Liquid Solid Contact Line Research Articles

The fluid mechanics of spray cleaning: when the stress amplification at the contact lines of impacting droplets nano-scraps particles

In spray cleaning, a multitude of small drops, violently accelerated by a high-speed gas stream, strike a dirty surface. This process is extremely effective: very little dirt can resist it. This is true even for dirt particles whose characteristic size is less than 100 nm. Spray cleaning is classically modelled by balancing particle adhesion with either inertial stress or viscous shear near the surface, the latter being calculated using droplet size and velocity as the characteristic length and velocity. This results in dimensionless numbers that are often well below one, suggesting that the mechanical stress exerted on the surface by the drop impact that detaches the particle is not well captured. Using quantitative nanoscale measurements, we show that the remarkable efficiency of spray cleaning results from the forced spreading of each droplet on the surface, which generates an unsteady and inhomogeneous shear confined to a boundary layer entrained in the wake of the liquid–solid contact line. In the very first moments of impact, the boundary layer is extremely thin, yielding a gigantic stress: the contact line of the spreading droplets sweeps all the surface particles away. We propose a quantitative model of spray cleaning based on this unsteady surface stress, which agrees well with (i) experimental data obtained with spray droplets of $34\ \mathrm {\mu }$ m mean radius impacting the surface to be cleaned at a mean velocity ranging between 30 and 70 m s $^{-1}$ and contamination by nanoparticles of varying nature and shape and (ii) data in the literature on spray cleaning.

Pore-scale study of droplet settling on a heterogenous surface structure

Equilibrium contact angle of a droplet is influenced by surface characteristics and fluid properties. In addition to increasing the solid–liquid contact line, surface roughness also alters the surface free energy, which has a significant influence on contact angle values. Droplets are more likely to impinge on vertices as surface roughness increases. Anisotropic wetting of chemically heterogeneous surfaces further controls the total surface free energy. The free energy Lattice Boltzmann method is utilized to study the effects of wettability heterogeneity and roughened surfaces. Initial model comparisons with experiments showed excellent agreement. The rough surface is modeled with different pillar shapes on a smooth wall, with surface wettability ranging from hydrophilic to neutral conditions. The length scale of surface patterns matches the droplet size, making the Cassie–Baxter and Wenzel equations inapplicable. Results indicate that droplets pin on the vertices of rectangular pillars, while frustum shapes facilitate movement. Studies cover nearly neutral wet, moderately wet, and strongly wet conditions. The effects of relative surface roughness, roughness distribution, mixed wetting surfaces, and body force on equilibrium contact angle are examined. Additionally, the interaction between fluid flow and surface roughness elements shows that smaller spacing and greater height of roughness elements enhance thermal performance, with Nusselt numbers fluctuating significantly. Findings suggest that the ratio of droplet size to pillar surface area is crucial for minimizing surface free energy. On superhydrophilic surfaces, droplet pinning at pillar edges causes the surface to behave hydrophobically. In mixed-wet rough surfaces, pillar wettability significantly influences the equilibrium contact angle.

Designing Plastrons for Underwater Bubble Capture: From Model Microstructures to Stochastic Nanostructures.

Bubbles and foams are often removed via chemical defoamers and/or mechanical agitation. Designing surfaces that promote chemical-free and energy-passive bubble capture is desirable for numerous industrial processes, including mineral flotation, wastewater treatment, and electrolysis. When immersed, super-liquid-repellent surfaces form plastrons, which are textured solid topographies with interconnected gas domains. Plastrons exhibit the remarkable ability of capturing bubbles through coalescence. However, the two-step mechanics of plastron-induced bubble coalescence, namely, rupture (initiation and location) and subsequent absorption (propagation and drainage) are not well understood. Here, the influence of 1) topographical feature size and 2) gas fraction on bubble capture dynamics is investigated. Smaller feature sizes accelerate rupture while larger gas fractions markedly improve absorption. Rupture is initiated solely on solid domains and is more probable near the edges of solid features. Yet, rupture time becomes longer as solid fraction increases. This counterintuitive behavior represents unexpected complexities. Upon rupture, the bubble's moving liquid-solid contact line influences its absorption rate and equilibrium state. These findings show the importance of rationally minimizing surface feature sizes and contact line interactions for rapid bubble rupture and absorption. This work provides key design principles for plastron-induced bubble coalescence, inspiring future development of industrially-relevant surfaces for underwater bubble capture.

Wetting and spreading of AgCuTi on Fe substrate at high temperatures: A molecular dynamics study

In this study, the wetting and spreading behavior of AgCuTi ternary alloys on Fe substrate was investigate using a molecular dynamics (MD) modeling method. Modeling indicates that precursor films consisted of single-layer atoms are formed and that the wetting and spreading morphologies of the molten droplets on various crystal surfaces are distinct. Diffusive processes play a key role in the formation of the precursor film, and the droplet spreading morphology is correlated critically with the atomic arrangement of the substrate. The droplet spreading process can be divided into two stages of rapid and slow spreading, and there is an obvious interdiffusion phenomenon close to the solid-liquid contact line. The rate at which droplets spread quickens as the temperature rises. Furthermore, the spreading and diffusion capacities of various elements vary, and these properties are closely related to their chemical reactivity.

Fabrication of biomimetic anisotropic crescent-shaped microstructured surfaces by laser shock imprinting

Abstract The crescent-shaped microstructure bionic to the slip zone of the slippery zone of the carnivorous plant genus Nepenthes was fabricated on the surface of copper foil by laser shock imprinting (LSI). The microstructure of crescent-shaped grooves was initially fabricated on the surface of the micro-mold by etching, and then the microstructure was replicated on the surface of copper foil through plastic deformation under laser shock loading. Increasing the laser shock energy or the number of shocks can increase the degree of replication of the crescent-shaped microstructure, the height of the crescent-shaped microstructure, and the contact angle of water droplets on the surface. The wettability of the surface of the crescent microstructure is anisotropic and increases with an increase in offset distance. The anisotropy of the crescent-shaped microstructure causes the solid–liquid contact line in the direction of the bottom of the arc to become a long and approximately straight line. According to the rule that controlling LSI processing parameters can fabricate surfaces with different heights and wettability, a gradient wetting surface consisting of crescent-shaped microstructures was designed to achieve the directional spreading of droplets. By altering the distribution of crescent-shaped microstructures, a type-I flow channel with the ability to limit the spreading range of water droplets was fabricated.

Kinetic process of upward gas hydrate growth and water migration on the solid surface

Gas hydrates have gained great interest in the energy and environmental field as a medium for gas storage and transport, gas separation, and carbon dioxide sequestration. The presence of small doses of surfactants in the aqueous phase has been reported to enhance hydrate formation; however, the underlying mechanisms remain poorly understood. Thus, in situ high-resolution X-ray computed tomography measurements were performed to monitor the upward water migration and the resulting hydrate nucleation and growth. It was found that the presence of hydrate crystals at the gas–liquid–solid contact line triggered the enhanced growth of hydrates on the reactor wall. A time delay was observed between the disappearance of the bulk water reservoir and its transformation into hydrate. The lower interfacial tension between the hydrate surface and the solution facilitated its adsorption onto the reactor wall once a thin film of hydrate nucleated on the solid wall surface. These hydrate layers present on the reactor wall were found to be porous, wherein the porosity decreased with increased subcooling. These fundamental results will be of value in understanding the mechanism of hydrate growth in the presence of surfactants and its potential application in hydrate-based technologies.

Giant fluidic impedance of nanometer-sized water bridges: Shear capillary force at the nanoscale.

We analytically show that the interfacial fluid's molecular dynamics of capillary bridges induces both elastic and dissipative forces to the shearing plane. Surprisingly, the nanometer-sized, liquid-solid contact line of the bridges exerts a giant "shear" force on the solid surface, which is 10^{5} higher than the usual viscous interaction and comparable to that of solid-solid direct-contact friction. These results are consistent with previously reported experimental data and may provide clues to longstanding questions on the apparent viscosity of the nanoconfined fluids.

Bouncing modes and heat transfer of a dielectric droplet in the presence of an external electric field

A numerical investigation of droplet bouncing and heat transfer over a heated surface in the presence of an external electric field has been reported. The coupled set of governing equations including the electrostatic and incompressible Navier-Stokes equations, have been implemented in the finite-volume framework of OpenFOAM®. The coupled level set and volume of fluid (CLSVOF) approach has been used to capture the droplet interface. The influence of the electric field over the droplet dynamics and bouncing modes are systematically studied. Different bouncing modes are observed and they have been mapped with respect to the electric capillary number, CaE and Weber number, We. Two new modes have been identified at CaE=0.1. The Coulombic attraction at the solid-liquid contact line extends the total contact time of the droplet. The local electric field distribution depends on the droplet’s local curvature. The stronger distribution of electrostatic pressure near the tip of the droplet induces a stretching behavior. The stretched droplet, extended contact time and enhanced fluid circulation increase the heat transfer. This work provides a deeper understanding of droplet impact, bouncing dynamics and related heat transfer characteristics influenced by an external electric field.

Intrinsically Viscoelastic Supramolecular Conjugated Polymer toward Suppressing Coffee-Ring Effect

Intrinsically Viscoelastic Supramolecular Conjugated Polymer toward Suppressing Coffee-Ring Effect

Interaction of proteins with phase boundaries in aqueous two-phase systems under electric fields.

The electric-field driven transport of proteins across the liquid-liquid interface in an aqueous two-phase system (ATPS) is studied in a microfluidic device using fluorescence microscopy. An ATPS containing polyethylene glycol (PEG) and dextran is employed, and bovine serum albumin (BSA) and bovine γ-globulins (BγG) are considered as model proteins. It is shown that both proteins, initially in the dextran-rich phase, accumulate at the liquid-liquid interface, preferably close to the three-phase contact line between the two liquid phases and the microchannel wall. It is in these regions where the proteins penetrate into the PEG-rich phase. The transport resistance of the liquid-liquid interface is higher for BγG than for BSA, such that a much larger molar flux of BSA into the PEG phase is observed. This opens up the opportunity of separating different protein species by utilizing differences in the transport resistance at the interface. A mathematical model is developed, accounting for adsorption and desorption processes at the liquid-liquid interface. The underlying theoretical concept is that of an electrostatic potential minimum formed by superposing the applied electric field and the field due to the Donnan potential at the interface. A fit of the model parameters to the experimental data results in good agreement between theory and experiments, thereby corroborating the underlying picture.

Control of Droplet Evaporation on Oil-Coated Surfaces for the Synthesis of Asymmetric Supraparticles.

Controlling the droplet evaporation on surfaces is desired to get uniform depositions of materials in many applications, for example, in two- and three-dimensional printing and biosensors. To explore a new route to control droplet evaporation on surfaces and produce asymmetric particles, sessile droplets of aqueous dispersions were allowed to evaporate from surfaces coated with oil films. Here, we applied 1–50 μm thick films of different silicone oils. Two contact lines were observed during droplet evaporation: an apparent liquid–liquid–air contact line and liquid–liquid–solid contact line. Because of the oil meniscus covering part of the rim of the drop, evaporation at the periphery is suppressed. Consequently, the droplet evaporates mainly in the central region of the liquid–air interface rather than at the droplet’s edge. Colloidal particles migrate with the generated upward flow inside the droplet and are captured by the receding liquid–air interface. A uniform deposition ultimately forms on the substrate. With this straightforward approach, asymmetric supraparticles have been successfully fabricated independent of particle species.

Initiation of the Worthington jet on the droplet impact

The deformation of liquid droplets upon impact induces Worthington jets for a certain range of impact velocities. Although the growth of such a jet and its tip velocity are predicted from cases similar to droplet impact, the mechanism behind jet formation is yet to be understood. The present study uses high-speed visualization of droplet impact on a superhydrophobic surface to understand jet initiation in terms of the collapse of an air cavity. Water droplets with diameters of 2.0 and 3.0 mm are generated with the droplet Weber number varying from 2 to 20. The jet velocity is measured from the captured images, from which the maximum velocity is found to be We ∼ 7. The jet velocity at We ∼ 7 is approximately 15 times greater than the impact velocity. Moreover, surface waves are generated upon impact with the solid surface, and they induce an oscillation of the droplet cap as they propagate from the solid–liquid contact line to the top portion of the droplet. Furthermore, we find that the phase of the oscillation is related to the Weber number and greatly influences the jet velocity because it determines the initial conditions for jet generation.

Modelling the spreading behaviour of plasma-sprayed nickel droplets under different impact conditions

Droplet spreading behaviour is critical in influencing the spreading diameters, material splashing and interfacial bonding conditions with the substrate during plasma spraying. Numerical simulations were performed to understand the effects of droplet impact temperatures, velocities and contact angle on spreading dynamics during the deposition of plasma-sprayed nickel splats. It was found that increasing droplet superheat (droplet temperature of 3000 K) was beneficial for increasing the degree of substrate melting and the droplet spreading diameters due to constrained solidification. However, solidification occurring at the droplet expanding front pinned the liquid–solid contact line and induced finger splashing for the case of 2800 K droplet temperature. The solidified layer disturbed droplet spreading and induced material jetting at the early spreading stage under the circumstance of high droplet impact velocities. A new simplified equation relating the maximum spreading ratios and Reynolds number was proposed. The effect of contact angle influenced droplet spreading under the condition of a large interfacial thermal contact resistance.

Empirical study and prediction of liquids retention on structured polymer surfaces

Liquids' contact angle hysteresis and critical retention volumes on five commonly used plastics with surface structures were studied. The chevron‐like groove structures, which are orthogonally arranged, make the liquid–solid contact line elongated while the droplet found staying in the Wenzel state. Various dimensions of surface structures were represented by contact length ratio σ. Advancing and receding contact angles of liquids on polymer surfaces with various conditions were reported. Reduced hysteresis H, which links between advancing and receding contact angles, was also studied and found to extend its availability on structured surfaces. The research found that surface structures have linear effects on liquids' advancing contact angles in the range of σ = 1.0 to 1.42. Linear regression analysis was hence proposed to predict advancing contact angles, and the results indicate that approximate 80% of data points have less than 6% error. An empirical model, which adopts liquid–solid surface tension as the source of liquids' retention force, was proposed to estimate liquids' critical retention volumes on inclined surfaces. The proposed model found good agreements with existing experiment data and demonstrated its superiority over previous ones. The present model provides an approach to predict liquids' storage/repellency on structured surfaces when the advancing contact angles are predictable. Copyright © 2016 John Wiley & Sons, Ltd.

Evaporation of Condensate Droplets on Structured Surfaces with Gradient Roughness

The study of evaporation dynamics of droplets is of scientific interest and has numerous practical applications. Here, we studied the evaporation of small condensate droplets on structured surfaces with one-tier microscale roughness and two-tier micro/nanoscale roughness (the top and valley of micropillars are covered by nanograss), respectively. On both surfaces, the micropillar arrays are arranged in a radical lattice with the decreasing pillar-to-pillar spacing towards the center of the surface (The first figures in Figs. 1 and 2). The condensate droplets on structured surfaces were formed by conducting condensation inside environmental scanning electron microscope (ESEM, Philips XL-30, ~4.9 Torr, stage temperature ~ 3°C). The condensate droplet on the one-tier surface stays in a Cassie-state (0 s in Fig. 1). However, owing to the preferential droplet nucleation on the smooth sidewall of micropillars, the condensate droplet on the two-tier surface maintains in the composite state (0 s in Fig. 2). To visualize the evaporation dynamics of condensate droplet, we gradually decreased the vapor pressure in the chamber from ~4.9 Torr to ~4.2 Torr. On the one-tier surface (Fig. 1), the droplet first evaporates in a constant contact radius mode (CCR, 0-124 s), followed by a constant contact angle mode (CCA, 136-166 s), and a mixed mode of both CCR and CCA (188-224 s). By contrast, on the two-tier surface (Fig. 2), the condensate droplet first evaporates in the CCR mode, with the solid-liquid contact line remain pinned until the formation of a flat liquid-air interface at the top of micropillars at ~86 s. After that, the liquid-air interface at the top of surface remains flat and the liquid evaporation is dominant in the lateral direction (96-170 s), with the liquid cylinder symmetrically shrinking towards the center of the surface. The presence of a stable and flat liquid/air interface at the top of surface is due to the stabilization effect rendered by the nanograss on the micropillars.

Molecular dynamics simulation on the wetting characteristic of micro-droplet on surfaces with different free energies

The wetting characteristic of micro-droplets on surfaces with different free energies is crucial to heterogeneous nucleation theory and the growth mechanism of micro-droplets during vapor condensation. In this paper, the spreading processes and wetting characteristics of nanoscale water droplets on various surfaces are explored by molecular dynamics simulation method. The surfaces are constructed from face centered cubic copper-like atoms with different Lennard-Jones potential parameters. The Lennard-Jones interaction energy well-depth of the surface atoms is adjusted to acquire different surface free energies, and the ratio of surface-water interaction energy well-depth to the water-water interaction energy well-depth is defined as the interaction intensity. In the present study, the relationship between interfacial free energies and solid-liquid interaction intensities is evaluated using molecular dynamics simulations. The wetting characteristics of TIP4P/2005 water droplets on surfaces with various free energies are simulated and analyzed as well, using molecular dynamics simulations under an NVT ensemble. Results indicate that the solid-liquid interfacial free energy increases as the solid-liquid interaction intensity increases, with different spreading processes and wetting characteristics achieved for the water droplets on these surfaces. For the surfaces with lower interaction intensities, water cannot spread on the solid surfaces and hydrophobic surfaces are obtained when the interaction intensity ratio between surface atoms and water molecules is lower than 1.6. As the interaction intensity increases, the surface translates from hydrophobic into hydrophilic, and finally into a complete wetting state as the interaction intensity reaches up to 3.5. Due to the limitation of nanoscale dimensions, the forces that exert on droplet surface are non-continuous and asymmetric. As a result, significant fluctuations of liquid-vapor interface and local solid-liquid contact line can be observed for the droplet in nanoscale. The transient contact angle of nano-droplets is also fluctuating within a certain range, which is different from that observed for macro-droplets. From the viewpoint of statistics, an apparent contact angle can be obtained for the droplet on each surface. The contact angle decreases with solid-liquid interaction intensities linearly, which is in accordance with the calculated results of classic Young's theory using the interfacial free energies obtained from molecular dynamics simulations. The fact that an apparent contact angle is already established for a droplet in nanoscale, supporting the capillary assumption that is widely adopted in classic nucleation theory. The fluctuation of liquid-vapor interface and contact angle also provides a qualitative explanation for the discrepancy between experimental nucleation rates and predictions in classic nucleation theory.

Evaporation of a droplet on a heated spherical particle

A three-dimensional, CLSVOF-based numerical model was developed to study the hydrodynamics of water droplets of various diameters impacting a heated solid particle. The temperature of the particle was set to be above the Leidenfrost temperature of the fluid, such that the influence of several key parameters on the dynamics of film boiling of the droplet could be examined. The simulation results were validated against experimental observations, where it was found that the numerical model could satisfactorily reproduce the dynamics of the droplet. The spread of the droplets upon impact was found to be dependent on the Weber number, with surface tension and viscous forces then acting to recoil the droplet. The rate of droplet recoil was found to be highly dependent on the Reynolds number, as fluid advection tends to enhance the rate of heat transfer within the droplet and the evaporation at the solid–liquid contact line. Eventually, evaporation causes build-up of vapour pressure at the bottom of the liquid, and the droplet lifts-off from the heated particle. It was found that the onset of the droplet lift-off could be estimated through the first-order vibration of a freely oscillating droplet, particularly in cases with low values of Weber number. Finally, the rate of evaporation of the droplet was found to be highly dependent on the capillary length of the fluid and the stability of the vapour layer formation underneath the droplet.

Spontaneous Inertial Imbibition in Porous Media Using a Fractal Representation of Pore Wall Rugosity

Considering the separable phenomena of imbibition in complex fine porous media as a function of timescale, it is noted that there are two discrete imbibition rate regimes when expressed in the Lucas–Washburn (L–W) equation. Commonly, to account for this deviation from the single equivalent hydraulic capillary, experimentalists propose an effective contact angle change. In this work, we consider rather the general term of the Wilhelmy wetting force regarding the wetting line length, and apply a proposed increase in the liquid–solid contact line and wetting force provided by the introduction of surface meso/nanoscale structure to the pore wall roughness. An experimental surface pore wall feature size regarding the rugosity area is determined by means of capillary condensation during nitrogen gas sorption in a ground calcium carbonate tablet compact. On this nano size scale, a fractal structure of pore wall is proposed to characterize for the internal rugosity of the porous medium. Comparative models based on the Lucas–Washburn and Bosanquet inertial absorption equations, respectively, for the short timescale imbibition are constructed by applying the extended wetting line length and wetting force to the equivalent hydraulic capillary observed at the long timescale imbibition. The results comparing the models adopting the fractal structure with experimental imbibition rate suggest that the L–W equation at the short timescale cannot match experiment, but that the inertial plug flow in the Bosanquet equation matches the experimental results very well. If the fractal structure can be supported in nature, then this stresses the role of the inertial term in the initial stage of imbibition. Relaxation to a smooth-walled capillary then takes place over the longer timescale as the surface rugosity wetting is overwhelmed by the pore condensation and film flow of the liquid ahead of the bulk wetting front, and thus to a smooth walled capillary undergoing permeation viscosity-controlled flow.

Peculiarities of evaporation of a thin water layer in the presence of a solvable surfactant

Evaporation of a thin layer of a polar liquid (water) having a free surface and located on a solid substrate is investigated. A solvable surfactant is placed on the free liquid-vapor interface. The surface tension is a linear function of the surface concentration of the surfactant. The surface energy of the solid-liquid contact line is a nonmonotonic function of the layer thickness and is the sum of the Van der Waals interaction and the specific interaction of the double electric layer on the interface. The effect of the solvable surfactant on the dynamics and stability of the propagation of the evaporation front in the thin liquid film is analyzed in the long-wave approximation in the system of Navier-Stokes equations.

Enhancement of dynamic wetting properties by direct fabrication on robust micro–micro hierarchical polymer surfaces

Understanding evaporation phenomena on hierarchical surfaces is of crucial importance for the design of robust superhydrophobic polymer structures for various applications. This fabrication method enables precise control of the dimensions to elucidate the dynamic wetting behavior affected by geometric parameters. That behavior exhibits three distinct evaporation modes: a constant contact line (CCL), a constant contact angle (CCA), and mixed mode during the droplet evaporation. The droplet evaporation results show that the sticky CCL mode and the Cassie–Wenzel transition can be prevented by engineering hierarchy integration. Moreover, the CCL–CCA transition point time scale exhibits remarkable dependence on surface dimensions such as the area fraction and solid–liquid contact line. Finally, the fabricated hierarchical structures indicate remarkable superhydrophobic properties, static contact angle above 160° and low sliding angle under 10°, with good durability in terms of aging effect and mechanical robustness for 2 months.