation's validity and branching's effect on fundamental properties, including solid-liquid surface tension γsl and line tension τ.

SIMULATIONS

The simulations were performed on a linear alkane, triacontane (C30H62), as well as four of its branched isomers: 2,6,13,17-tetrapropyloctadecane,2,6,9,10,13,17-hexaethyloctadecane, 2,5,7,8,11,12,15-heptaethylhexadecane and 2,3,6,7,10,11-hexapropyldodecane. Nanodroplets with a diameter of approximately 15 nm were released onto the surfaces, and their contact angles were measured. Additionally, using a novel approach, the solid-liquid surface tension (γsl), the validity of Young's equation and line tension for all alkane and surface combinations are determined.

FINDINGS

It was discovered that the calculated γsl, deviated from the theoretical γsl,Young predicted from Young's equation for all alkanes on oleophilic surfaces. However, this deviation was minimal for branched alkanes on the oleophobic surfaces but more significant for the linear alkane. The findings indicated that γsl < 0 for oleophilic surfaces and γsl > 0 for oleophobic surfaces. Moreover, it was observed that |γsl| was lower for branched molecules and decreased as branching increased. Line tension values were then determined through a novel method, showing τ was positive for oleophilic surfaces ranging from 1.30 × 10-10 to 6.27 × 10-11N. On an oleophobic surface, linear alkane shows a negative line tension of -1.15 × 10-10N and branched alkanes up to two orders of magnitude lower values ranging from -2.09 × 10-12 to 2.43 × 10-11N. Line tension values between -1.15 × 10-10 and + 1.1 × 10-10N are calculated for various linear alkane and surface combinations. These findings show the dependence of line tension on the contact angle and branching, demonstrating that for linear alkanes, τ is significant, whereas, for branched alkanes, line tension is smaller or negligible for large contact angles.

Discrete Femtolitre Pipetting with 3D Printed Axisymmetrical Phaseguides

The capacity to precisely pipette femtoliter volumes of liquid enables many applications, for example, to functionalize a nanoscale surface and manipulate fluids inside a single-cell. A pressure-controlled pipetting method is the most preferred, since it enables the widest range of working liquids. However, precisely controlling femtoliter volumes by pressure is challenging. In this work, a new concept is proposed that makes use of axisymmetrical phaseguides inside a microfluidic channel to pipette liquid in discrete steps of known volume. An analytical model for the design of the femtopipettes is developed and verified experimentally. Femtopipettes are fabricated using a multi-scale 3D printing strategy integrating a digital light processing printed part and a two-photon-polymerization printed part. Three different variants are designed and fabricated with pipetting resolutions of 10 picoliters, 180 femtoliters and 50 femtoliters. As a demonstration, controlled amounts of a water-glycerol mixture were first aspirated and then dispensed into a mineral oil droplet.

Whether membranes developed for organic solvent nanofiltration (OSN) tend to be hydrophilic or hydrophobic? ── a review

In the past few decades, organic solvent nanofiltration (OSN) has attracted numerous researchers and broadly applied in various fields. Unlike conventional nanofiltration, OSN always faced a broad spectrum of solvents including polar solvents and non-polar solvents. Among those recently developed OSN membranes in lab-scale or widely used commercial membranes, researchers preferred to explore intrinsic materials or introduce nanomaterials into membranes to fabricate OSN membranes. However, the hydrophilicity of the membrane surface towards filtration performance was often ignored, which was the key factor in conventional aqueous nanofiltration. The influence of surface hydrophilicity on OSN performance was not studied systematically and thoroughly. Generally speaking, the hydrophilic OSN membranes performed well in the polar solvents while the hydrophobic OSN membranes work well in the non-polar solvent. Many review papers reviewed the basics, problems of the membranes, up-to-date studies, and applications at various levels. In this review, we have focused on the relationship between the surface hydrophilicity of OSN membranes and OSN performances. The history, theory, and mechanism of the OSN process were first recapped, followed by summarizing representative OSN research classified by surface hydrophilicity and types of membrane, which recent OSN research with its contact angles and filtration performance were listed. Finally, from the industrialization perspective, the application progress of hydrophilic and hydrophobic OSN membranes was introduced. We started with history and theory, presented many research and application cases of hydrophilic and hydrophobic OSN membranes, and discussed anticipated progress in the OSN field. Also, we pointed out some future research directions on the hydrophilicity of OSN membranes to deeply develop the effect made by membrane hydrophilicity on OSN performance for future considerations and stepping forward of the OSN industry.

The growth and the decay of a visco-elastocapillary ridge by localized forces

A soft solid layer develops a ridge-like deformation below the contact line due to the pulling force of the liquid-air surface tension when a droplet is in contact with it. We investigate the growth and the decay of a viscoelastic wetting ridge. The global features, e.g. the ridge height, evolve with time scales corresponding to the relaxation of the viscoelastic material. In contrast, we show that locally around the tip of the ridge, the surface tensions not only determine the equilibrium shape, but also have a significant impact on the dynamics, for which the relaxation has a characteristic spreading velocity depending on the solid surface tension. The relaxation time to an equilibrium state depends on the distance from the contact line, which can be much smaller than the long-term relaxation time scale of the viscoelastic material. The different dynamics between the global features of the ridge and the tip morphology suggests an alternative focus when investigating the contact line dynamics in soft wetting, such as stick-slip motion.

Linking intermolecular interactions and rheological behaviour in capillary suspensions

HYPOTHESIS

Capillary suspensions feature networks of particles connected by liquid bridges, which are obtained by adding a small amount of a second immiscible liquid to a suspension. It is possible to link the network formation as well as the rheological behaviour of capillary suspensions to the intermolecular interactions of their constituents.

EXPERIMENTS AND SIMULATIONS

Through a combination of experimental and numerical methods, we present a novel approach, based on Hansen solubility parameters computed from Molecular Dynamics (MD) simulations, to rationalize and predict the rheological behaviour of capillary suspensions. We investigated the formation of capillary suspensions for various combinations of bulk and secondary liquids mixed with hydrophilic silica particles. The predictions were confirmed experimentally by rheological analysis, interfacial tension measurements and microscopy (CLSM) imaging.

FINDINGS

Numerical and experimental results show that the Hansen solubility parameters theory allows to predict the formation of capillary suspensions, whose strength exponentially decays with decreasing intermolecular interactions between the secondary liquids and the dispersed particles. High immiscibility between the bulk and secondary liquid strengthens the gel up to a critical immiscibility point, above which the strength of the gel remains mostly affected by the affinity between the secondary liquids and the dispersed particles. Furthermore, we find that hydrogen-bonding and polar interactions control the formation of capillary suspensions. This simple approach can guide the selection of adequate solvents and immiscible secondary liquids, allowing an easy formulation of new particulate-based gels.

The challenge of lubricant-replenishment on lubricant-impregnated surfaces

Lubricant-impregnated surfaces are two-component surface coatings. One component, a fluid called the lubricant, is stabilized at a surface by the second component, the scaffold. The scaffold can either be a rough solid or a polymeric network. Drops immiscible with the lubricant, hardly pin on these surfaces. Lubricant-impregnated surfaces have been proposed as candidates for various applications, such as self-cleaning, anti-fouling, and anti-icing. The proposed applications rely on the presence of enough lubricant within the scaffold. Therefore, the quality and functionality of a surface coating are, to a large degree, given by the extent to which it prevents lubricant-depletion. This review summarizes the current findings on lubricant-depletion, lubricant-replenishment, and the resulting understanding of both processes. A multitude of different mechanisms can cause the depletion of lubricant. Lubricant can be taken along by single drops or be sheared off by liquid flowing across. Nano-interstices and scaffolds showing good chemical compatibility with the lubricant can greatly delay lubricant depletion. Often, depletion of lubricant cannot be avoided under dynamic conditions, which warrants lubricant-replenishment strategies. The strategies to replenish lubricant are presented and range from spraying or stimuli-responsive release to built-in reservoirs.

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.

Dynamic wetting of solid-liquid-liquid system by molecular kinetic theory

HYPOTHESIS

The mechanisms of dynamic wetting of solid-liquid-liquid (SLL) system, especially the viscosity effects of two liquids, can be investigated by the molecular kinetic theory (MKT).

METHODS

The molecular kinetic theory combined with published data was used to study the roles of a fluid viscosity and a solid surface in dynamic wetting.

FINDINGS

First, the MKT on dynamic wetting was introduced and its limitation was analyzed. Second, a viscosity effect and a solid surface effect were considered. The viscosity effect was divided into three parts for the first time, including two pure liquid zones and a mixing zone. Third, a coefficient activation free energy model was proposed, considering the effects of mixing liquids and a solid surface. Finally, the key parameters in the MKT and the application and validation of the coefficient activation free energy model were discussed in detail. This model can explain the energy dissipation in a vicinity of a three-phase contact-line successfully in a SLL wetting system. This work sheds light on the physical mechanisms of fluid and solid surface properties on the dynamic wetting in a SLL system.

Size-dependent behavior and failure of young's equation for wetting of two-component nanodroplets

HYPOTHESIS

For macroscopic systems, the interfacial properties are size-independent and Young's equation is generally valid for smooth substrates. For nanoscale systems, however, size-dependence and failure of Young's equation may emerge.

EXPERIMENTS

The wetting behavior of a nanodroplet containing two miscible liquids on a smooth substrate is explored by many-body dissipative particle dynamics simulations. The size-dependent surface tension of nanofilms is investigated as well.

FINDINGS

It is found that Young's equation is valid for nanodroplets of pure fluids but fails for two-component nanodroplets. The actual contact angle is always larger than the Young's contact angle, and their difference is getting smaller as the composition approaches pure fluids or the compatibility of the mixture is increased. The failure of Young's equation is closely associated with the size-dependent behavior in two-component nanodroplets and nanofilms. As the nanodroplet size is increased, the actual contact angle is found to decline but approaches a constant expected in macroscopic systems. Similarly, as the nanofilm thickness is increased, surface tension decreases and reaches its macroscopic value. The change of surface tension is attributed to the size-dependent surface composition, which is responsible for the failure of Young's equation.

Adaptive Wetting of Polydimethylsiloxane

To better understand the wetting of cross-linked polydimethylsiloxane (PDMS), we measured advancing and receding contact angles of sessile water drops on cross-linked PDMS as a function of contact line velocity (up to 100 μm/s). Three types of samples were investigated: pristine PDMS, PDMS where oligomers were removed by toluene treatment, and PDMS with an enriched concentration of oligomers. Depending on the velocity of advancing contact lines and the contact time with water, different modes of wetting were observed: one with a relatively low contact angle hysteresis (Δθ ≈ 10°) and one with a larger hysteresis. We attribute the low hysteresis state, called the lubricated state, to the enrichment of free oligomers at the water-PDMS interface. The enrichment of oligomers is induced by drop contact. The kinetics of the transition to the lubricated state can be described by adaptation theory. PDMS adapts to the presence of water by an enrichment of free oligomers at the interface and a correlated reduction in interfacial tension.

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.

Systematic approach for wettability prediction using molecular dynamics simulations

We present a fast and efficient approach to predict the wettability and spreading of liquids on polymeric substrates. First, a molecular dynamics parameterization is proposed for the calculation of the solubility parameter for 74 compounds including surfactants typically used in inkjet printing. Then, we introduce a molecular geometrical factor to relate the solubility parameter to the surface tension, obtaining estimates in remarkable agreement with experiments. By using a modified Young-Fowkes equation, the contact angles of liquids on various polymeric substrates are determined and their dependence on the hydrogen bonding, dispersion and polar contribution of the solubility parameter are investigated. We find that wetting properties are obtained with a good accuracy when taking into account the hydrogen-bonding and polar interactions in the geometric sum of the solubility parameter. Based on these findings, a 3D wetting space is proposed to evaluate liquids wettability and judge their suitability for specific substrates. This will enable easy formulation of liquids with wettability tailored for a particular surface and application.

Controlling the pinning time of a receding contact line under forced wetting conditions

HYPOTHESIS

The contact line pinning that appears in a flow coating process over substrates patterned with chemical or physical heterogeneities has been recently applied to deposit micro- and nanoparticles with great precision. However, the mechanism underlying pinning of a receding contact line at the nanoscale is not yet well understood. In the case of a contact line pinned at a chemical heterogeneity, we hypothesise that it is possible to establish a relation between the pinning time, the contact line velocity and the liquid/plate/heterogeneity affinity that can help to optimize particle deposition.

METHODS

We use large-scale molecular dynamic (MD) simulations of a finite liquid bridge formed between two parallel, non-identical, smooth solid plates. The top plate slides relative to the bottom plate inducing a displacement of the four different contact lines of the liquid bridge. The introduction of a chemical heterogeneity on the bottom plate by modifying locally the liquid-solid affinity provokes the transient pinning of the contact line in contact with the bottom substrate. By means of this simple MD simulation, we can study the mechanism of contact line pinning and its relation with the liquid/heterogeneity affinity and the contact line velocity. Additionally, we compare this mechanism with the case of the receding contact line pinned on a physical heterogeneity (a simple step discontinuity).

FINDINGS

We propose an analytical model that predicts the values of the dynamic contact angles in the general case of a capillary liquid bridge confined between two parallel plates with different wettabilities versus the relative velocity of the top plate. These predictions are successfully validated by the results of the large-scale MD simulations. The model allows thus to predict the value of the dynamic contact angles for the different contact lines of the system versus the relative speed of the moving plate. Once the chemical heterogeneity is introduced in the bottom plate, we show that when the receding contact line reaches the patch it remains temporarily pinned while the receding contact angle evolves with time. Once the receding angle reaches the value of the equilibrium contact angle of the patch, the receding contact line overcomes pinning. A geometrical model able to predict the pinning time is proposed and validated by our MD simulations. The pinning time depends not only on the relative plate velocity and plate wettability properties but also on the separation distance between the plates confining the capillary bridge. The model can consequently be used to select the substrate wettability or meniscus geometry suitable to impose the pinning time required for specific applications.

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.

Moving contact lines and Langevin formalism

HYPOTHESIS

In previous work [J.-C. Fernández-Toledano, T. D. Blake^, J. De Coninck, J. Colloid Interface Sci. 540 (2019) 322-329], **we used molecular dynamics (MD) to show that the thermal oscillations of a contact line formed between a liquid and a solid at equilibrium may be interpreted in terms of an overdamped 1-D Langevin harmonic oscillator. The variance of the contact-line position and the rate of damping of its self-correlation function enabled us to determine the coefficient of contact-line friction ζ and so predict the dynamics of wetting. We now propose that the same approach may be applied to a moving contact line.

METHODS

We use the same MD system as before, a liquid bridge formed between two solid plates, but now we move the plates at a steady velocity U_plate in opposite directions to generate advancing and receding contact lines and their associated dynamic contact angles θ^d. The fluctuations of the contact-line positions and the dynamic contact angles are then recorded and analyzed for a range of plate velocities and solid-liquid interaction.

FINDINGS

We confirm that the fluctuations of a moving contact line may also be interpreted in terms of a 1-D harmonic oscillator and derive a Langevin expression analogous to that obtained for the equilibrium case, but with the harmonic term centered about the mean location of the dynamic contact line x^d, rather than its equilibrium position x⁰, and a fluctuating capillary force arising from the fluctuations of the dynamic contact angle around θ^d, rather than the equilibrium angle θ⁰. We also confirm a direct relationship between the variance of the fluctuations over the length of contact line considered L_y, the time decay of the oscillations, and the friction ζ. In addition, we demonstrate a new relationship for our systems between the distance to equilibrium x^d-x⁰ and the out of equilibrium capillary force γ_Lcosθ⁰-cosθ^d, where γ_L is the surface tension of the liquid, and show that neither the variance of the fluctuations nor their time decay depend on U_plate. Our analysis yields values of ζ nearly identical to those obtained for simulations of spreading drops confirming the common nature of the dissipation mechanism at the contact line.

Surface nanobubbles: Theory, simulation, and experiment. A review

Surface nanobubbles (NBs) are stable gaseous phases in liquids that form at the interface with solid substrates. They have been particularly intriguing for their high stability that contradicts theoretical expectations and their potential relevance for many technological applications. Here, we present the current state of the art in this research area by discussing and contrasting main results obtained from theory, simulation and experiment, and presenting their limitations. We also provide future perspectives anticipating that this review will stimulate further studies in the research area of surface NBs.

A note on evolution of pressure and flow within an evaporating capillary bridge

Experiments with evaporation of capillary bridges between two glass spheres show that the bridge gorge radius decreases much faster than the contact radius, distorting the original constant mean curvature bridge shape. In addition, the Laplace pressure calculated from local principal curvatures exhibits high gradients along the bridge moving external surface, most commonly with a high suction near the triple phase contact and positive pressure near the gorge. The high suction results from a negative external curvature at contact. Numerical dynamic simulations with a moving evaporating interface do not currently allow for reproducing a negative external curvature at contact. A series of static simulations are shown based on a representation of an experimentally observed interface, which does include the negative curvature at contact. The resulting Laplace pressure distribution is close to the experimental ones. Most importantly, the pressure gradients induce a consistent flow of liquid from the central area of the bridge, axially toward the solid contact, and then along the solid interface toward the contact area. The flow is believed to contribute to contact pinning. Pinning is viewed as one of the precursors of capillary bridge rupture.

Universality of Droplet Impingement: Low-to-High Viscosities and Surface Tensions

When a droplet impinges on a solid surface, its kinetic energy is mainly converted to capillary energy and viscous dissipation energy, the ratio of which depends on the wettability of the target surface and the liquid properties. Currently, there is no experimental or theoretical evidence that suggests which types of liquids exhibit the capillary energy-dominated impingement behavior. In this paper, we reported the droplet impingement behavior for a wide range of liquid viscosities, surface tensions and target surface wettabilities. Then, we showed that a recently developed energy balance equation for the droplet impingement behavior can be universally employed for predicting the maximum spreading contact area diameter of a droplet for Newtonian liquids in deposition process by modelling the droplet surface deformation. Subsequently, applicability limitations of recent existing models are discussed. The newly developed model demonstrated that the capillary energy-dominated impingement behavior can be observed at considerably low viscosities of liquid droplets such as that of the superfluid of liquid helium.

Probing Boundary Conditions at Hydrophobic Solid-Water Interfaces by Dynamic Film Drainage Measurement

A newly developed dynamic force apparatus was used to determine hydrodynamic boundary conditions of a liquid on a hydrophobic silica surface. For a given approach velocity of bubble to solid surfaces in an electrolyte solution, a reduced dimple formation and faster film drainage were observed by increasing the hydrophobicity of silica surfaces, indicating a significant change in hydrodynamic boundary conditions of water molecules from an immobile to a mobile water-hydrophobic silica interface. By comparing the measured film profiles with the predictions from the Stokes-Reynolds-Young-Laplace model, the slippage boundary condition of water on the hydrophobic silica surface of surface nanoroughness was quantified. Increasing the surface hydrophobicity was found to increase the mobility of water in the thin liquid film, promoting faster drainage of the liquid. For a given hydrophobicity of solids, the mobility of water occurred only above a critical bubble approach velocity and increased with increasing bubble approach velocity. In contrast, similar experiments with hydrophobized mica surfaces showed no-slip boundary condition of water at the molecularly smooth hydrophobic surface. The results collectively suggest that the observed mobility of water with more than 100 nm in thickness on the studied hydrophobic silica surfaces was due to the nanoroughness of hydrophobic surfaces. Such finding sheds light on one possible way of reducing the friction of water on hydrophobic solid surfaces by creating nanostructured surface of nanoroughness.

Adaptive Wetting-Adaptation in Wetting

Many surfaces reversibly change their structure and interfacial energy upon being in contact with a liquid. Such surfaces adapt to a specific liquid. We propose the first order kinetic model to describe dynamic contact angles of such adaptive surfaces. The model is general and does not refer to a particular adaptation process. The aim of the proposed model is to provide a quantitative description of adaptive wetting and to link changes in contact angles to microscopic adaptation processes. By introducing exponentially relaxing interfacial energies and applying Young's equation locally, we predict a change of advancing and receding contact angles depending on the velocity of the contact line. Even for perfectly homogeneous and smooth surfaces, a dynamic contact angle hysteresis is obtained. As possible adaptations, we discuss changes and reconstruction of polymer surfaces or monolayers, diffusion and swelling, adsorption of surfactants, replacement of contaminants, reorientation of liquid molecules, or formation of an electric double layer.

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.

Pinning of a drop by a junction on an incline

The shape of a drop pinned on an inclined substrate is a long-standing problem where the complexity of real surfaces, with heterogeneities and hysteresis, makes it complicated to understand the mechanisms behind the phenomena. Here we consider the simple case of a drop pinned on an incline at the junction between a hydrophilic half plane (the top half) and a hydrophobic one (the bottom half). Relying on the equilibrium equations deriving from the balance of forces, we exhibit three scenarios depending on the way the contact line of the drop on the substrate either simply leans against the junction or overfills (partly or fully) into the hydrophobic side. We draw some conclusions on the geometry of the overlap and the stability of these tentative equilibrium states. In the corresponding retention force factor, we find that a major role is played by the wetted length of the junction line, in the spirit of Furmidge's observations. The predictions of the theory are compared with extensive molecular dynamics simulations.

Insights into the Impact of Surface Hydrophobicity on Droplet Coalescence and Jumping Dynamics

Droplet coalescence jumping on superhydrophobic surfaces attracts much research attention owing to its capability in enhancing condensation for energy and water applications. In this work, we reveal the impact of the finite surface adhesion to explain velocity discrepancies observed in recent droplet jumping studies, particularly when droplet sizes are a few micrometers (1-10 μm). Surface adhesion, which is usually neglected, can significantly affect both droplet coalescence and departure dynamics. It causes oscillations on velocity and contact area in the droplet coalescence process, as observed numerically and experimentally. Comparing the increasing rate of jumping velocity with contact angle for three different droplet sizes, we show that smaller droplets exhibit higher sensitivity to the change of surface hydrophobicity. We also specify the range of surface superhydrophobicity where the jumping velocity monotonically decreases (θ ≳ 170°), increases (θ ≲ 160°), or changes non-monotonically in transition (160° ≲ θ ≲170°) with droplet size. As a result, there exists a broad jumping velocity range for micrometer-sized droplets on a superhydrophobic surface with a slight contact angle variation. This work offers an extended understanding of the droplet coalescence and jumping dynamics to resolve the discrepancies in recent experimental observations.