Motion Of Three-phase Contact Line Research Articles

Electrostatic Surface Charging by Water Dewetting.

Water dewetting generates static electricity. We reviewed historical experiments of this phenomenon, and we studied the charging of polymer slides and metal electrode supported polymer films withdrawn vertically from a pool of aqueous solutions. For pure water, charging was negative and surface charge densities increased with the speed of dewetting, which we explain by the thermally activated entrainment of nanometer-sized water droplets or clusters charged by unbalanced adsorbed electric double-layer ions. Surface charge densities increased for reduced polymer film thickness following a power law, which we explain by reduced discharge of the entrained water volumes. At low salinity c ≲ 10 μM, charging was proportional to electrokinetic interfacial charge densities: the negative charging was increased for alkaline solutions and for most salts at μM concentrations and the charge polarity was inversed to positive for a cationic surfactant, a salt with a highly positively charged cation, and for a strong acid at approximately pH 4. Charging was reduced again for c ≳ 100 μM, especially at high dewetting speeds and for chaotropic ions, which we explain by the entrainment of larger and more discharged droplets. We determined adsorption energies of the charged water clusters on the dewetted surface from thermally stimulated discharge of the charged polymer slides and we show that the surface charge distribution, imaged by charged toner powders and measured microscopically by Kelvin probe force microscopy, is a record of the dewetting process that provides spatial and kinetic information about the three-phase contact line motion.

Effect of viscosity on bubble spreading on flat solid surfaces

The behavior and dynamics of bubble spreading has a great impact on interfacial contact area and time, which is significant for the heat/mass transfer or separation efficiency. In this work, the dynamical behavior of bubble spreading especially the three-phase contact line (TPL) on solid flat surfaces in low viscous liquids was investigated. The results show that the final length of TPL on homogeneous solid surfaces tend to decrease with the increasing liquid viscosity. For heterogenous solid surfaces, TPL motion on non-stick coal surface is basically the same as that on homogeneous solid surfaces, whereas that on anthracite surface shows an anomalous morphology. By applying the power-law model, the fast and slow spreading stages of bubble on homogeneous surfaces show the universal exponent of b = 1/2 and b = 1/10, respectively. While the exponent for bubble spreading on heterogeneous surface is complicated due to the special surface physico-chemical properties.

Droplet evaporation dynamics on heterogeneous surfaces: Numerical modeling of the stick-slip motion

The interplay between the solid surface properties and transport phenomena during sessile droplet evaporation is extremely important in solid deposition processes. Engineering design requires realistic modeling of evaporation dynamics, on heterogeneous surfaces, which is very challenging. In this study, a continuum level, sharp-interface, ALE (Arbitrary Lagrangian- Eulerian) numerical model is developed. The model can efficiently deal with the problem of the moving three-phase contact line (TPL) during evaporation by incorporating the solid-liquid interactions in a Derjaguin pressure (commonly called disjoining pressure) term. It is found that, depending on the surface roughness and the material wettability, the evaporation dynamics proceeds following the Constant Contact Angle (CCA), Constant Contact Radius (CCR) or a mixed mode (stick-slip behavior). Numerical predictions concerning droplets evaporating on rough, hydrophobic substrates, are experimentally validated showing exceptional agreement. The stick-slip motion is found to appear during evaporation and is particularly affected by specific roughness features of the surface. Our findings are compared to Shanahan's theory. Interesting insights into the mechanisms of the stick-slip motion are presented for a rough hydrophobic substrate with weak pinning effects.

Droplet Impact on Surfaces with Asymmetric Microscopic Features.

The impact of liquid drops on a rigid surface is central in cleaning, cooling, and coating processes in both nature and industrial applications. However, it is not clear how details of pores, roughness, and texture on the solid surface influence the initial stages of the impact dynamics. Here, we experimentally study drops impacting at low velocities onto surfaces textured with asymmetric (tilted) ridges. We found that the difference between impact velocity and the capillary speed on a solid surface is a key factor of spreading asymmetry, where the capillary speed is determined by the friction at a moving three-phase contact line. The line-friction capillary number Caf = μfV0/σ (where μf,V0, and σ are the line friction, impact velocity, and surface tension, respectively) is defined as a measure of the importance of the topology of surface textures for the dynamics of droplet impact. We show that when Caf ≪ 1, the droplet impact is asymmetric; the contact line speed in the direction against the inclination of the ridges is set by line friction, whereas in the direction with inclination, the contact line is pinned at acute corners of the ridges. When Caf ≫ 1, the geometric details of nonsmooth surfaces play little role.

A fully Eulerian hybrid immersed boundary-phase field model for contact line dynamics on complex geometries

We present a fully Eulerian hybrid immersed-boundary/phase-field model to simulate wetting and contact line motion over any arbitrary geometry. The solid wall is described with a volume-penalisation ghost-cell immersed boundary whereas the interface between the two fluids by a diffuse-interface method. The contact line motion on the complex wall is prescribed via slip velocity in the momentum equation and static/dynamic contact angle condition for the order parameter of the Cahn-Hilliard model. This combination requires accurate computations of the normal and tangential gradients of the scalar order parameter and of the components of the velocity. However, the present algorithm requires the computation of averaging weights and other geometrical variables as a preprocessing step. Several validation tests are reported in the manuscript, together with 2D simulations of a droplet spreading over a sinusoidal wall with different contact angles and slip length and a spherical droplet spreading over a sphere, showing that the proposed algorithm is capable to deal with the three-phase contact line motion over any complex wall. The Eulerian feature of the algorithm facilitates the implementation and provides a straight-forward and potentially highly scalable parallelisation. The employed parallelisation of the underlying Navier-Stokes solver can be efficiently used for the multiphase part as well. The procedure proposed here can be directly employed to impose any types of boundary conditions (Neumann, Dirichlet and mixed) for any field variable evolving over a complex geometry, modelled with an immersed-boundary approach (for instance, modelling deformable biological membranes, red blood cells, solidification, evaporation and boiling, to name a few).

Modelling of droplet impacts on dry and wet surfaces using depth-averaged form

An efficient time-adaptive multigrid algorithm is used to solve a range of normal and oblique droplet impacts on dry surfaces and liquid films using the Depth-Averaged Form (DAF) method of the governing unsteady Navier–Stokes equations. The dynamics of a moving three-phase contact line on dry surfaces is predicted by a precursor film model. The method is validated against a variety of experimental results for droplet impacts, looking at factors such as crown height and diameter, spreading diameter and splashing for a range of Weber, Reynolds and Froude numbers along with liquid film thicknesses and impact angles. It is found that, while being a computationally inexpensive methodology, the DAF method produces accurate predictions of the crown and spreading diameters as well as conditions for splash, however, underpredicts the crown height as the vertical inertia is not included in the model.

Directed motion of two-component droplets on wedge-shaped composite copper surfaces without back-end pinning

The motion of three-phase contact line of a droplet is always halted by the contact angle hysteresis on a common solid surface. In this work, the Ag/Cu surface and Cu(OH)2/Cu surface with water contact angle of 25.0° were fabricated and found favorable for two-component droplet moving. The droplet, water with propylene glycol in irregular shape could restore to a circle (top view) on these prepared surfaces. Inspired by the shape restoration, the directed motion of two-component droplet without back-end pinning was achieved on both the wedge-shaped Ag/Cu and Cu(OH)2/Cu composite surfaces. The two-component droplet moves in a way of the front-end spreading with the subsequent back-end shrinking. The needle-like Cu(OH)2 microstructure is more conducive to the front-end spreading, while the spheroidal Ag particles on Cu substrate is in favor of the back-end shrinking. In addition, the segmented Ag@Cu(OH)2/Cu wedge-shaped composite surfaces with Ag film on the narrow end of the track and Cu(OH)2 on the wide end could enhance the droplet moving. Finally, a micro-chemical reactor was designed capable of driving two dispersed droplets to move in a specific direction, converge, and then react with each other.

Bubble Attachment to Cellulose and Silica Surfaces of Varied Surface Energies: Wetting Transition and Implications in Foam Forming.

To better understand the complex system of wet foams in the presence of cellulosic fibers, we investigate bubble–surface interactions by following the effects of surface hydrophobicity and surface tension on the contact angle of captive bubbles. Bubbles are brought into contact with model silica and cellulose surfaces immersed in solutions of a foaming surfactant (sodium dodecyl sulfate) of different concentrations. It is observed that bubble attachment is controlled by surface wetting, but a significant scatter in the behavior occurs near the transition from partial to complete wetting. For chemically homogeneous silica surfaces, this transition during bubble attachment is described by the balance between the energy changes of the immersed surface and the frictional surface tension of the moving three-phase contact line. The situation is more complex with chemically heterogeneous, hydrophobic trimethylsilyl cellulose (TMSC). TMSC regeneration, which yields hydrophilic cellulose, causes a dramatic drop in the bubble contact angle. Moreover, a high interfacial tension is required to overcome the friction caused by microscopic (hydrophilic) pinning sites of the three-phase contact line during bubble attachment. A simple theoretical framework is introduced to explain our experimental observations.

Discontinuous contact line motion of evaporating particle-laden droplet on superhydrophobic surfaces.

The three-phase contact line motion on a superhydrophobic surface through particle-laden sessile droplet evaporation was investigated. Sample surfaces with micro- and nanoscale structures were generated by various durations of chemical treatment and SiO_{2} spherical particles with different sizes were used as additives of test liquid. The contact angle and contact radius profiles were studied, and the discontinuous motion of those profiles on micro- and nanostructured hierarchical surfaces was observed, while it was not observed on a nanostructured superhydrophobic surface. Suspensions with low particle concentration induced a relatively large contact radius jump compared to the high-concentrated condition; in contrast, the previous report showed the opposite trend for flat surfaces. In order to explain this result, a simple explanation was provided-that the stacked particles at the contact line region suppressed to the deformation of the liquid-vapor interface near the contact line. This is confirmed by side-view images of the deposition results because the contact line region after evaporation of the dense suspension showed a large contact angle compared to that of the diluted suspension. In addition, deposition at the contact line region was observed by scanning electron microscopy to discuss the effect of the characteristic length scale of the surface structure and particles on the contact line motion. We believe that these results will help one to understand the deposition phenomenon during particle-laden droplet evaporation on the superhydrophobic surface and its applications such as evaporation-driven materials deposition.

Dynamic Chemically Driven Dewetting, Spreading, and Self-Running of Sessile Droplets on Crystalline Silicon.

A chemically driven dewetting effect is demonstrated using sessile droplets of dilute hydrofluoric acid on chemically oxidized silicon wafers. The dewetting occurs as the thin oxide is slowly etched by the droplet and replaced by a hydrogen-terminated surface; the result of this is a gradual increase in the contact angle of the droplet with time. The time-varying work of adhesion is calculated from the time-varying contact angle; this corresponds to the changing chemical nature of the surface during dewetting and can be modeled by the well-known logistic (sigmoid) function often used for the modeling of restricted growth, in this case, the transition from an oxidized surface to a hydrogen-terminated silicon surface. The observation of the time-varying contact angle allows one to both measure the etch rate of the silicon oxide and estimate the hydrogenation rate as a function of HF concentration and wafer type. In addition to this, at a certain HF concentration, a self-running droplet effect is observed. In contrast, on hydrogen-terminated silicon wafers, a chemically induced spreading effect is observed using sessile droplets of nitric acid. The droplet spreading can also be modeled using a logistical function, where the restricted growth is the transition from hydrogen-terminated to a chemically induced oxidized silicon surface. The chemically driven dewetting and spreading observed here add to the methods available to study dynamic wetting (e.g., the moving three-phase contact line) of sessile droplets on surfaces. By slowing down chemical kinetics of the wetting, one is able to record the changing profile of the sessile droplet with time and gather information concerning the time-varying surface chemistry. The data also indicates a chemical interface hysteresis (CIH) that is compared to contact angle hysteresis (CAH). The approach can also be used to study the chemical etching and deposition behavior of thin films using liquids by monitoring the macroscopic droplet profile and relating this to the time-varying physical and chemical interface phenomena.

Mechanisms of single bubble cleaning

The dynamics of collapsing bubbles close to a flat solid is investigated with respect to its potential for removal of surface attached particles. Individual bubbles are created by nanosecond Nd:YAG laser pulses focused into water close to glass plates contaminated with melamine resin micro-particles. The bubble dynamics is analysed by means of synchronous high-speed recordings. Due to the close solid boundary, the bubble collapses with the well-known liquid jet phenomenon. Subsequent microscopic inspection of the substrates reveals circular areas clean of particles after a single bubble generation and collapse event. The detailed bubble dynamics, as well as the cleaned area size, is characterised by the non-dimensional bubble stand-off γ=d/Rmax, with d: laser focus distance to the solid boundary, and Rmax: maximum bubble radius before collapse. We observe a maximum of clean area at γ≈0.7, a roughly linear decay of the cleaned circle radius for increasing γ, and no cleaning for γ>3.5. As the main mechanism for particle removal, rapid flows at the boundary are identified. Three different cleaning regimes are discussed in relation to γ:(I) For large stand-off, 1.8<γ<3.5, bubble collapse induced vortex flows touch down onto the substrate and remove particles without significant contact of the gas phase.(II) For small distances, γ<1.1, the bubble is in direct contact with the solid. Fast liquid flows at the substrate are driven by the jet impact with its subsequent radial spreading, and by the liquid following the motion of the collapsing and rebounding bubble wall. Both flows remove particles. Their relative timing, which depends sensitively on the exact γ, appears to determine the extension of the area with forces large enough to cause particle detachment.(III) At intermediate stand-off, 1.1<γ<1.8, only the second bubble collapse touches the substrate, but acts with cleaning mechanisms similar to an effective small γ collapse: particles are removed by the jet flow and the flow induced by the bubble wall oscillation.Furthermore, the observations reveal that the extent of direct bubble gas phase contact to the solid is partially smaller than the cleaned area, and it is concluded that three-phase contact line motion is not a major cause of particle removal.Finally, we find a relation of cleaning area vs. stand-off γ that deviates from literature data on surface erosion. This indicates that different effects are responsible for particle removal and for substrate damage. It is suggested that a trade-off of cleaning potential and damage risk for sensible surfaces might be achieved by optimising γ.

Influence of the governing dimensionless parameters on heat transfer during single drop impingement onto a hot wall

The cooling effectiveness of spray cooling is strongly influenced by droplet size and velocity as well as by the fluid properties. To enhance the understanding of the entire process, first of all basic processes occurring in the spray have to be addressed. Therefore, in this study the heat transfer during a single drop impingement onto a dry, superheated wall is investigated numerically, and the effects of the dominating dimensionless parameters on the convective and evaporative heat transfer are analyzed. In order to be able to distinguish between the influences of the individual dimensionless groups, each parameter is varied individually. The study is performed using fluid properties of the refrigerant FC-72. The droplet is surrounded by a saturated vapor atmosphere. The numerical model accounts for the complex two-phase flow, the transient conductive heat transfer within the solid domain and the evaporative mass transfer. Special attention is paid to the local heat and mass transfer close to the moving three-phase contact line. The spreading phase appears to be dominated by the Reynolds number, while in the receding phase the Weber number has the strongest influence on heat transfer. For the evaporation of a sessile droplet, which is the final stage of the impact process, the heat transfer is governed by the Bond number.

Contact Line Motion on Nanorough Surfaces: A Thermally Activated Process

The motion of a solid-liquid-liquid contact line over nanorough surfaces is investigated. The surface nanodefects are varied in size, density, and shape. The dynamics of the three-phase contact line on all nanorough substrates studied is thermally activated. However, unlike the motion of a liquid-vapor interface over smooth surfaces, this thermally activated process is not adequately described by the molecular kinetic theory. The molecular parameters extracted from the experiments suggest that on the nanorough surfaces, the motion of the contact line is unlikely to simply consist of molecular adsorption-desorption steps. Thermally activated pinning-depinning events on the surface nanodefects are also important. We investigate the effect of surface nanotopography on the relative importance of these two mechanisms in governing contact line motion. Using a derivation for the hysteresis energy based on Joanny and de Gennes's model, we evaluate the effect of nanotopographical features on the wetting activation free energy and contact line friction. Our results suggest that both solid-liquid interactions and surface pinning strength contribute to the energy barriers hindering the three-phase contact line motion. For relatively low nanodefect densities, the activation free energy of wetting can be expressed as a sum of surface wettability and surface topography contributions, thus providing a direct link between contact line dynamics and roughness parameters.

Local heat transfer and phase change phenomena during single drop impingement on a hot surface

Heat and mass transfer at a droplet impinging on a hot wall is investigated experimentally and numerically. The experiments are conducted with refrigerant FC-72 within a saturated vapour atmosphere. The droplet dynamics and the heater temperature very close to the solid–fluid interface are captured with high spatial and temporal resolution. The boundary conditions for the numerical simulations are chosen according to the experiments. The simulation accounts for the complex two-phase flow including evaporative mass transfer. Special attention is given to the local heat and mass transfer close to the moving three-phase contact line. Numerical and experimental results are compared to give insight into the basic heat transport mechanisms occurring during drop impact and to quantify their relevance for the overall heat transfer. It turns out that convective heat transfer is dominant during the initial stage of the impact corresponding to the droplet spreading, while at the final stage of the impact, corresponding to evaporation of a sessile droplet, a considerable part of the total heat transfer occurs in the direct vicinity of the three-phase contact line.

Molecular dynamics studies on spreading of nanofluids promoted by nanoparticle adsorption on solid surface

Spreading of nanofluids on solid substrate was studied via molecular dynamics simulations. Simulation models for two immiscible fluids (oil and water based nanofluids) confined in a slit between two planar solid walls were set up. The influence of the volume concentration of the nanoparticles on the three-phase contact line motion was investigated. We found that the larger volume concentration results in more visible nanoparticle adsorption on solid surface. This effect further induces an advancing displacement of the contact line compared with the meniscus profiles in low concentration case and that with the absence of nanoparticles. These findings are consistent with the previous experimental and theoretical results and provide the atomic-scale understanding on nanofluid spreading.

A variational approach to a differential equation modeling thin-film flows and pertinent to Tanner's Law

This study is intended to provide a modified variational algorithm for the numerical solution of the third-order ordinary differential equation y″′ = y−2 which arises in the modeling of thin viscous films with surface tension. The resulting solution is used to solve a problem relevant to Tanner's Law for the speed of a moving three-phase contact line. Numerical results, computational comparisons, suitable error measures and illustrations are provided to testify and demonstrate the convergence and efficiency of the method.

Local heating at convection fronts and moving contact lines on hygroscopic fluids

A temperature rise on the order of tenths of a degree is observed as one fluid spreads over a hygroscopic fluid. While this behavior is only exhibited with hygroscopic fluids, it is independent of the properties of the spreading fluid. The spreading induces a ‘rolling’ motion in the subphase which brings ‘fresh’ fluid to the surface, exposing it to the water vapor in the air. As water is absorbed into the hygroscopic liquid, heat is released. The same behavior is observed whether the spreading fluid has a spreading monolayer that drives a convection front or is a spreading lens with a moving three-phase contact line.

Spreading of Aqueous Solutions of Trisiloxanes and Conventional Surfactants over PTFE AF Coated Silicone Wafers

Kinetics of spreading of aqueous trisiloxane surfactant T(n) (with n = 4, 6, and 8 ethoxy groups) solutions and conventional aqueous surfactant solutions (Tween 20, C12E4, SDS) over silicon wafers coated with PTFE AF is experimentally investigated. It has been found that trisiloxane solutions spread on highly hydrophobic PTFE AF coated silicone wafers; however, they do not show superspreading behavior on these highly hydrophobic substrates. Solutions of conventional nonionic surfactants investigated show kinetics of spreading similar to trisiloxanes. Three regimes of spreading have been identified (i) complete non-wetting during the spreading process at low concentrations, (ii) a transition from initial nonwetting to partial wetting at the end of the spreading process at intermediate concentrations, and (iii) partial wetting both at the beginning and the end of the spreading process at higher concentrations. Transition from the first regime (i) to the second regime (ii) takes place at the critical aggregation concentration (CAC) or critical micelle concentration (CMC), transition from regime (ii) to regime (iii) happens at the critical wetting concentration (CWC). In the case of regime (i) the spreading of nonionic surfactants solutions investigated on PTFE AF coated silicone wafers is slow and follows a theoretically predicted law (Starov; et al. J. Colloid Interface Sci. 2000, 227 (1), 185). In the case of regimes (ii) and (iii), the spreading of the nonionic surfactant solutions investigated proceeds in two stages: the fast short first stage, which is followed by a much slower second stage. It is shown that the slow stage develops according to a previously described theoretical model. According to this theory the surfactant molecules adsorb in front of the moving three-phase contact line (autophilic phenomenon), which results in a partial hydrophilisation of an initially hydrophobic substrate and a spreading as a consequence. We assume that the first stage of the spreading is related to the disintegration of surfactant aggregates in the vicinity of the moving three-phase contact line.

Flows with quasi-equilibrium free boundaries in the dynamics of wetting of solids

Slow flows of a viscous fluid with free boundary over the solid surface when there is the moving three-phase contact line are considered. The second-order asymptotic theory, which describes the regularities of free boundary variations under the action of capillary forces, is developed.

Back Extraction of an Acid in a Two-Layer System with a Moving Three-Phase Contact Line

Back Extraction of an Acid in a Two-Layer System with a Moving Three-Phase Contact Line