Contact Line Pinning Research Articles

Complex evaporation kinetics of a volatile droplet of methanol

An experimental study is carried out to investigate the different stages of the evaporation phenomenon of a methanol drop that exhibits a complex behavior because of its high volatility. An optical technique is employed with top and side view cameras; it allows to follow the drop shape evolution and determine the geometric parameters: contact angle and base diameter from which the volume of the droplet is computed. The outcomes of this study show three distinct stages. First, the evaporation kinetics is very fast (33% of the droplet lifetime) where 85% of the volume evaporates with a nearly pinned contact line. It is followed by a short stage (12% of lifetime) where 8% of the volume evaporates. In this stage, the drop forms a thin liquid film followed by a motion of the contact line in which the drop retracts. The wetting surface deforms and loses its quasi-circular shape. Then, the wetting area shrinks drastically to form a smaller droplet with a higher contact angle. In the third stage (55% of lifetime), the 7% remaining drop volume evaporates with a low evaporation rate accompanied by a strong decrease of contact angle and a slight decline of wetting area until total evaporation.

Weak-anchoring effects in a thin pinned ridge of nematic liquid crystal.

A theoretical investigation of weak-anchoring effects in a thin two-dimensional pinned static ridge of nematic liquid crystal resting on a flat solid substrate in an atmosphere of passive gas is performed. Specifically, we solve a reduced version of the general system of governing equationsrecently derived by Cousins etal. [Proc. R. Soc. A 478, 20210849 (2022)10.1098/rspa.2021.0849] valid for a symmetric thin ridge under the one-constant approximation of the Frank-Oseen bulk elastic energy with pinned contact lines to determine the shape of the ridge and the behavior of the director within it. Numerical investigations covering a wide range of parameter values indicate that the energetically preferred solutions can be classified in terms of the Jenkins-Barratt-Barbero-Barberi critical thickness into five qualitatively different types of solution. In particular, the theoretical results suggest that anchoring breaking occurs close to the contact lines. The theoretical predictions are supported by the results of physical experiments for a ridge of the nematic 4^{'}-pentyl-4-biphenylcarbonitrile (5CB). In particular, these experiments show that the homeotropic anchoring at the gas-nematic interface is broken close to the contact lines by the stronger rubbed planar anchoring at the nematic-substrate interface. A comparison between the experimental values of and the theoretical predictions for the effective refractive index of the ridge gives a first estimate of the anchoring strength of an interface between air and 5CB to be (9.80±1.12)×10^{-6}Nm^{-1} at a temperature of (22±1.5)^{∘}C.

CONTACT ANGLE HYSTERESIS ON SOLID CRYSTALLINE SURFACES

The article presents the results of experimental studying the hysteresis of water contact angles at crystalline surfaces. Receding and advancing contact angles and their hysteresis at hydrophilic and hydrophobic substrates with different surface structures (silica, mica, and calcite) have been studied under the action of an external pressure applied to the three-phase contact line of a sessile air bubble. Hysteresis of the contact angles has been observed on hydrophobized samples of silica and mica. The anchoring of the three-phase contact line (pinning) facilitates a change in the contact angles under the applied external pressure. When the three-phase contact line moves along the hydrophilic surfaces of silica and mica no marked changes in the advancing and receding contact angles are observed, and the hysteresis is actually absent. The stable pinning observed on the polished surface of a calcite crystal brought in contact with water leads to the appearance of contact angle hysteresis and hydrophilization of the calcite surface, with the hydrophilization being related to structural displacements in the crystal lattice.

Coffee stain effect on a fibre from axisymmetric droplets

The so-called coffee stain effect has been intensively studied over the past decades, but most of the studies have focused on sessile droplets. In this paper, we analyse the origin of the difference between the deposition of suspended particles in a sessile drop and in an axisymmetric drop deposited on a fibre. First, we model the shape of a drop on a fibre and its evaporative flux with some approximations to derive analytical calculations. Then, for pinned contact lines, we solve the hydrodynamics equations in the liquid phase under the lubrication approximation to determine the flow velocity toward the contact lines. We comment on these results by comparison to a sessile drop of similar evaporating conditions, and we show that the substrate curvature plays a role on the contact line depinning, the local evaporative flux and the liquid flow field. The competition between the advection and the Brownian motion indicates that the transport of the particles toward the contact line occurs in a volume localised in the close vicinity of the contact lines for a drop on a fibre. Thus, the fibre geometry induces a weaker accumulation of particles at the contact line compared to a sessile drop, leading to the more homogeneous deposit observed experimentally.

Energy Loss for Droplets Bouncing Off Superhydrophobic Surfaces.

A water droplet can bounce off superhydrophobic surfaces multiple times before coming to a stop. The energy loss for such droplet rebounds can be quantified by the ratio of the rebound speed UR and the initial impact speed UI; i.e., its restitution coefficient e = UR/UI. Despite much work in this area, a mechanistic explanation for the energy loss for rebounding droplets is still lacking. Here, we measured e for submillimeter- and millimeter-sized droplets impacting two different superhydrophobic surfaces over a wide range of UI (4-700 cm s-1). We proposed simple scaling laws to explain the observed nonmonotonic dependence of e on UI. In the limit of low UI, energy loss is dominated by contact-line pinning and e is sensitive to the surface wetting properties, in particular to contact angle hysteresis Δ cos θ of the surface. In contrast, e is dominated by inertial-capillary effects and does not depend on Δ cos θ in the limit of high UI.

An Isoperimetric Sloshing Problem in a Shallow Container with Surface Tension

In 1965, B. A. Troesch solved the isoperimetric sloshing problem of determining the container shape that maximizes the fundamental sloshing frequency among two classes of shallow containers: symmetric canals with a given free surface width and cross-sectional area, and radially symmetric containers with a given rim radius and volume (Commun Pure Appl Math 18(1–2):319–338, 1965, https://doi.org/10.1002/cpa.3160180124 ). Here, we extend these results in two ways: (i) we consider surface tension effects on the fluid free surface, assuming a flat equilibrium free surface together with a pinned contact line, and (ii) we consider sinusoidal waves traveling along the canal with wavenumber $$\alpha \ge 0$$ and spatial period $$2\pi /\alpha $$ ; two-dimensional sloshing corresponds to the case $$\alpha = 0$$ . Generalizing our recent variational characterization of fluid sloshing with surface tension to the case of a pinned contact line, we derive the pinned-edge linear shallow sloshing problem, which is an eigenvalue problem for a generalized Sturm-Liouville system. In the case without surface tension, we show that the optimal shallow canal is a rectangular canal for any $$\alpha > 0$$ . In the presence of surface tension, we solve for the maximizing cross-section explicitly for shallow canals with any given $$\alpha \ge 0$$ and shallow radially symmetric containers with m azimuthal nodal lines, $$m = 0, 1$$ . Our results reveal that the squared maximal sloshing frequency increases considerably as surface tension increases. Interestingly, both the optimal shallow canal for $$\alpha = 0$$ and the optimal shallow radially symmetric container are not convex. As a consequence of our explicit solutions, we establish convergence of the maximizing cross-sections, as surface tension vanishes, to the maximizing cross-sections without surface tension.

A three-dimensional numerical scheme for modeling discontinuous pinning at sharp edges using the Volume-of-Fluid method

We present a novel three-dimensional (3D) numerical scheme for modeling the discontinuous contact line pinning along sharp straight edges. The proposed scheme is devised for multi-phase flow solvers that rely on the Volume-of-Fluid (VOF) method, although its fundamental concepts can be extended and applied to other methods. Following the Piecewise-Linear-Interface-Construction (PLIC) approach in VOF, the discontinuous pinning is modeled by adjusting the orientation of PLIC polygons located near a sharp edge according to the pinning stage. That is achieved by solving a root-finding problem and using a 3D geometrical toolbox, where the advancing contact angle determines critical volume fractions in numerical cells neighboring the sharp edge. Implementing the proposed scheme in our multi-phase flow solver, we assessed its performance using several test cases where contact line pinning effects dominate. To demonstrate the scheme's efficacy, we present quantitative comparisons of our results at various grid resolutions and with a theoretical study. Furthermore, we show quantitatively that without a numerical treatment of contact line pinning, the simulation results will be drastically different. Contact line pinning plays a critical role in several technologies including separation, lithography, lens fabrication, micro-fluidic flow control among numerous others. The proposed scheme will help to accurately capture the pinning effects in computational simulations of such applications.

Surface tension gradient driven autonomous fatty acid-tetrahydrofuran liquid moving drops: Spreading to pinning

In this work, we have studied the drop dynamics of binary tetrahydrofuran (THF) solutions containing fatty acids (stearic acid and myristic acid) or surfactants (N-Cetyl-N, N, N trimethyl ammonium bromide, and sodium dodecyl sulfate). Highly volatile non-aqueous pure THF drop shows dynamic wetting behaviour i.e., droplet expansion and contraction behaviour·THF spreads continuously on fabricated total wetting surface without pinning, however addition of fatty acids causes formation of drops (instead of thin films). Such drops show autonomous motility which can be tuned by maintaining the concentration of fatty acids. The addition of fatty acids provides evaporation driven surface tension gradient (Marangoni stress) which initialize the autonomous drop motion and reduces the innate contact line pinning. It is found that addition of fatty acids showed drop dynamics which was concentration dependent. At low concentrations drop moves, while contact line pinning and subsequent evaporation was noticed at higher concentrations. The study of drop area with respect to time conveyed about the slowdown of evaporation timing of THF. This work proclaims the novel combination of highly evaporating THF with solutes (fatty acids/surfactants) showing its potential applications in self-propelled motion of non-aqueous drops.

Thermal capillary waves on bounded nanoscale thin films.

The effect of confining walls on the fluctuation of a nanoscale thin film's free surface is studied using stochastic thin-film equations(STFEs). Two canonical boundary conditions are employed to reveal the influence of the confinement: (1) an imposed contact angle and (2) a pinned contact line. A linear stability analysis provides the wave eigenmodes, after which thermal-capillary-wave theory predicts the wave fluctuation amplitudes. Molecular dynamics (MD) simulations are performed to test the predictions, and a Langevin diffusion model is proposed to capture oscillations of the contact lines observed in MD simulations. Good agreement between the theoretical predictions and the MD simulation results is recovered, and it is discovered that confinement can influence the entire film. Notably, a constraint on the length scale of wave modes is found to affect fluctuation amplitudes from our theoretical model, especially for 3D films. This opens up challenges and future lines of inquiry.

Capillary detachment of a microparticle from a liquid-liquid interface.

The attachment and detachment of microparticles at a liquid-liquid interface are common in many material systems, from Pickering emulsions and colloidal assemblies to capillary suspensions. Properties of these systems rely on how the particles interact with the liquid-liquid interface, including the detachment process. In this study, we simultaneously measure the capillary detachment force of a microparticle from a liquid-liquid interface and visualize the shape of the meniscus by combining colloidal probe microscopy and confocal microscopy. The capillary behavior is studied on both untreated (hydrophilic) and fluorinated (hydrophobic) glass microparticles. The measured force data show good agreement with theoretical calculations based on the extracted geometric parameters from confocal images of the capillary bridge. It is also evident that contact line pinning is an important aspect of detachment for both untreated and fluorinated particles.

Scalloped pattern deposition during the spreading and drying of polymer droplets.

Droplets containing polyvinylpyrrolidone (PVP) dissolved in ethanol display a distinctive scalloped pattern at the rim while spreading and drying on a high-energy surface. Two distinct spreading regimes are observed, leading to the formation of a thin film with a uniform height that extends from the original droplet. An experimental study indicates polymer accumulation at the edge containing trace water, resulting in a surface tension gradient across the droplet, enhancing the droplet's spreading. This fast-spreading film develops a ridge at the contact line and becomes unstable. The influence of evaporation within the droplet shows no significant effect on the wavelength of the instability. Instead, the magnitude of the surface tension gradient and the surface energy of the substrate emerge as the dominant factors influencing the instability. This observation is validated by saturating the environment surrounding the droplet with ethanol vapour to reduce evaporation or employing solvents with low vapour pressure. Additionally, PVP in ethanol droplets deposited on hydrophobic substrates demonstrate a stable and pinned contact line, contrasting the behaviour observed on high-energy surfaces. By identifying the critical overlap concentration of the polymer, the transitional threshold between the scalloped instability and ringlike morphology is determined. The scalloped instability can be suppressed by removing residual water from the solution, eliminating the surface tension gradient, indicating that Marangoni forces are the underlying cause of the observed instability. The long-wave evolution equation, assuming a constant Marangoni shear flow, accurately predicts the most unstable wavelength, demonstrating good agreement with experimental observations.

Light-manipulated binary droplet transport on a high-energy surface.

Flexible and precise manipulation of droplet transport is of significance for scientific and engineering applications, but real-time and on-demand droplet manipulation remains a challenge. Herein, we report a strategy using light for the outstanding manipulation of binary droplet motion on a high-energy surface and reveal the underlying mechanism. Upon irradiation to a substrate by a focused light beam, the substrate can provide a localized heating source via photothermal conversion, and a binary droplet can be flexibly transported on a high-energy surface with free contact-line pinning, exhibiting light-propelled droplet transport. We theoretically showed that the surface tension gradient across the droplet interface resulting from the localized photothermal effect is responsible for actuating droplet transport. Remarkably, the high reconfigurability and flexibility of light allowed for binary droplet transport with dynamically tunable velocity and direction as well as arbitrary trajectory assisted by 2D channels on a high-energy surface. Complex droplet transportation, controllable droplet coalescence, and anti-gravity motion were realized. The promising applicability of this light-fueled droplet platform was also demonstrated by directional transport of biosample droplets containing DNA molecules and cells, as well as successional microreactions.

Influence of Surface Roughness on Droplet Evaporation and Absorption: Insights into Experiments from Lubrication-Theory-Based Models

While solid substrates are often idealized as being perfectly smooth, all real surfaces possess some level of topographical and chemical heterogeneity. This heterogeneity can greatly influence droplet dynamics. Mathematical models based on lubrication theory that account for surface roughness reveal how topographical defects induce contact-line pinning and affect the deposition patterns of colloidal particles suspended in the droplet. Contact-line pinning profoundly changes the behavior of droplet evaporation on horizontal and inclined impermeable substrates and droplet absorption on horizontal permeable substrates. Models accounting for surface roughness yield predictions that are qualitatively consistent with experimental observations and also provide insight into the underlying physical mechanisms. These models are a foundation for the exploration of a rich array of problems concerning droplet dynamics which are of both fundamental and practical interest.

Effect of Nanoparticle Addition on Evaporation of Jet Fuel Liquid Films and Nanoparticle Deposition Patterns during Evaporation.

Jet fuel-based nanofluid fuel has been proposed for improving the energy density and utilization efficiency of jet fuel that is widely applied in aircraft powered by aviation turbine engines. To recognize the evaporation behavior of the formed liquid film as a jet fuel-based nanofluid sprayed onto the engine wall or blades, this paper presents the evaporation and deposition characteristics of the jet fuel-based nanofluid liquid film adhering on the hydrophilic substrate. The changes in contact line, contact angle, volume, and deposition pattern during liquid film evaporation under different substrate temperatures, different nanoparticle concentrations, and different kinds of nanoparticle additions were investigated. The effect of nano-Al addition on the evaporation kinetics and deposition pattern of the nano-Al/jet fuel (nAl/JF) nanofluid fuel liquid film was explored. Repeated pinning and de-pinning of contact lines during evaporation occurred, resulting in the formation of concentric multi-ring deposition patterns. The addition of nano-Al increased the evaporation rate and shortened the evaporation lifetime, demonstrating a promotion effect on jet fuel liquid film evaporation. The existence of an energy barrier shows that the movement of three-phase contact lines on the hydrophilic solid surface presented not a continuous sliding behavior but a "stick-slip" behavior, and there were multiple jumps in contact lines and contact angles. Finally, a comparison was made with the deposition pattern of jet fuel liquid films with different graphite and Fe nanoparticle additions during evaporation. The mechanism of deposition phenomena was deeply revealed by the analysis of capillary flow and Marangoni recirculation.

Counter-Intuitive Evaporation in Nanofluids Droplets due to Stick-Slip Nature.

We experimentally investigate the evaporation characteristics of a sessile ethanol droplet containing Al2O3 and Cu nanoparticles of sizes 25 and 75 nm on a heated substrate using shadowgraphy and infrared imaging techniques. Our results demonstrate that the droplet contact line dynamics resulting from the presence of various nanoparticles plays a dominant role in the evaporation process. This is in contrast to the widely held assumption that the enhanced evaporation rate observed in sessile nanofluid droplets is due to the higher thermal conductivity of the added nanoparticles. We observe that even though the thermal conductivity of Al2O3 is an order of magnitude lower than that of Cu, droplets containing 25-nm-sized Al2O3 exhibit pinned contact line dynamics and evaporate much more rapidly than droplets containing Cu nanoparticles of both sizes and 75 nm Al2O3 nanoparticles that exhibit stick-slip behavior. We also found that the droplets with different nanoparticles display distinct thermal patterns due to the difference in contact line behavior, which alters the heat transfer inside the droplets. We establish this counter-intuitive observation by analyzing the temporal variations of the perimeter, free surface area, and deposition patterns on the substrate.

Unified inviscid dispersion relation and Ohnesorge number effect on the rivulet instability

Effects of the Ohnesorge (Oh) number and contact angle on the instability of a sessile rivulet are theoretically studied in this paper for both the pinned contact line (PCL) and moving contact line with invariant contact angle (MCL) conditions. Inviscid dispersion relations of unstable modes for rivulets with different static contact angles are shown to be transformed analytically into a unified form for both PCL and MCL conditions, reflecting the same intrinsic instability mechanism. The growth rate becomes lower at higher Oh due to the stabilization effect of viscosity. It is found for both PCL and MCL conditions that the deviation of the maximum growth rate from its inviscid counterpart varies as Oh1/2 when Oh is so small that the viscous effect mainly exists in a thin layer near the wall. For the MCL condition, the maximum growth rate of the unstable mode decreases and increases monotonically with the augment of the static contact angle at low and high Oh, respectively, while at moderate Ohnesorge numbers, increasing the static contact angle will first enlarge and then decrease the maximum growth rate for cases with hydrophilic bottom walls.

Pinning and depinning in imbibition beyond a sharp edge: A lattice Boltzmann study

The phenomenon of capillary rise or imbibition is governed by the inertia, the capillary force, the gravitational force and viscous force of fluids. Besides, the geometry also plays an important role on the imbibition dynamics since the motion of contact line could be affected by the sharp transition of geometry, and the oscillation of meniscus could be observed due to the confinement of contact line. The imbibition is a multiphase flow problem, which involves the movement of contact line and differences of fluid density and viscosity. In this paper, an axisymmetric lattice Boltzmann (LB) model based on the phase-field theory is proposed for investigating the oscillation phenomenon in the imbibition process. We also introduce a dimensionless Weber number to further analyze the pinning and depinning of contact line at the edge of capillary tube, and consider the effects of tube length and contact angle. The process of liquid spreading onto the top surface of capillary tube is presented, and several distinct phenomena are observed: depinning up and depinning down, pinning up and depinning down, pinning up and pinning down, pinning below the top edge. These transitions among different phenomena are dependent on the Weber number, which indicates the relative importance of inertial force compared to the surface tension force.

Imbibition dynamics and steady flows in graphene nanochannels with sparse geometric and chemical defects

Geometric and chemical defects are frequently found or created on smooth graphene for applications of nanofluidics. In this work, imbibition dynamics and steady flows of water in graphene nanochannels with sparse defects are explored by molecular dynamics. The water contact angle is raised slightly by geometric defects (hole and protrusion) but lowered significantly by chemical defects (hydroxyl and epoxide groups). In steady flows, the mean velocity and slip length are always reduced by sparse defects and the effect of chemical defects is more significant than that of geometric defects. Moreover, it is interesting to find that the velocity profile is plug-like for geometric defects but becomes parabolic for chemical defects, regardless of the slip length. Sparse defects on graphene nanoslits also affect the imbibition dynamics remarkably, which generally follows Washburn's equation with the slip length. For chemical defects, surface friction (slip length) dominates over the driving force associated with surface wettability (contact angle). Nonetheless, for protrusion defects, the stick-slip behavior caused by contact line pinning and thermal fluctuations can be observed. Our new and novel findings indicate that the defect nature is crucial in nanoscale flows and imbibition processes, which the conventional hydrodynamic theory fails to depict.

Evaporation‐driven octagonal particle deposition on the patterned substrate

AbstractUnderstanding noncircular deposition patterns can offer broad applications; however, the phenomena have not been thoroughly studied. We experimentally investigate particle self‐assembly of microspherical polystyrene particle‐laden sessile droplets dried on a micropyramid cavity substrate. The particle sizes and concentrations in the droplets are found to modify the inner particle deposition with the octagonal perimeter. The droplets with mass concentrations of 0.5% and higher evaporate with the pinned contact lines. The capillary flow flushes the 3 µm particles to the contact line and creates octagonal outer‐ring patterns. The 10 µm particles are more evenly distributed in the depositions of the dried droplets. However, at a high mass concentration of 2.6%, the particles adsorbed at the droplet liquid–air interface form an agglomerate and deposit toward the centerline, leading to the crater‐shaped pattern. Higher concentrations provoke the thicker octagonal outer‐ring depositions regardless of the particle sizes in the droplets. The findings could inspire applications to control noncircular wetting and drying of particle‐laden sessile droplets.

Solvent engineering in inkjet-printed perovskite solar cells

Inkjet printing is a sterling technique in the fabrication of large-scale perovskite solar cells (PSCs). Whereas, to obtain high quality perovskite films remains challenging because of the control of the drying of droplets. In this work, FAI is totally dissolved in n-Butanol and isopropanol (IPA) to react with PbI2/CsBr films. The addition of n-Butanol prolongs the drying time and inhibits the contact line pinning. Accordingly, the inkjet-printed CsxFA1-xPb(IyBr1-y)3 perovskite films show great uniformity with large grain size. We ultimately achieve a champion device with a power conversion efficiency (PCE) of 18.26 % (0.15 cm2).