Phase Contact Line Research Articles

Magnetically Induced Low Adhesive Direction of Nano/Micropillar Arrays for Microdroplet Transport

AbstractA kind of superhydrophobic magnetic nano/micropillar array (MNA) with optimized intrinsic dynamic wetting property has characteristics of magnetically induced dynamic tilt‐angle changes, which achieves the controlling of the directional droplet transport effectively. It is revealed that MNA has a low adhesive gradient along the direction of magnetically induced tilt‐angles. A tilt‐angles of nano/micropillars in the range of 0°–59° is realized by controlling the magnetic field intensity (0–490 mT), so that a droplet (10 µL) can be transported on MNA from one pillar to the next along the tilt‐angle direction. It is proposed that the continuous changes of magnetically induced dynamic tilt‐angles on MNA induce a gradient driving force to act on the droplet, in addition to cooperation with the low adhesive direction that results from unidirectional gradient discontinuous solid–liquid–gas three phase contact lines. The finding offers insight into designing of surface materials that can be extended into microfluidics for controlling of droplet motion and others.

Liquid–vapor phase behavior and operating characteristics of the capillary evaporator of a loop heat pipe at start-up

The liquid–vapor phase distribution and displacement in the capillary evaporator of a loop heat pipe (LHP) are key phenomena affecting the steady-state and transient operating behavior. This study conducts optical observation of liquid–vapor phase behavior in the evaporator using a transparent glass tube heated by far-infrared radiation during start-up of the LHP. A quartz wick-acetone LHP system is designed, fabricated, and operated successfully with a heat flux of 1 W/cm2 transported by the cylindrical evaporator. To investigate effect of the liquid–vapor phase distribution in the evaporator at the initial state, start-up experiments with eight phase patterns—which are either liquid-saturated or two-phase in each of the inlet of the vapor line, grooves, and compensation chamber (CC)—are performed. The phase distribution affects the temperature profile although it has no effect upon the steady-state characteristics, and nucleate boiling occurs in the wick or groove simultaneously with evaporator-temperature drop when both the grooves and the inlet of the vapor line are completely filled with liquid. Liquid–vapor displacements from start-up to the steady-state are classified into four transient behaviors, which include boiling in the CC and meniscus oscillation at the three phase contact line within the case, wick, and groove.

Effect of Micropillar Spacing and Temperature of Substrate on Contact Angle Dynamics

ABSTRACTContact angle dynamics of droplets deposited on a structured surface were studied in this work and the effects of substrate microstructure and temperature were investigated. Microstructures consisting of uniformly-sized, cubic micropillars with varying pillar spacings were constructed by microfabrication. Droplets (of the order of tens of microlitres in volume) were deposited on these surfaces and dynamic contact angles were observed using various techniques. Advancing and receding contact angles were measured using tilting of the surfaces or by injection and aspiration of fluid from a horizontal droplet by syringe. Droplets on these surfaces appeared to be mainly in the Wenzel state. Contact angle hysteresis was obtained as a function of pillar spacing or, equivalently, surface roughness. Depinning force was deduced and a linear dependence on maximal three phase contact line was found. The techniques of tilting the surface on which the droplet was deposited and uniformly increasing and reducing the volume of the droplet via the syringe both gave the same contact angle hysteresis for a given micropillar spacing. The effect of temperature was then assessed using a heated tilting plate. Contact angle hysteresis was found to increase with temperature. Further work to elucidate mechanisms governing this dependence will be undertaken.

Wettability of AFM tip influences the profile of interfacial nanobubbles

To accurately characterize the shape of interfacial nanobubbles using atomic force microscopy (AFM), we investigated the effect of wettability of the AFM tip while operating in the peak force tapping (PFT) mode. The AFM tips were made hydrophobic and hydrophilic by Teflon AF coating and oxygen plasma treatment, respectively. It was found that the measured base radius of nanobubbles differed between AFM height images and adhesion images, and that this difference depended on the tip wettability. The force curves obtained during the measurements were also different depending on the wettability, especially in the range of the tip/nanobubble interaction and in the magnitude of the maximum attractive force in the retraction period. The difference suggests that hydrophobic tips penetrate the gas/liquid interface of the nanobubbles, with the three phase contact line being pinned on the tip surface; hydrophilic tips on the other hand do not penetrate the interface. We then quantitatively estimated the pinning position and recalculated the true profiles of the nanobubbles by comparing the height images and adhesion images. As the AFM tip was made more hydrophilic, the penetration depth decreased and eventually approached zero. This result suggests that the PFT measurement using a hydrophilic tip is vital for the acquisition of reliable nanobubble profiles.

Influence of polar and dispersive part of surface tension on the self-assembly of droplets on PDMS surfaces

Self-assembly of droplets deposited on a polymer solution of PDMS over a constrained surface is studied experimentally. The effect of constraints on the pinning of the droplets is explained in terms of the surface tension of the droplet forming liquid. The nucleation, growth and evaporation of water, methanol and ethanol droplets on PDMS surface and the resulting patterns are analysed. Results are compared with similar experiments carried out on smooth surfaces. Surface morphology of the patterned surfaces are carried out using Confocal Laser Scanning microscope. Analysis of pore formation reflects the difference in patterns formed on constrained surface and smooth surface. The constrained surface showed a distorted hexagonal ring inside which closely arranged pores of smaller diameter are formed; whereas the smooth surface showed the ideal honey comb pattern. In both cases, the pore dimension and the diameter/shape of ring formed depends on the surface tension of the liquid. Although ethanol and methanol have nearly same surface tension of 22 mN/m, the self-assembled droplet patterns formed by them show considerable differences in shape and size. The wetting studies are carried out using the contact angle goniometer with distilled water as reference liquid. All the surfaces showed hydrophobicity with a Wenzel’s state of wetting. Wetting studies for surfaces patterned in alcohol environment indicate that the contact angle decreases with increase in chain length of alcohols. The differences are attributed to the variation in polar and dispersive parts of the surface tension of liquids, polar component of Hansen’s solubility parameter and the effect of constraints present in the underlying surface which lead to de-pinning of the three phase contact line.

Elastic capsules at liquid-liquid interfaces.

We investigate the deformation of elastic microcapsules adsorbed at liquid-liquid interfaces. An initially spherical elastic capsule at a liquid-liquid interface undergoes circumferential stretching due to the liquid-liquid surface tension and becomes lens- or discus-shaped, depending on its bending rigidity. The resulting elastic capsule deformation is qualitatively similar, but distinct from the deformation of a liquid droplet into a liquid lens at a liquid-liquid interface. We discuss the deformed shapes of droplets and capsules adsorbed at liquid-liquid interfaces for a whole range of different surface elasticities: from droplets (only surface tension) deforming into liquid lenses, droplets with a Hookean membrane (finite stretching modulus, zero bending modulus) deforming into elastic lenses, to microcapsules (finite stretching and bending modulus) deforming into rounded elastic lenses. We calculate capsule shapes at liquid-liquid interfaces numerically using shape equations from nonlinear elastic shell theory. Finally, we present theoretical results for the contact angle (or the capsule height) and the maximal capsule curvature at the three phase contact line. These results can be used to infer information about the elastic moduli from optical measurements. During capsule deformation into a lens-like shape, surface energy of the liquid-liquid interface is converted into elastic energy of the capsule shell giving rise to an overall adsorption energy gain by deformation. Soft hollow capsules exhibit a pronounced increase of the adsorption energy as compared to filled soft particles and, thus, are attractive candidates as foam and emulsion stabilizers.

Numerical study of the effect of forced convective flow on dropwise condensation by thermal LBM simulation

The enhancement mechanism of forced convective flow on dropwise condensation over a cold spot is numerically investigated by two-dimensional hybrid thermal lattice Boltzmann (LB) model based on the Shan-Chen pseudopotential LB model. After validating the present LB model, dropwise condensation over a cold spot as the nucleation region is simulated. The well-known power law for the growth of a single condensing droplet is demonstrated. Finally, the simulation of dropwise condensation considering the convection flow or not is carried out in the constant contact radius (CCR) mode. Using the CCR model, the effect of contact angle can be also investigated. The result of streamline field indicates that the forced convectional flow complicates the internal flow of droplet and main flow. The dragging force from main flow changes the size of two symmetric vortices inside the droplet. And the channel flow is also strongly influenced by the suction effect caused by condensation at the three phase contact line. By comparison, the heat transfer enhancement of the superimposed flow is not worth mentioning. The present study illustrates the mechanisms of dropwise condensation under forced convectional flow.

A general strategy for printing colloidal nanomaterials into one-dimensional micro/nanolines.

Though patterned one-dimensional (1D) micro/nanoline arrays are of great importance in the field of integrated circuits and optoelectronics, the fabrication of high-precision micro/nanolines with excellent optical and electrical performance remains a great challenge. Herein, a general strategy for printing 1D micro/nanolines is proposed by manipulating the self-assembly of functional nanoparticles as a multilayer or monolayer stack with a single-nanoparticle width. This method is universal for dispersible nanoparticles, and the silver nanoparticle was selected as a model nanoparticle due to its good conductivity, dispersibility and narrow-size distribution. The results indicate that the morphologies of printed micro/nanolines can be precisely regulated by the substrate wettability and the suspension concentration. Specifically, 1D nanoparticle-assembled architectures are printed as a monolayer stack on the substrate with a low contact angle (below 45°), while a multilayer stack is formed on the substrate with a high contact angle (above 50°) or a high concentration (more than 0.12%). The controllability of micro/nanoline morphologies can be interpreted through the influence of the three phase contact line slipping motion and the nanoparticle diffusion on diverse substrates at different concentrations. Alteration of the printing template structures enables the intervals of 1D micro/nanolines to span from 16 μm to 48 μm. These results provide an efficient methodology for fabricating micro/nano-circuits or optics and strengthening the understanding of the self-assembling process.

Porous micropillar structures for retaining low surface tension liquids

The ability to manipulate fluid interfaces, e.g., to retain liquid behind or within porous structures, can be beneficial in multiple applications, including microfluidics, biochemical analysis, and the thermal management of electronic systems. While there are a variety of strategies for controlling the disposition of liquid water via capillarity, such as the use of chemically modified porous adhesive structures and capillary stop valves or surface geometric features, methods that work well for low surface tension liquids are far more difficult to implement. This study demonstrates the microfabrication of a silicon membrane that can retain exceptionally low surface tension fluorinated liquids against a significant pressure difference across the membrane via an array of porous micropillar structures. The membrane uses capillary forces along the triple phase contact line to maintain stable liquid menisci that yield positive working Laplace pressures. The micropillars have inner diameters and thicknesses of 1.5–3 μm and ∼1 μm, respectively, sustaining Laplace pressures up to 39 kPa for water and 9 kPa for Fluorinert™ (FC-40). A theoretical model for predicting the change in pressure as the liquid advances along the porous micropillar structure is derived based on a free energy analysis of the liquid meniscus with capped spherical geometry. The theoretical prediction was found to overestimate the burst pressure compared with the experimental measurements. To elucidate this deviation, transient numerical simulations based on the Volume of Fluid (VOF) were performed to explore the liquid pressure and evolution of meniscus shape under different flow rates (i.e., Capillary numbers). The results from VOF simulations reveal strong dynamic effects where the anisotropic expansion of liquid along the outer micropillar edge leads to an irregular meniscus shape before the liquid spills along the micropillar edge. These findings suggest that the analytical prediction of burst Laplace pressure obtained under quasi-static condition (i.e., equilibrium thermodynamic analysis under low capillary number) is not applicable to highly dynamic flow conditions, where the liquid meniscus shape deformation by flow perturbation cannot be restored by surface tension force instantaneously. Therefore, the critical burst pressure is dependent on the liquid velocity and viscosity under dynamic flow conditions. A numerical simulation using Surface Evolver also predicts that surface defects along the outer micropillar edge can yield up to 50% lower Laplace pressures than those predicted with ideal feature geometries. The liquid retention strategy developed here can facilitate the routing and phase management of dielectric working fluids for application in heat exchangers. Further improvements in the retention performance can be realized by optimizing the fabrication process to reduce surface defects.

Effect of Interaction of Nanoparticles and Surfactants on the Spreading Dynamics of Sessile Droplets.

While a body of literature on the spreading dynamics of surfactants and a few studies on the spreading dynamics of nanocolloids exist, to the best of the authors' knowledge, there are no reports on the effect of presence of surfactants on the spreading dynamics of nanocolloidal suspensions. For the first time the present study reports an extensive experimental and theoretical study on the effect of surfactant impregnated nanocolloidal complex fluids in modulating the spreading dynamics. A segregation analysis of the effect of surfactants alone, nanoparticle alone, and the combined effect of nanoparticle and surfactants in altering the spreading dynamics have been studied in detail. The spreading dynamics of nanocolloidal solutions alone and of the surfactant impregnated nanocolloidal solutions are found to be grossly different, and particle morphology is found to play a predominant role. For the first time the present study experimentally proves that the classical Tanner's law is disobeyed by the complex fluids in the case of particle alone and combined particle and surfactant case. We also discuss the role of imbibitions across the particle wedge in the precursor film in tuning spreading dynamics. We propose an analytical model to predict the nature of dependency of contact radius on time for the complex colloids. A detailed theoretical examination of the governing factors, the interacting forces at the three phase contact line, and the effects of interplay of surfactants and the nanoparticles at the precursor film in modulating the spreading dynamics has been presented for such complex colloids.

A computational study of wetting on chemically contaminated substrates

The partial wetting of droplets on rigid, chemically contaminated substrates is investigated numerically for Bond numbers Bo≤5. To this end a recently developed numerical framework (Sauer [1] and Sauer et al. [2]) based on a finite element discretisation and a computational contact algorithm is used. Its applicability to wetting on chemically heterogeneous substrates is demonstrated. An analytical expression for the change in the apparent contact angle in the presence of an arbitrarily strong chemical contamination is derived based on a perturbed force equilibrium analogy at the triple phase contact line. The analytical prediction is compared to the theory by de Gennes [3] as well as to the modified Cassie's law [4] with perfect agreement in the limit of small perturbations, i.e. small chemical contaminations. The predicted change in the apparent contact angle is used to define a mapping between the droplet shape for wetting on homogeneous substrates and chemically heterogeneous substrates. Numerical results are presented for circular, patterned substrates (axial and radial patterns) as well as locally introduced perturbations on otherwise homogeneous substrates. The results for the droplet shape on chemically contaminated substrates show good agreement with the analytical solution for the droplet's height and wetting radius on homogeneous substrates when the presented mapping is applied. Moreover, the present results are in good quantitative agreement to results reported in literature.

Mechanism study on shape evolution and wetting transition of droplets during evaporation on superhydrophobic surfaces

A model about the shape evolution and wetting transition of a droplet on superhydrophobic surfaces during evaporation was founded through analyzing the driving force and resistance on the three phase contact line (TPCL) of the droplet. The driving force to shift the TPCL was derived by calculating the gradient of interface free energy and the resistance was based on adhesion. The calculation results show that the volume reduction process of a droplet will undergo several stages. The first one is the constant contact line (CCL) stage with the resistance on TPCL larger than driving force. The second period is the constant contact angle (CCA) stage when the driving force is greater than the resistance. Later, the TPCL will move down along micro pillars until the substrate is wetted and the wetting transition is completed. Then, the drop will experience another CCL period before entering into the mixed mode stage. The evolution of droplet on micro/nano hierarchical surfaces is similar to that on micro structure surfaces, but with shorter CCL stage and without obvious contact angle reduction after the wetting transition because only micro structure is wetted. Finally, the reasonable agreement between the model and experimental results has been illustrated.

Static wetting characteristics of micro-textured stainless steel surfaces under uniaxial loading condition

The wetting behaviour associated with the surface micro asperities is investigated on the groove and pillar textured SS304 solid surface which is widely used in the flight vehicles where the stresses are induced by uniaxial compressive loads for both positive and negative curvature. By varying the applied load on the groove-textured surfaces in the direction perpendicular to grooves, the positive curvature shows a decrease in static contact angle initially then increases for further increase in deflection; however, the negative curvature induced by the same applied load shows an opposite trend. At the same time, in the pillar-textured surface, the static contact angle decreases with increase in applied load for the positive curvature and the same wetting parameter shows an opposite trend for the negative curvature. This phenomenon is mainly attributed to the pinning behaviour of the three phase contact line of the liquid drop on these two surfaces.

Dynamic surface properties of mixed monolayers of polystyrene micro- and nanoparticles with DPPC

The dynamic surface properties of mixed monolayers of 1,2-Dipalmitoyl-sn-glycerol-3-phosphocholine (DPPC) and negatively charged polystyrene particles (PS) of different size were investigated with the aim to model the interactions of particles with biointerfaces. Special attention was paid to the aggregation of the particles at the water/air interface. The particle aggregates have a weaker influence on the dynamic properties of DPPC monolayers as compared with non-aggregated particles because of a shorter three phase contact line. The incorporation of particles into a DPPC monolayer leads to disordering of the monolayer structure, decreases the changes of surface properties in the course of two-dimensional phase transitions and the dynamic surface elasticity of the condensed lipid film. The influence of particles on the properties of mixed monolayers depends strongly on the ratio of lipid molecules and particles, and decreases with the decrease of particle surface concentration. The Brewster angle microscopy gives direct evidence of the PS particle aggregation in the course of compression of mixed monolayers.

Influence of a Propagating Megahertz Surface Acoustic Wave on the Pattern Deposition of Solute Mass off an Evaporating Solution.

We study the influence of a megahertz Rayleigh surface acoustic wave (SAW), propagating in a solid substrate, on the pattern deposition of a solute mass off an evaporating solution. An experimental procedure, where a film of a solution undergoes a controlled evaporation in a chamber, shows that the SAW alters the state of the pattern deposition. Increasing the power of the SAW supports an increase in the density of the deposited patterns. Beyond threshold conditions, the deposited patterns merge and we observe the deposition of a solid film. A simplified theory suggests that the SAW deforms the geometry of the film, which is predominantly governed by the capillary stress. The deformation of the film taking place alongside with the evaporation of the solution increases the concentration near the pinned three phase contact line at the front of the film, which is closer to the source of the SAW, on the expense of the concentration at the rear. The increased concentration translates to the deposition of solute mass over an increased area near the front of the film, which explains the experimental observation.

Critical fall height for particle capture in film flotation: Importance of three phase contact line velocity and dynamic contact angle

The capture of a falling particle at a horizontal gas–liquid interface (film flotation) is determined by the particle impact velocity and the subsequent motion of the three phase contact line (TPCL) as the particle penetrates into the liquid. In this study, the three phase contact lines were observed experimentally using high speed video camera for a number of different particle liquid systems. The particles comprised hydrophilic glass bead particles with and without surface hydrophobicity treatment. The liquid comprised water, and NaCl, sucrose and hexadecyltrimethylammonium bromide (CTAB) aqueous solutions with different concentrations. Previous modelling of Liu et al. (2010a) was extended to include the advancing velocity of TPCL on dynamic contact angle. The critical fall height predictions by the modified model compared favourably with experimental measurements.

Heat Transfer through a Condensate Droplet on Hydrophobic and Nanostructured Superhydrophobic Surfaces.

Understanding the fundamental mechanisms governing vapor condensation on nonwetting surfaces is crucial to a wide range of energy and water applications. In this paper, we reconcile classical droplet growth modeling barriers by utilizing two-dimensional axisymmetric numerical simulations to study individual droplet heat transfer on nonwetting surfaces (90° < θa < 170°). Incorporation of an appropriate convective boundary condition at the liquid-vapor interface reveals that the majority of heat transfer occurs at the three phase contact line, where the local heat flux can be up to 4 orders of magnitude higher than at the droplet top. Droplet distribution theory is incorporated to show that previous modeling approaches underpredict the overall heat transfer by as much as 300% for dropwise and jumping-droplet condensation. To verify our simulation results, we study condensed water droplet growth using optical and environmental scanning electron microscopy on biphilic samples consisting of hydrophobic and nanostructured superhydrophobic regions, showing excellent agreement with the simulations for both constant base area and constant contact angle growth regimes. Our results demonstrate the importance of resolving local heat transfer effects for the fundamental understanding and high fidelity modeling of phase change heat transfer on nonwetting surfaces.

Equilibrium of droplets on a deformable substrate: Influence of disjoining pressure

Equilibrium of liquid droplets on soft deformable substrates is investigated. Disjoining pressure action in the vicinity of the apparent three phase contact line is taken into account. It is shown that the combined disjoining and capillary pressure action determine the substrate deformation. A simplified linear disjoining pressure isotherm and simple Winkler's model to account for the substrate deformation are used which allows deducing analytical solutions for both the liquid profile and the substrate deformation. The apparent equilibrium contact angle of the liquid droplet with the deformable substrate is calculated and its dependency on the system parameters is investigated.

Phase field modeling and simulation of three-phase flow on solid surfaces

Phase field models are widely used to describe the two-phase system. The evolution of the phase field variables is usually driven by the gradient flow of a total free energy functional. The generalization of the approach to an N phase (N≥3) system requires some extra consistency conditions on the free energy functional in order for the model to give physically relevant results. A projection approach is proposed for the derivation of a consistent free energy functional for the three-phase Cahn–Hilliard equations. The system is then coupled with the Navier–Stokes equations to describe the three-phase flow on solid surfaces with moving contact line. An energy stable scheme is developed for the three-phase flow system. The discrete energy law of the numerical scheme is proved which ensures the stability of the scheme. We also show some numerical results for the dynamics of triple junctions and four phase contact lines.

Surface and Wetting Properties of Embiopteran (Webspinner) Nanofiber Silk.

Insects of the order Embioptera, known as embiopterans, embiids, or webspinners, weave silk fibers together into sheets to make shelters called galleries. In this study, we show that silk galleries produced by the embiopteran Antipaluria urichi exhibit a highly hydrophobic wetting state with high water adhesion macroscopically equivalent to the rose petal effect. Specifically, the silk sheets have advancing contact angles above 150°, but receding contact angle approaching 0°. The silk sheets consist of layered fiber bundles with single strands spaced by microscale gaps. Scanning and transmission electron microscopy (SEM, TEM) images of silk treated with organic solvent and gas chromatography mass spectrometry (GC-MS) of the organic extract support the presence of a lipid outer layer on the silk fibers. We use cryogenic SEM to demonstrate that water drops reside on only the first layer of the silk fibers. The area fraction of this sparse outer silk layers is 0.1 to 0.3, which according to the Cassie-Baxter equation yields an effective static contact angle of ∼130° even for a mildly hydrophobic lipid coating. Using high magnification optical imaging of the three phase contact line of a water droplet receding from the silk sheet, we show that the high adhesion of the drop stems from water pinning along bundles of multiple silk fibers. The bundles likely form when the drop contact line is pinned on individual fibers and pulls them together as it recedes. The dynamic reorganization of the silk sheets during the droplet movement leads to formation of "super-pinning sites" that give embiopteran silk one of the strongest adhesions to water of any natural hydrophobic surface.