Critical Contact Angle Research Articles

Limit for Small Spheres To Float by Dynamic Analysis.

Small spheres released above the liquid surface experience a dynamic process to ultimately float or sink, and thus, their behaviors should be considered by dynamic analysis instead of static equilibrium. This study numerically investigates the motion of small spheres after contacting the liquid surface with zero velocity, and the flotation condition is proposed based on the analyses of acting forces and the sphere's motion. Whether the small spheres float is determined by the density ratio, Bond number, and contact angle. A critical contact angle exists, below which the flotation of small spheres is impossible. The decrease in Bond number and increase in hydrophobicity enlarge the limit density ratio for small spheres to float, while exerting little effect on large spheres. The theoretical formulas of the limit density ratio are obtained based on energy balance and agree well with numerical results. The limit density ratio predicted in consideration of a dynamic process is far less than the maximum density ratio predicted by static equilibrium.

Contact Line Pinning Is Not Required for Nanobubble Stability on Copolymer Brushes.

Whereas nanobubble stability on solid surfaces is thought to be based on local surface structure, in this work, we show that nanobubble stability on polymer brushes does not appear to require contact-line pinning. Glass surfaces were functionalized with copolymer brushes containing mixtures of hydrophobic and hydrophilic segments, exhibiting water contact angles ranging from 10 to 75°. On unmodified glass, dissolution and redeposition of nanobubbles resulted in reformation in mostly the same locations, consistent with the contact line pinning hypothesis. However, on polymer brushes, the nucleation sites were random, and nanobubbles formed in new locations upon redeposition. Moreover, the presence of stable nanobubbles was correlated with global surface wettability, as opposed to local structure, when the surface exceeded a critical water contact angle of 50 or 60° for polymers containing carboxyl or sulfobetaine groups, respectively, as hydrophilic side chains. The critical contact angles were insensitive to the identity of the hydrophobic segments.

Spontaneous wetting transition of droplet coalescence on immersed micropillared surfaces

• The possibility of spontaneous Wenzel-to-Cassie transition is verified by an energy analysis. • The wetting transition of droplets during coalescence depends on small interpillar spacing and wettability. • The dynamical contact angle hysteresis of droplets can be decreased via spontaneous Wenzel-to-Cassie transition. • Robust superhydrophobicity and efficient droplet transportation rely on surface geometry and wettability. The spontaneous wetting transition of droplet coalescence on immersed micropillared surfaces was investigated by using many-body dissipative particle dynamics (MDPD). The simulation results show that wetting states are influenced by both the interpillar spacing and intrinsic contact angle of surfaces during droplet coalescence. The overestimation of the contact angle by the Cassie equation was modified by introducing a penetration factor, and the energy analysis suggests that the spontaneous Wenzel-to-Cassie transition could be predicted from critical contact angles. For surfaces with small interpillar spacing and large intrinsic contact angle, the spontaneous Wenzel-to-Cassie transition occurs during droplet coalescence, irrespective of the size of the immersed area. The contact angle hysteresis was also studied, in which the droplet was driven on immersed micropillared surfaces. It was found that reducing interpillar spacing is a feasible option to maintain robust superhydrophobicity, and that it is possible to realize the spontaneous Wenzel-to-Cassie transition. Otherwise, larger interpillar spacing and larger size of the immersed region will result in longer contact lines pinned by pillars if the spontaneous Wenzel-to-Cassie transition fails to occur. Meanwhile, it leads to the weakening of droplet mobility during transportation. The outcomes demonstrate that appropriate geometrical structures and wettability properties should be taken into consideration in order to achieve robust superhydrophobicity and high efficiency of the droplet transportation.

A New Theoretical Model for Coalescence-Induced Droplet Jumping on Hydrophobic Fibers

A new theoretical model that accounts for the excess surface energy, viscous dissipation, surface adhesion, the droplet wetting state, the droplet and fiber radii, and the fiber surface property is developed to predict the coalescence-induced droplet jumping velocity on hydrophobic fibers. The effects of the droplet and fiber radii on the energy terms, the jumping velocity, and the jumping critical contact angle of symmetric and/or asymmetric coalescence are investigated. The results indicate that for the symmetric coalescence, the jumping velocity falls after first increasing along with the increase of the radii of the droplets, despite the larger excess surface energy. However, for the asymmetric coalescence, the highest jumping velocity is achieved when the droplets have the same size. With the increase of the radii difference between the two coalesced droplets, the jumping velocity gradually decreases, even if a greater excess surface energy is released upon coalescence.

Dynamics of Contact Line Pinning and Depinning of Droplets Evaporating on Microribs.

The contact line dynamics of evaporating droplets deposited on a set of parallel microribs is analyzed with the use of a recently developed entropic lattice Boltzmann model for two-phase flow. Upon deposition, part of the droplet penetrates into the space between ribs because of capillary action, whereas the remaining liquid of the droplet remains pinned on top of the microribs. In the first stage, evaporation continues until the droplet undergoes a series of pinning-depinning events, showing alternatively the constant contact radius and constant contact angle modes. While the droplet is pinned, evaporation results in a contact angle reduction, whereas the contact radius remains constant. At a critical contact angle, the contact line depins, the contact radius reduces, and the droplet rearranges to a larger apparent contact angle. This pinning-depinning behavior goes on until the liquid above the microribs is evaporated. By computing the Gibbs free energy taking into account the interfacial energy, pressure terms, and viscous dissipation due to drop internal flow, we found that the mechanism that causes the unpinning of the contact line results from an excess in Gibbs free energy. The spacing distance and the rib height play an important role in controlling the pinning-depinning cycling, the critical contact angle, and the excess Gibbs free energy. However, we found that neither the critical contact angle nor the maximum excess Gibbs free energy depends on the rib width. We show that the different terms, that is, pressure term, viscous dissipation, and interfacial energy, contributing to the excess Gibbs free energy, can be varied differently by varying different geometrical properties of the microribs. It is demonstrated that, by varying the spacing distance between the ribs, the energy barrier is controlled by the interfacial energy while the contribution of the viscous dissipation is dominant if either rib height or width is changed. Main finding of this is study is that, for microrib patterned surfaces, the energy barrier required for the contact line to depin can be enlarged by increasing the spacing or the rib height, which can be important for practical applications.

Wettability and Flow Rate Impacts on Immiscible Displacement: A Theoretical Model

AbstractWhen a more viscous fluid displaces a less viscous one in porous media, viscous pressure drop stabilizes the displacement front against capillary pressure fluctuation. For this favorable viscous ratio conditions, previous studies focused on the front instability under slow flow conditions but did not address competing effects of wettability and flow rate. Here we study how this competition controls displacement patterns. We propose a theoretical model that describes the crossover from fingering to stable flow as a function of invading fluid contact angle θ and capillary number Ca. The phase diagram predicted by the model shows that decreasing θ stabilizes the displacement for θ≥45° and the critical contact angle θc increases with Ca. The boundary between corner flow and cooperative filling for θ < 45° is also described. This work extends the classic phase diagram and has potential applications in predicting CO2 capillary trapping and manipulating wettability to enhance gas/oil displacement efficiency.

Mechanoresponsive Tuning of Anisotropic Wetting on Hierarchically Structured Patterns

Here, we propose a simple mechanoresponsive system on patterned soft surfaces to manipulate both anisotropy and orientation of liquid wetting. On the poly(dimethylsiloxane) embedding line patterned structures, additional topographies, such as wrinkles and cracks, can be provided by applying compressive and tensile stress, respectively. This tunable hierarchy of structures with the different scales and directions of lines, wrinkles, and cracks allow the mechanoresponsive control of anisotropic wetting in a single platform. In addition, the wetting behavior on those surfaces is precisely investigated based on the concept of critical contact angle to overcome the ridges in a step flow.

Fluid Flow and Thin-Film Evolution near the Triple Line during Droplet Evaporation of Self-Rewetting Fluids.

The microscopic region near the triple line plays an important role in the heat and mass transfer of droplets, although the mechanisms of evaporation and internal flow remain unclear. This paper describes an experimental study of fluid flow and thin-film evolution near the triple line in sessile droplets of self-rewetting fluids, aqueous solutions of alcohols with the number of carbon atoms varying from 1 to 7, to analyze the influence of various factors on the mesoscale flows. The mechanism of internal flow for self-rewetting fluid droplets was different from that of conventional fluids, and hence, a novel expression of the in-plane average velocity was fitted for them. The temporal and spatial evolution of the thin-film thickness near the triple line during droplet evaporation was obtained by using a proposed subregion method, which was developed from an evanescent-wave-based multilayer nanoparticle image velocimetry technique. The self-rewetting fluids are conducive to increase the microscopic critical contact angle and the energy barrier of the contact line, which reduces the rate of thin-film thickness variation. The inhibited impact of self-rewetting fluids on evaporation increases gradually with an increasing number of carbon atoms.

The mechanism and relief method of the coal seam water blocking effect (WBE) based on the surfactants

In order to study the mechanism and relief method of coal seam water blocking effect (WBE) to improve the efficiency of gas drainage, the causes and the influencing factors of the coal seam WBE are analyzed, and the critical micelle concentration (CMC), surface tension, viscosity and contact angle changes of the surfactants on the surface of coal are investigated. The capillary force and viscous hysteresis effect are the two reasons for WBE, which is affected by five factors: physical property, surface tension, contact angle, viscosity and intruding depth. The surfactants can reduce the surface tension of water, which decreases with the increasing surfactant concentration. Moreover, the anionic and nonionic surfactants to be reduced are higher than the cationic ones. The contact angle of the surfactant solution on the coal surface decreases with time. The greater the degree of coal metamorphism, the bigger the equilibrium contact angle, and the less the adhesion work of the surfactant solution on the coal surface. The anionic, cationic and nonionic surfactants all reduce the capillary force, and the anionic surfactant has the largest reduction amplitude of the capillary force. Therefore, the surfactant SDS can be selected as the best additive for removing the WBE, the reasonable concentration of which is 0.022%. The results reveal the mechanism of the WBE and provide a method to remove the WBE.

Interface‐shrinkage‐driven breakup of droplets in microdevices with different dispersed fluid channel shape

A new droplet breakup mechanism is previously proposed—interface‐shrinkage‐driven breakup. In coaxial microdevices, when the contact angle between the continuous phase and dispersed fluid channel (DFC) is sufficiently low, the new mechanism instead of the classic shear‐driven mechanism dominates the breakup. The present study further investigated the new mechanism in microdevices with DFCs of different shape. Critical contact angles in different devices were determined by theoretical analysis and verified by experiments. It was found that the critical contact angle for the new mechanism depends on the shape of the DFC. The droplet size was measured for different devices when the new mechanism dominated the breakup. In contrast to the case for the shear‐driven mechanism, the droplet size is little affected by the capillary number. Mathematical models were established to predict the droplet size in different devices and results were found to agree well with experimental results. © 2017 American Institute of Chemical Engineers AIChE J, 63: 367–375, 2018

Thermodynamic formulation of the barrier for heterogeneous pinned nucleation: Implication to the crossover scenarios associated with barrierless and homogeneous nucleation.

The effect of contact line pinning on nucleation is reported using continuum thermodynamics. Based on the principle of the free-energy maximization, closed-form expressions in the dimensionless form for the free-energy of the three-phase metastable system and the thermodynamic barrier are formulated with respect to the system geometry and the substrate wettability. The condition of maximality limits the dynamic contact angle within the cluster-phase-phobic regime. The dimensionless nucleation barrier or the potency factor can be divided into two components related to the system geometry and the pinning effect. Depending on the relative value of the equilibrium and the critical dynamic contact angle, the contact line pinning can either have favorable or adverse effects. Associated pinning-depinning transition can also lead to the crossovers related to barrierless and homogeneous nucleation. Contact line tension is found to have a considerable effect during these transitional scenarios. Complete wetting transition associated with barrierless nucleation can take place due to the presence of tensile (negative) line tension. On the other hand, complete drying transition related to homogeneous nucleation can occur when line tension is compressive (positive) in nature. The pinning has a favorable effect only when the substrate wettability is within the cluster-phase-philic regime. There can be favorable, adverse, or no pinning effects when the substrate wettability is within the cluster-phase-phobic regime. Although the contact line is pinned, the minimum value of the potency factor is obtained when equilibrium and dynamic contact angles are equal.

Facile determination of foamability index of non-ionic and cationic frothers and its effect on flotation of quartz

ABSTRACTIn this work, a facile method for determination of foaming properties of frothers was used. It was based on measuring the foam height in a flotation machine at different concentrations of frothers. Based on the foam height-concentration curve, a new foaming parameter, so-called concentration at half of the maximum foam height CMH, was proposed. Assessment and usefulness of CMH were shown in flotation of quartz. The concentration of amine at the critical contact angle CCA, at which amine starts to be a collector, was also determined. The determined values of CCA were similar to CMH and were equal to 1.3, 0.14 and 0.03 mM for ButNH2, HexNH2 and OctNH2, respectively. The values of CMH and CCA depended on the alkyl chain of frothers.

Transmittance of transparent windows with non-absorbing cap-shaped droplets condensed on their backside

This study aims to quantify systematically the effect of non-absorbing cap-shaped droplets condensed on the backside of transparent windows on their directional-hemispherical transmittance and reflectance. Condensed water droplets have been blamed to reduce light transfer through windows in greenhouses, solar desalination plants, and photobioreactors. Here, the directional-hemispherical transmittance was predicted by Monte Carlo ray-tracing method. For the first time, both monodisperse and polydisperse droplets were considered, with contact angle between 0 and 180°, arranged either in an ordered hexagonal pattern or randomly distributed on the window backside with projected surface area coverage between 0 and 90%. The directional-hemispherical transmittance was found to be independent of the size and spatial distributions of the droplets. Instead, it depended on (i) the incident angle, (ii) the optical properties of the window and droplets, and on (iii) the droplet contact angle and (iv) projected surface area coverage. In fact, the directional-hemispherical transmittance decreased with increasing incident angle. Four optical regimes were identified in the normal-hemispherical transmittance. It was nearly constant for droplet contact angles either smaller than the critical angle θcr (predicted by Snell’s law) for total internal reflection at the droplet/air interface or larger than 180°-θcr. However, between these critical contact angles, the normal-hemispherical transmittance decreased rapidly to reach a minimum at 90° and increased rapidly with increasing contact angles up to 180°-θcr. This was attributed to total internal reflection at the droplet/air interface which led to increasing reflectance. In addition, the normal-hemispherical transmittance increased slightly with increasing projected surface area coverage for contact angle was smaller than θcr. However, it decreased monotonously with increasing droplet projected surface area coverage for contact angle larger than θcr. These results can be used to select the material or surface coating with advantageous surface properties for applications when dropwise condensation may otherwise have a negative effect on light transmittance.

Universal wetting transition of an evaporating water droplet on hydrophobic micro- and nano-structures

Water-repellent, rough surfaces have a remarkable and beneficial wetting property: when a water droplet comes in contact with a small fraction of the solid, both liquid-solid adhesion and hydrodynamic drag are reduced. As a prominent example from nature, the lotus leaf-comprised of a wax-like material with micro- and nano-scaled roughness-has recently inspired numerous syntheses of superhydrophobic substrates. Due to the diverse applications of superhydrophobicity, much research has been devoted to the fabrication and investigations of hydrophobic micro-structures using established micro-fabrication techniques. However, wetting transitions remain relatively little explored. During evaporation, a water droplet undergoes a wetting transition from a (low-frictional) partial to (adhesive) complete contact with the solid, destroying the superhydrophobicity and the self-cleaning properties of the slippery surface. Here, we experimentally examine the wetting transition of a drying droplet on hydrophobic nano-structures, a previously unexplored regime. In addition, using a theoretical analysis we found a universal criterion of this wetting transition that is characterized by a critical contact angle. Different from previous results showing different critical droplet sizes, our results show a universal, geometrically-dependent, critical contact angle, which agrees well with various data for both hydrophobic micro- and nano-structures.

The Effect of Interfacial Properties and Liquid Flow on the Stability of Powder Islands

This study aims at understanding the interplay between the interfacial properties of the powder grains and the characteristics of the liquid flow used to disperse them, in order to obtain an effective dispersion of a powder in a liquid, avoiding air entrainment. The dispersion of grain “rafts” and powder islands “stacks” was investigated both on a static and on a moving air-liquid interface. Powder wicking prevents the formation of a powder island when the grain contact angle is below a critical contact angle. Above the critical contact angle, a powder island forms and grows to a critical depth that depends on grain radius and contact angle. Imposing a flow on the air-liquid interface can either promote water impregnation, reducing the depth of the powder island or destabilise the whole island. In the latter case, the island sinks, forming a heterogeneous powder structure that is wet outside and dry inside.

Water-repellent hydrophilic nanogrooves.

The wetting behavior of a nanodrop atop a nanogroove on a smooth or a rough surface is explored by many-body dissipative particle dynamics and Surface Evolver. The nanogroove possesses the same contact angle (θY) as that of the surface. Depending on whether the groove is initially wetted or not, two critical contact angles beyond which the groove cannot be wetted are determined. Three regimes are identified: (i) as θY ≤ θ, the groove is always wetted; (ii) as , both impregnated and unwetted states can be observed; (iii) as , the groove cannot be impregnated. As the drop volume is increased, both θ and decrease but become insensitive to the volume eventually. Surface roughness tends to hamper the impregnation of grooves by liquid. Compared to a smooth surface, both critical contact angles of a rough surface with regular shallow pits are smaller. As a result, a large drop is unable to wet the groove with a rough surface even when the surface becomes slightly hydrophilic. When the surface structure within the groove is modified from shallow pits to straight trenches, the critical contact angle is further reduced. Our simulation outcomes show that the surface structure within the groove is crucial for liquid imbibition and it is possible to fabricate hydrophilic cavities that can prevent impregnation, without resorting to chemical modification processes.

Effect of pillar height on the wettability of micro-textured surface: Volume-of-fluid simulations

The wetting and spreading characteristics of a water drop on a surface is highly dependent on the geometric parameters of the micro-texture of the surface. To obtain a stable Cassie drop, the condition that the pillar height must be higher than the sag height of the meniscus is a necessary, yet not a sufficient, condition. From the viewpoint of energy minimization, a new criterion was proposed to design the height of the pillar for achieving a stable and robust anti-adhesive drop state. To ensure such a composite interface, the height of the pillars should be taller than the critical height where the critical contact angle is equal to the intrinsic contact angle. If this height requirement is not met, the drop exists in either a Wenzel or a metastable Cassie state. The numerical simulations using the Volume-of-Fluid method in Fluent support the above proposals.

Undercooling and Wettability Behavior of Interstitial-Free Steel on TiN, Al2O3 and MgAl2O4 Under Controlled Oxygen Partial Pressure

The heterogeneous undercooling degree of interstitial-free steel (IF steel) on various substrates was measured through observing the recalescence phenomenon by sessile drop method at the oxygen partial pressure of 10−23 atm, where there was no obvious interaction between the steel and the substrate. The wetting behavior of liquid IF steel against different substrates was also studied during the sessile drop test. The results suggested that the undercooling degree increased with the increase of cooling rate, and the effective contact surface area between the liquid steel and the solid substrate could not fully explain the undercooling behavior of the designed cases as there is no interaction layer. Furthermore, a method to calculate the critical contact angle for IF steel against its substrate was developed in this study, which could be adapted to explain the undercooling variance of IF steel with the change of its substrate. The undercooling degree increased with the increase of the critical contact angle, and the critical contact angle was also improved with the increase of lattice disregistry.

Study on “interface – shrinkage – driven” breakup of droplets in co-flowing microfluidic devices

In co-flowing microfluidic device, it is usually thought the droplet size is significantly influenced by the capillary number in dripping flow. However, it was found in this study that when the contact angle of the dispersed fluid with the dispersed fluid channel was sufficiently large, the droplet size would be little affected by the capillary number. To explain this phenomenon, an “interface – shrinkage – driven” breakup mechanism was proposed. Three different systems and six different microfluidic devices were used in the experiment to prove the universality of the mechanism. The critical contact angle of the dispersed fluid with the dispersed fluid channel was finally discussed.

Effect of adsorption of catanionic surfactant mixtures on wettability of quartz surface

The adsorption behaviors of dodecyl trimethyl ammonium bromide (C12TAB) and the catanionic mixtures of C12TAB with sodium dodecyl sulfate (SDS), sodium dodecyl sulfonate (SDDS) and sodium dodecanoate (DAS) on quartz surface have been investigated. Physicochemical parameters such as the critical micelle concentration (CMC), surface tension, contact angle, adhesional tension and work of adhesion have been estimated. At the interface of quartz and aqueous solution of catanionic mixture, there is a competition between anionic surfactants and quartz surface in attracting cationic surfactants. SDDS and DAS fail to inhibit the adsorption of C12TAB because of the smaller size and less negative charge of the head-groups, even the amount of anionic surfactants well surpasses that of C12TAB. Instead the anionic surfactants are dragged by cationic surfactants to quartz surface and form a mixed monolayer on the quartz surface. The insert of anionic surfactants reduces the repulsion between the cationic molecules and results in closer packing of molecules in adsorption layers. Thus, SDDS-C12TAB and DAS-C12TAB have displayed stronger hydrophobic modification at quartz surface than pure C12TAB. However, the electrostatic attraction between excessive SDS and C12TAB is strong enough to constrain C12TAB and decreases the adsorption on quartz surface. Only a small amount of catanionic complexes with the structure like zwitterionic surfactant adsorb on quartz through the interaction between the positive sites of surfactant complexes and negative sites of quartz. Over CMC, bilayers are formed on quartz surface in the systems of SDDS-C12TAB and DAS-C12TAB, while micelle structures are adsorbed on quartz surface for SDS-C12TAB.