Contact Line Pinning Research Articles

Modeling nanofluid sessile drop evaporation

Modeling predictions for the evaporation of nanofluid pinned sessile drops are reported. Drops of fluids containing suspended nanoparticles have reduced evaporation rates relative to their pure fluid counterparts due to the agglomeration of nanoparticles at the surface resulting in a reduction in available liquid at the drop surface for evaporation. The present model implements a mechanism for the reduction in the surface concentration of the evaporating liquid based on the fractal geometry of nanoparticle agglomerates. Nanoparticle packing near the drop pinned contact line results in regions where a maximum nanoparticle volume fraction is attained, leading to significant reductions in the evaporative mass flux. Model predictions for the evaporation rate of pure ethanol and ethanol containing suspended aluminum nanoparticles are compared to experiments from the literature with excellent agreement for the reduction in evaporation rate due to nanoparticle loading and in reasonable quantitative agreement for the evaporation rate. The maximum allowable nanoparticle volume fraction is shown to be an important parameter in governing the evaporation rate of nanofluid sessile drops.

Slippery Liquid-Infused Porous Surfaces and Droplet Transportation by Surface Acoustic Waves

On a solid surface a droplet of liquid will stick due to the capillary adhesion and this causes low droplet mobility. To reduce contact line pinning, surface chemistry can be coupled to micro- and/or nano-structures to create superhydrophobic surfaces on which a droplet balls-up into an almost spherical shape thus minimising contact area. Recent progress in soft matter has now led to alternative lubricant impregnated surfaces capable of almost zero contact line pinning and high droplet mobility without causing droplets to ball-up and minimize contact area. Here we report a new approach to Surface Acoustic Wave (SAW) actuated droplet transportation enabled using such a surface. These surfaces maintain the contact area required for efficient energy and momentum transfer of the wave energy into the droplet, whilst achieving high droplet mobility and large footprint, therefore reducing the threshold power required to induce droplet motion. In our approach we used a slippery layer of lubricating oil infused into a self-assembled porous hydrophobic layer, which is significantly thinner than the SAW wavelength and so avoided damping of the wave. A significant reduction (up to 85%) in the threshold power for droplet transportation was found compared to that using a conventional surface treatment method. Moreover, unlike droplets on superhydrophobic surfaces, where interaction with the SAW induced a transition from a Cassie–Baxter state to a Wenzel state, the droplets on our liquid impregnated surfaces remained in a mobile state after interaction with the SAW.

Morphological Transformation of Surface Femtodroplets upon Dissolution.

Constructing controllable liquid patterns with high resolution and accuracy is of great importance in droplet depositions for a range of applications. Simple surface chemical micropatterns have been popularly used to regulate the shape of liquid droplets and the final structure of deposited materials. In this work, we study the morphological evolution of a dissolving femtoliter droplet pinned on multiple microdomains. On the basis of minimization of interfacial energy, the numerical simulations predict various symmetric droplet profiles in equilibrium at different liquid volumes. However, our experimental results show both symmetric and asymmetric shapes of droplets due to contact line pinning and symmetry breaking during droplet dissolution. Upon slow volume reduction, the deposited microdroplet arrays on one single type of simple surface prepatterns spontaneously morphed into a series of complex regular 3D shapes. The findings in this work offer insights into design and prepararion of the rich and complex morphology of liquid patterns via simple surface premicropatterns.

Multi-MHz micro-electro-mechanical sensors for atomic force microscopy

Silicon ring-shaped micro-electro-mechanical resonators have been fabricated and used as probes for dynamic atomic force microscopy (AFM) experiments. They offer resonance frequency above 10MHz, which is notably greater than that of usual cantilevers and quartz-based AFM probes. On-chip electrical actuation and readout of the tip oscillation are obtained by means of built-in capacitive transducers. Displacement and force resolutions have been determined from noise analysis at 1.5fm/√Hz and 0.4 pN/√Hz, respectively. Despite the high effective stiffness of the probes, the tip-surface interaction force is kept below 1 nN by using vibration amplitude significantly below 100pm and setpoint close to the free vibration conditions. Imaging capabilities in amplitude- and frequency-modulation AFM modes have been demonstrated on block copolymer surfaces. Z-spectroscopy experiments revealed that the tip is vibrating in permanent contact with the viscoelastic material, with a pinned contact line. Results are compared to those obtained with commercial AFM cantilevers driven at large amplitudes (>10nm).

Nanoscale pinning effect evaluated from deformed nanobubbles.

Classical thermodynamics theory predicts that nanosized bubbles should disappear in a few hundred microseconds. The surprisingly long lifetime and stability of nanobubbles are therefore interesting research subjects. It has been proposed that the stability of nanobubbles arises through pinning of the three-phase contact line, which results from intrinsic nanoscale geometrical and chemical heterogeneities of the substrate. However, a definitive explanation of nanobubble stability is still lacking. In this work, we examined the stability mechanism by introducing a "pinning force." We investigated nanobubbles at a highly ordered pyrolytic graphite/pure water interface by peak force quantitative nano-mechanical mapping and estimated the pinning force and determined its maximum value. We then observed the shape of shrinking nanobubbles. Because the diameter of the shrinking nanobubbles was pinned, the height decreased and the contact angle increased. This phenomenon implies that the stability results from the pinning force, which flattens the bubble through the pinned three-phase contact line and prevents the Laplace pressure from increasing. The pinning force can also explain the metastability of coalesced nanobubbles, which have two semispherical parts that are joined to form a dumbbell-like shape. The pinning force of the semispherical parts was stronger than that of the joint region. This result demonstrates that the contact line of the semispherical parts is pinned strongly to keep the dumbbell-like shape. Furthermore, we proposed a nanobubble generation mechanism for the solvent-exchange method and explained why the pinning force of large nanobubbles was not initially at its maximum value, as it was for small nanobubbles.

Drop spreading on a superhydrophobic surface: pinned contact line and bending liquid surface.

In this study, we employ molecular dynamics (MD) simulations to probe the spreading of a drop on a superhydrophobic (SH) surface. The SH surface consists of nanopillars and the drop spreads while being in the Cassie-Baxter (CB) state on the nanopillared surface. Most remarkably, unlike the spreading on non-SH surfaces, we witness that the spreading on SH surfaces is not dominated by the motion of the three-phase contact line (TPCL). Rather, the TPCL remains pinned at the edge of a nanopillar and the spreading is ensured by the liquid surface or the liquid-vapor interface (of this pinned TPCL) bending down and wetting the solid adjacent to the TPCL. Such bending may actually enforce a progressive temporal increase in the instantaneous local contact angle eventually making it equal to or more than 180°. This is in sharp contrast to the classical spreading dynamics, where, with the spreading being dictated by the TPCL motion, the local contact angle always decreases with time. We carry out simulations where the solids supporting the nanopillars have vastly different wettabilities; however, this principle of bending-driven spreading is invariably witnessed. In fact, given the recent experimental study on the rolling of drops on SH surfaces manifesting exactly identical liquid-surface-bending-driven drop motion, we can infer that regardless of the drop size (e.g., nanoscopic or millimetric) or the nature of drop motion (spreading or rolling), the motion of drops in the CB state on SH surfaces is universally driven by the bending of liquid surfaces and not by the motion of the TPCL.

Spreading dynamics of a precursor film of nanodrops on total wetting surfaces.

The spreading dynamics of a nanodrop on a total wetting surface is explored by many-body dissipative particle dynamics. Both smooth and rough surfaces with various spreading coefficients (S) are considered. The evolution of the spreading film is mainly characterized by the radius of the wetting area (Rp) and the apparent base radius (Rb) and the contact angle (θ) of the spherical cap. The difference between Rp and Rb reveals the presence of the precursor film. The dynamic behavior can be described by the power law: Rp ∼ tm, Rb ∼ tn, and θ ∼ t-α. Regardless of the surface roughness, the exponents n = 0.1 and α = 0.3 agree with Tanner's law and are independent of the spreading coefficient. However, the expansion of the precursor film depends on the surface roughness and the spreading coefficient. As the cavity size corresponding to the roughness decreases or S increases, the exponent m can rise approximately from 0.1 to 0.2. That is, the spontaneous expansion is driven by the spreading coefficient but impeded by the surface roughness. Forced spreading of a nanodrop on a smooth surface leads to anisotropic expansion. The length along the force direction L(t) follows the power law L ∝ tp and the exponent p ≈ 0.274 is insensitive to S. Nonetheless, the length along the direction perpendicular to the force direction is dominated by the spontaneous spreading. Contact line pinning of the rear end is only observed for intermediate forces.

Alternative mechanism for coffee-ring deposition based on active role of free surface.

When a colloidal sessile droplet dries on a substrate, the particles suspended in it usually deposit in a ringlike pattern. This phenomenon is commonly referred to as the "coffee-ring" effect. One paradigm for why this occurs is as a consequence of the solutes being transported towards the pinned contact line by the flow inside the drop, which is induced by surface evaporation. From this perspective, the role of the liquid-gas interface in shaping the deposition pattern is somewhat minimized. Here, we propose an alternative mechanism for the coffee-ring deposition. It is based on the bulk flow within the drop transporting particles to the interface where they are captured by the receding free surface and subsequently transported along the interface until they are deposited near the contact line. That the interface captures the solutes as the evaporation proceeds is supported by a Lagrangian tracing of particles advected by the flow field within the droplet. We model the interfacial adsorption and transport of particles as a one-dimensional advection-generation process in toroidal coordinates and show that the theory reproduces ring-shaped depositions. Using this model, deposition patterns on both hydrophilic and hydrophobic surfaces are examined in which the evaporation is modeled as being either diffusive or uniform over the surface.

Detachment Force of Particles with Pinning of Contact Line from Fluid Bubbles/Droplets.

Deformation of a spherical droplet or bubble containing a pair of particles on its surface is considered when equal but opposite forces are applied to the particles. The particles are placed opposite each other, thus providing a symmetric problem that is more amenable to analytical treatment. We extend our previous calculations concerning such arrangements with constant contact angles to situations where it is the contact line now that is pinned on the surface of the particles. The force-displacement curves are calculated as the particles are pulled apart and are found to be linear for small displacements. However, it is also found that the "Hookean constant" for the pinned contact line problem is different from the one derived for systems with a constant contact angle, the constant being larger if the pinned line is at the equator of the particles.

Simultaneous observation of asymmetric speed-dependent capillary force hysteresis and slow relaxation of a suddenly stopped moving contact line.

We report direct atomic-force-microscope measurements of capillary force hysteresis (CFH) and relaxation of a circular moving contact line (CL) formed on a long micron-sized hydrophobic fiber intersecting a liquid-air interface. By using eight different liquid interfaces with varying solid-liquid molecular interactions, we find a universal behavior of the asymmetric speed dependence of CFH and CL relaxation. A unified model based on force-assisted barrier crossing is used to connect the mesoscopic measurements of CFH and CL relaxation with the energy barrier height E_{b} and size λ associated with the surface defects. The experiment demonstrates that the CL pinning (relaxation) and depinning dynamics are closely related and can be described by a common microscopic framework.

Three-gradient regular solution model for simple liquids wetting complex surface topologies.

We use regular solution theory and implement a three-gradient model for a liquid/vapour system in contact with a complex surface topology to study the shape of a liquid drop in advancing and receding wetting scenarios. More specifically, we study droplets on an inverse opal: spherical cavities in a hexagonal pattern. In line with experimental data, we find that the surface may switch from hydrophilic (contact angle on a smooth surface θY < 90°) to hydrophobic (effective advancing contact angle θ > 90°). Both the Wenzel wetting state, that is cavities under the liquid are filled, as well as the Cassie–Baxter wetting state, that is air entrapment in the cavities under the liquid, were observed using our approach, without a discontinuity in the water front shape or in the water advancing contact angle θ. Therefore, air entrapment cannot be the main reason why the contact angle θ for an advancing water front varies. Rather, the contact line is pinned and curved due to the surface structures, inducing curvature perpendicular to the plane in which the contact angle θ is observed, and the contact line does not move in a continuous way, but via depinning transitions. The pinning is not limited to kinks in the surface with angles θkink smaller than the angle θY. Even for θkink > θY, contact line pinning is found. Therefore, the full 3D-structure of the inverse opal, rather than a simple parameter such as the wetting state or θkink, determines the final observed contact angle.

Effects of the Molecular Structure of a Self-Assembled Monolayer on the Formation and Morphology of Surface Nanodroplets

The formation and morphology of microscopic droplets on a chemically modified surface are important for many droplet-related applications. In this study, we examined the formation and morphological characteristics of nanodroplets produced in the same process of solvent exchange on a gold surface coated with a methyl-terminated alkanethiol monolayer. From atomic force microscopy images, we obtained the contact angles of polymerized nanodroplets in 12 combinations of the length of a straight alkyl chain and the type of droplet liquid. Our results show a significant decrease in the number density of the droplets as the number of methyl groups extends from 8 to 12 or 14. The contact angle of the droplets on octanethiol is significantly larger than that on dodecanethiol or tetradecanethiol, possibly because of the screening effect from the monolayer. Our results demonstrate that under the same solution conditions the morphology of surface nanodroplets is sensitive to the detailed molecular structures of the monolayer on the substrate. This finding has important implications for understanding static wetting on the microscopic scale and the origin of three-phase contact line pinning.

Photocontrol of fluid slugs in liquid crystal polymer microactuators.

The manipulation of small amounts of liquids has applications ranging from biomedical devices to liquid transfer. Direct light-driven manipulation of liquids, especially when triggered by light-induced capillary forces, is of particular interest because light can provide contactless spatial and temporal control. However, existing light-driven technologies suffer from an inherent limitation in that liquid motion is strongly resisted by the effect of contact-line pinning. Here we report a strategy to manipulate fluid slugs by photo-induced asymmetric deformation of tubular microactuators, which induces capillary forces for liquid propulsion. Microactuators with various shapes (straight, 'Y'-shaped, serpentine and helical) are fabricated from a mechanically robust linear liquid crystal polymer. These microactuators are able to exert photocontrol of a wide diversity of liquids over a long distance with controllable velocity and direction, and hence to mix multiphase liquids, to combine liquids and even to make liquids run uphill. We anticipate that this photodeformable microactuator will find use in micro-reactors, in laboratory-on-a-chip settings and in micro-optomechanical systems.

Self-pinning of a nanosuspension droplet: Molecular dynamics simulations.

Results are presented from molecular dynamics simulations of Pb(l) nanodroplets containing dispersed Cu nanoparticles (NPs) and spreading on solid surfaces. Three-dimensional simulations are employed throughout, but droplet spreading and pinning are reduced to two-dimensional processes by modeling cylindrical NPs in cylindrical droplets; NPs have radius R_{NP}≅3nm while droplets have initial R_{0}≅42nm. At low particle loading explored here, NPs in sufficient proximity to the initial solid-droplet interface are drawn into advancing contact lines; entrained NPs eventually bind with the underlying substrate. For relatively low advancing contact angle θ_{adv}, self-pinning on entrained NPs occurs; for higher θ_{adv}, depinning is observed. Self-pinning and depinning cases are compared and forces on NPs at the contact line are computed during a depinning event. Though significant flow in the droplet occurs in close proximity to the particle during depinning, resultant forces are relatively low. Instead, forces due to liquid atoms confined between the particles and substrate dominate the forces on NPs; that is, for the NP size studied here, forces are interface dominated. For pinning cases, a precursor wetting film advances ahead of the pinned contact line but at a significantly slower rate than for a pure droplet. This is because the precursor film is a bilayer of liquid atoms on the substrate surface but it is instead a monolayer film as it crosses over pinning particles; thus, mass delivery to the bilayer structure is impeded.

AFM Study of Surface Nanobubbles on Binary Self-Assembled Monolayers on Ultraflat Gold with Identical Macroscopic Static Water Contact Angles and Different Terminal Functional Groups.

All experimental findings related to surface nanobubbles, such as their pronounced stability and the striking differences of macroscopic and apparent nanoscopic contact angles, need to be addressed in any theory or model of surface nanobubbles. In this work we critically test a recent explanation of surface nanobubble stability and their consequences and contrast this with previously proposed models. In particular, we elucidated the effect of surface chemical composition of well-controlled solid-aqueous interfaces of identical roughness and defect density on the apparent nanoscopic contact angles. Expanding on a previous atomic force microscopy (AFM) study on the systematic variation of the macroscopic wettability using binary self-assembled monolayers (SAMs) on ultraflat template stripped gold (TSG), we assessed here the effect of different surface chemical composition for macroscopically identical static water contact angles. SAMs on TSG with a constant macroscopic water contact angle of 81 ± 2° were obtained by coadsorption of a methyl-terminated thiol and a second thiol with different terminal functional groups, including hydroxy, amino, and carboxylic acid groups. In addition, surface nanobubbles formed by entrainment of air on SAMs of a bromoisobutyrate-terminated thiol were analyzed by AFM. Despite the widely differing surface potentials and different functionality, such as hydrogen bond acceptor or donor, and different dipole moments and polarizability, the nanoscopic contact angles (measured through the condensed phase and corrected for AFM tip broadening effects) were found to be 145 ± 10° for all surfaces. Hence, different chemical functionalities at identical macroscopic static water contact angle do not noticeably influence the apparent nanoscopic contact angle of surface nanobubbles. This universal contact angle is in agreement with recent models that rely on contact line pinning and the equilibrium of gas outflux due to the Laplace pressure and gas influx due to gas oversaturation in the aqueous medium.

Tuning the Receding Contact Angle on Hydrogels by Addition of Particles.

Control of the swelling, chemical functionalization, and adhesivity of hydrogels are finding new applications in a wide range of material systems. We investigate experimentally the effect of adsorbed particles on hydrogels on the depinning of contact lines. In our experiments, a water drop containing polystyrene microspheres is deposited on a swelling hydrogel, which leads to the drop absorption and particle deposition. Two regimes are observed: a decreasing drop height with a pinned contact line followed by a receding contact line. We show that increasing the particles concentration increases the duration of the first regime and significantly decreases the total absorption time. The adsorbed particles increase the pinning force at the contact line. Finally, we develop a method to measure the receding contact angle with the consideration of the hydrogel swelling.

Contact Angle Hysteresis on Graphene Surfaces and Hysteresis-free Behavior on Oil-infused Graphite Surfaces

Contact angle hysteresis (CAH) on graphitic surfaces, including chemical vapor deposition (CVD) graphene, reduced electrophoretic deposition (EPD) graphene, highly oriented pyrolytic graphite (HOPG), and polished graphite sheet, has been investigated. The hysteresis loops of water drops on the first three samples are similar but the receding contact angle is particularly small for the polished graphite sheet.The significant CAH observed on CVD graphene and HOPG associated with atom-scale roughness has to be attributed mainly to adhesion hysteresis (surface relaxation), instead of roughness or defects.The difference of the wetting behavior among those four graphitic samples has been further demonstrated by hexadecane drops. On the surface of HOPG or CVD graphene,the contact line expands continuously with time, indicating total wetting for which the contact angle does not exist and contact line pinning disappears. In contrast, on the surface of reduced EPD graphene, spontaneous spreading is halted by spikes on it and partial wetting with small contact angle (θ≈4°) is obtained. On the surface of polished graphite sheet, the superlipophilicity and porous structure are demonstrated by imbibition and capillary rise of hexadecane. Consequently, an oil-infused graphite surface can be fabricated and the ultralow CAH of water (∆θ≈2°) is achieved.

Acoustic Measurement of Surface Wave Damping by a Meniscus.

We investigate the reflection of gravity-capillary surface waves by a plane vertical barrier. The size of the meniscus is found to strongly affect reflection: the energy of the reflected wave with a pinned contact line is around twice the one corresponding to a fully developed meniscus. To perform these measurements, a new experimental setup similar to an acousto-optic modulator is developed and offers a simple way to measure the amplitude, frequency and direction of propagation of surface waves.

Stability of Surface Nanobubbles: A Molecular Dynamics Study.

The stability and growth or dissolution of a single surface nanobubble on a chemically patterned surface are studied by molecular dynamics simulations of binary mixtures consisting of Lennard-Jones (LJ) particles. Our simulations reveal how pinning of the three-phase contact line on the surface can lead to the stability of the surface nanobubble, provided that the concentration of the dissolved gas is oversaturated. We have performed equilibrium simulations of surface nanobubbles at different gas oversaturation levels ζ > 0. The equilibrium contact angle θe is found to follow the theoretical result of Lohse and Zhang (Phys. Rev. E 2015, 91, 031003(R)), namely, sin θe = ζL/Lc, where L is the pinned length of the footprint and Lc = 4γ/P0 is a capillary length scale, where γ is the surface tension and P0 is the ambient pressure. For undersaturation ζ < 0 the surface nanobubble dissolves and the dissolution dynamics shows a "stick-jump" behavior of the three-phase contact line.

Crown sealing and buckling instability during water entry of spheres

We present new observations from an experimental investigation of the classical problem of the crown splash and sealing phenomena observed during the impact of spheres onto quiescent liquid pools. In the experiments, a 6 m tall vacuum chamber was used to provide the required ambient conditions from atmospheric pressure down to $1/16\text{th}$ of an atmosphere, whilst high-speed videography was exploited to focus primarily on the above-surface crown formation and ensuing dynamics, paying particular attention to the moments just prior to the surface seal. In doing so, we have observed a buckling-type azimuthal instability of the crown. This instability is characterised by vertical striations along the crown, between which thin films form that are more susceptible to the air flow and thus are drawn into the closing cavity, where they atomize to form a fine spray within the cavity. To elucidate to the primary mechanisms and forces at play, we varied the sphere diameter, liquid properties and ambient pressure. Furthermore, a comparison between the entry of room-temperature spheres, where the contact line pins around the equator, and Leidenfrost spheres (i.e. an immersed superheated sphere encompassed by a vapour layer), where there is no contact line, indicates that the buckling instability appears in all crown sealing events, but is intensified by the presence of a pinned contact line.