The effect of contact angle hysteresis on droplet coalescence and mixing

In this work, droplet coalescence and the subsequent mixing in superhydrophobic surfaces is studied over a range of impact velocities and impact angles. Sanded Teflon surfaces are used as a novel two-dimensional microfluidics platform. These superhydrophobic surfaces exhibit a constant advancing contact angle of θ(A)=150° over a broad range of contact angle hysteresis. As a result, the effect of contact angle hysteresis on droplet coalescence and mixing can be studied. Based on the observed characteristics of coalescence, three different regimes of coalescence are identified as a function of both Weber number and impact angle. These regimes include oscillation dominated, rotation dominated, and mixed dynamics. It is shown that within Weber number ranges achievable in this experiment, hysteresis greatly reduces the deformation of the droplet coalescence process and the subsequent mixing. In head-on collisions, higher hysteresis is found to decrease the frequency at which the resulting dr oscillates. In the case of glancing collisions, where the resulting droplet is found to rotate, higher hysteresis increases the rate of rotation although the overall angular momentum is found to be independent of contact angle hysteresis.     

The dynamics of impacting water droplets on alkanethiol self-assembled monolayers with co-adsorbed CH3 and CO2H terminal groups

The impact of water droplets (diameter 3.6 mm) at a fixed Weber number of 59 on solid surfaces with precisely tailored surface wettabilities was studied experimentally using a high-speed imaging camera at 2500 frames per second. Solid surface wettability was varied using four fractional mixtures of self-assembled monolayers of 1-octadecanethiol and 16-mercaptohexadecanoic acid. The surfaces so obtained are characterized for contact angle and chemical functionality using the axisymmetric drop shape analysis profile (ADSA-P) technique and Fourier transform infrared spectroscopy (FT-IR). Our results correlate the wetting effects of the impacting droplets with the surface energy and contact angle measurements of the tailored surfaces. Literature models for the maximum spreading diameter are employed and compared with those from our experiments. An equation is also proposed for the maximum spreading diameter which makes use of the correct contact angles and results in the least error among the models considered. As a consequence of Young's equation, the correct contact angles to be used for droplet impact dynamics should be the corresponding advancing angles on a smooth substrate of interest. We also conclude that accurate examination of literature models requires careful experimentation on impact dynamic data on well-prepared and characterized surfaces such as those presented here.     

Wetting of nanogrooved polymer surfaces

Molecular dynamics simulations were used to study the wetting of nanogrooved PE and PVC polymer surfaces. The contact angles, equilibrium states, and equilibrium shapes of two nanosized water droplets were analyzed on surfaces with 1D-arranged periodic roughness of various dimensions. The composite solid-liquid contact, which is preferred in practical applications and in which a droplet rests on top of the surface asperities, was observed on the roughest PE surfaces, whereas water filled the similar but slightly deeper grooves on PVC surfaces. The transition from the wetted to composite contact regime occurred when the contact angle with a flat surface reached the value at which the apparent Wenzel and Cassie contact angles are equal. Droplets on grooved PE surfaces with the composite contact exhibited contact angles in agreement with Cassie's equation, but the increase in hydrophobicity on smoother surfaces with the wetted contact was less than expected from Wenzel's equation. The difference between the simulated and theoretical values decreased as the dimensions of the surface grooves increased. Only a slight increase or even a slight decrease in the contact angles was observed on the grooved PVC surfaces, owing to the less hydrophobic nature of the flat PVC surface. On both polymers, the nanodroplet assumed a spherical shape in the composite contact. Only minor anisotropy was observed in the wetted contact on PE surfaces, whereas even a highly anisotropic shape was seen on the grooved PVC surfaces. The contact angle in the direction of the grooves was smaller than that in the perpendicular direction, and the difference between the two angles decreased with the increasing size of the water droplet.     

Contact-angle hysteresis on super-hydrophobic surfaces

The relationship between perturbations to contact angles on a rough or textured surface and the super-hydrophobic enhancement of the equilibrium contact angle is discussed theoretically. Two models are considered. In the first (Wenzel) case, the super-hydrophobic surface has a very high contact angle and the droplet completely contacts the surface upon which it rests. In the second (Cassie-Baxter) case, the super-hydrophobic surface has a very high contact angle, but the droplet bridges across surface protrusions. The theoretical treatment emphasizes the concept of contact-angle amplification or attenuation and distinguishes between the increases in contact angles due to roughening or texturing surfaces and perturbations to the resulting contact angles. The theory is applied to predicting contact-angle hysteresis on rough surfaces from the hysteresis observable on smooth surfaces and is therefore relevant to predicting roll-off angles for droplets on tilted surfaces. The theory quantitatively predicts a "sticky" surface for Wenzel-type surfaces and a "slippy" surface for Cassie-Baxter-type surfaces.     

Drops on microstructured surfaces coated with hydrophilic polymers: Wenzel's model and beyond

In the experiments described in this paper, micromachined silicon post surfaces were coated with thin films of a polymer for which the contact angle on the smooth material was around 70 degrees . Drops wetted these surfaces in the Wenzel or "penetration" mode. We have determined the advancing and receding angles as a function of the roughness geometry and quantitatively compared our results to the contact angles predicted by Wenzel's model. We discuss reasons for discrepancies and propose a model for the motion of the meniscus where we take into account the precise shape of the liquid front during its movement through the post structure.     

Condensation-induced wetting state and contact angle hysteresis on superhydrophobic lotus leaves

In this paper, we demonstrate how condensed moisture droplets wet classical superhydrophobic lotus leaf surfaces and analyze the mechanism that causes the increase of contact angle hysteresis. Superhydrophobic lotus leaves in nature show amazing self-cleaning property with high water contact angle (>150°) and low contact angle hysteresis (usually <10°), causing droplets to roll off at low inclination angles, in accordance with classical Cassie–Baxter wetting state. However, when superhydrophobic lotus leaves are wetted with condensation, the condensed water droplets are sticky and exhibit higher contact angle hysteresis (40–50°). Compared with a fully wetted sessile droplet (classical Wenzel state) on the lotus leaves, the condensed water droplet still has relatively large contact angle (>145°), suggesting that the wetting state deviates from a fully wetted Wenzel state. When the condensed water droplets are subjected to evaporation at room conditions, a thin water film is observed bridging over the micropillar structures of the lotus leaves. This causes the dew to stick to the surface. This result suggests that the condensed moisture does not uniformly wet the superhydrophobic lotus leaf surfaces. Instead, there occurs a mixed wetting state, between classical Cassie–Baxter and Wenzel states that causes a distinct increase of contact angle hysteresis. It is also observed that the mixed Cassie–Baxter/Wenzel state can be restored to the original Cassie–Baxter state by applying ultrasonic vibration which supplies energy to overcome the energy barrier for the wetting transition. In contrast, when the surface is fully wetted (classical Wenzel state), such restoration is not observed with ultrasonic vibration. The results reveal that although the superhydrophobic lotus leaves are susceptible to being wetted by condensing moisture, the configured wetting state is intermediate between the classical Cassie–Baxter and Wenzel states.     

Mean-field theory of liquid droplets on roughened solid surfaces: application to superhydrophobicity

We present calculations of the density distributions and contact angles of liquid droplets on roughened solid surfaces for a lattice gas model solved in a mean-field approximation. For the case of a smooth surface, this approach yields contact angles that are well described by Young's equation. We consider rough surfaces created by placing an ordered array of pillars on a surface, modeling so-called superhydrophobic surfaces, and we have made calculations for a range of pillar heights. The apparent contact angle follows two regimes as the pillar height increases. In the first regime, the liquid penetrates the interpillar volume, and the contact angle increases with pillar height before reaching a constant value. This behavior is similar to that described by the Wenzel equation for contact angles on rough surfaces, although the contact angles are underestimated. In the second regime, the liquid does not penetrate the interpillar volume substantially, and the contact angle is independent of the pillar height. This situation is similar to that envisaged in the Cassie-Baxter equation for contact angles on heterogeneous surfaces, but the contact angles are overestimated by this equation. For larger pillar heights, two states of the droplet can be observed, one Wenzel-like and the other Cassie-like.     

Dependence of volatile droplet lifetime on the hydrophobicity of the substrate

In this Article, we demonstrate the dependence of the lifetime of a volatile droplet on the hydrophobicity of the substrate. Ethanol droplets placed on the molecularly smooth surfaces of three polymers, applied to substrates by spin-coating, showed distinct types of behavior depending on the hydrophobicity of the latter. High contact angles, θ, lead to fairly regular recession of the triple line during liquid evaporation at essentially constant θ, whereas low contact angle caused pinning, θ decreasing with time. The latter case leads to shorter drop lifetimes.     

Spreading of an inkjet droplet on a solid surface with a controlled contact angle at low Weber and Reynolds numbers

Even though the inkjet technology has been recognized as one of the most promising technologies for electronic and bio industries, the full understanding of the dynamics of an inkjet droplet at its operating conditions is still lacking. In this study, the normal impact of water droplets on solid substrates was investigated experimentally. The size of water droplets studied here was 46 microm and was much smaller than the most of the previous studies on drop impact. The Weber number (We) and Reynolds number (Re) were 0.05-2 and 10-100, respectively, and the Ohnesorge number was fixed at 0.017. The wettability of the solid substrate was varied by adsorbing a self-assembled monolayer of octadecyltrichlorosilane followed by the exposure to UV-ozone plasma. The impact scenarios for low We impacts were found to be qualitatively different from the high to moderate We impacts. Neither the development of a thin film and lamella under the traveling sphere nor the entrapment of small bubbles was observed. The dynamics of droplet impact at the conditions studied here is found to proceed under the combined influences of inertia, surface tension, and viscosity without being dominated by one specific mechanism. The maximum spreading factor (beta), the ratio of the diameter of the wetted surface and the drop diameter before impact, was correlated well with the relationship ln beta=0.090 ln We/(fs-cos theta)+0.151 for three decades of We/(fs-cos theta), where theta is the equilibrium contact angle, and fs is the ratio between the surface areas contacting the air and the solid substrate. The result implies that the final shape of the droplet is determined by the surface phenomenon rather than fluid mechanical effects.     

Investigations of drop impact on dry walls with a lattice-Boltzmann model

In this work, axisymmetric computations of drop impingement on dry walls are presented. The two-phase model employed is an axisymmetric lattice-Boltzmann model. Computations are performed in the parametric range of Weber number We of 7 to 8770, Ohnesorge number Oh of 0.02 to 0.137, and drop-wall equilibrium contact angle theta(eq) of 35 degrees to 150 degrees . Deposition and rebound outcomes are reported. In deposition, the different stages of drop evolution including spread, recoil and equilibration are reproduced and studied. Comparisons made with experimentally reported data of temporal evolution of the spread factor and the dynamic evolution of the contact angle show good agreement. Rebound is observed on non-wetting surfaces. The transition between deposition and rebound is shown to be influenced by the impact We, Oh, and advancing and receding static contact angles. Apart from impingement outcomes, the influence of We and Oh on the dynamic contact angle is investigated.     

Enhanced hydrophobicity of rough polymer surfaces

Molecular dynamics simulations were used to study the effect of periodic roughness of PE and PVC polymer surfaces on the hydrophobicity. Pillars of different lateral dimensions and heights were derived from flat crystalline surfaces, and the results of nanoscale simulations on the structured surfaces were compared with theoretical predictions of the Wenzel and Cassie equations. Hydrophobicity increased on all rough surfaces, but the increase was greater on the structured PE surfaces because of the larger water contact angle on the flat PE surface than the corresponding PVC surface. Equally sized pillar structures on the two polymers resulted in different equilibrium wetting geometries. Composite contacts were observed on rough PE surfaces, and the contact angle increased with decreasing contact area between the solid and the liquid. Opposite results were obtained for rough PVC surfaces; the contact angle increased with the solid-liquid contact area, in agreement with Wenzel's equation. However, the composite contact was observed if the energies of the wetted and composite contacts were almost equal. Good agreement was obtained between the simulated contact angles and equilibrium droplet shapes and the theories but there were also some limitations of the nanoscale simulations.     

Wetting film stability and flotation kinetics

Single bubble experiments performed with different size fractions of quartz particles and different, but known, contact angles revealed two modes of flotation dynamics in superclean water. (1.) A monotonic increase of collection efficiency Ecoll with increasing particle size was observed at high particle hydrophobicity and, correspondingly, a low wetting film stability (WFS). (2.) At low particle hydrophobicity and, correspondingly, high WFS, an extreme dependence of Ecoll on particle size was observed. The use of superclean water in our experiments prevented the retardation of bubble surface movement caused by surfactants or other impurities that is usual for other investigations and where particle-bubble inertial hydrodynamic interactions are suppressed. In the present study the free movement of the bubble surface enhances particle-bubble inertial interaction, creating conditions for different flotation modes, dependent on WFS. At the instant of inertial impact, a particle deforms the bubble surface, which may cause its rebound. Where the stability of the thin water film, formed between opposing surfaces of a bubble and a particle, is low, its rupture is accompanied with three phase contact line extension and contact angle formation before rebound. This prevents rebound, i.e. the first collision is accompanied by attachment. A high WFS prevents rupture during an impact. As a result, a contact angle does not arise and rebound is not prevented. However, rebound is accompanied by a second collision, the kinetic energy of which is smaller and can cause attachment at repetitive collision. These qualitative considerations are confirmed by the model quantification and comparison with measured Ecoll. For the first time the Sutherland equation (SE) for Ecoll is confirmed by experiment for smaller particle sizes and, correspondingly, very small Stokes numbers. The larger the particle size, the larger is the measured deviation from the SE. The SE is generalized, accounting for the centrifugal force, pressing hydrodynamic force and drainage in the low WFS case and, correspondingly, attachment occurs at first collision or during sliding. The derived generalized Sutherland equation (GSE) describes experimental data at low WFS. However, its application without account for possible rebound does not explain the measured extreme dependence in the case of high WFS. The theory for drainage during particle impact and the beginning of rebound enables conditions for either attachment or rebound in terms of the normal component of the impact velocity and the critical film thickness to be derived. Combining this condition with the GSE allowed the equation for Ecoll to be derived, accounting for attachment area shrinkage and attachment during a repetitive collision. This equation predicts the extreme dependence. Thus the WFS determines the modes of flotation dynamics and, in turn, probably affects the mechanisms, which control the flotation domain. At low WFS its upper boundary is controlled by the stability of the particle-bubble aggregate. At high WFS the upper boundary can be controlled by rebound because the latter reduces the attachment efficiency by a factor of 30 or more even with repetitive collision.     

VOF simulations of the contact angle dynamics during the drop spreading: Standard models and a new wetting force model

Introduction

In this study,a novel numerical implementation for the adhesion of liquid droplets impacting normally on solid dry surfaces is presented. The advantage of this new approach, compared to the majority of existing models, is that the dynamic contact angle forming during the surface wetting process is not inserted as a boundary condition, but is derived implicitly by the induced fluid flow characteristics (interface shape) and the adhesion physics of the gas–liquid-surface interface (triple line), starting only from the advancing and receding equilibrium contact angles. These angles are required in order to define the wetting properties of liquid phases when interacting with a solid surface.

Methodology

The physical model is implemented as a source term in the momentum equation of a Navier-Stokes CFD flow solver as an “adhesion-like” force which acts at the triple-phase contact line as a result of capillary interactions between the liquid drop and the solid substrate. The numerical simulations capture the liquid–air interface movement by considering the volume of fluid (VOF) method and utilizing an automatic local grid refinement technique in order to increase the accuracy of the predictions at the area of interest, and simultaneously minimize numerical diffusion of the interface.

Results

The proposed model is validated against previously reported experimental data of normal impingement of water droplets on dry surfaces at room temperature. A wide range of impact velocities, i.e. Weber numbers from as low as 0.2 up to 117, both for hydrophilic (θ_adv = 10° – 70°) and hydrophobic (θ_adv = 105° – 120°) surfaces, has been examined. Predictions include in addition to droplet spreading dynamics, the estimation of the dynamic contact angle; the latter is found in reasonable agreement against available experimental measurements.

Conclusion

It is thus concluded that theimplementation of this model is an effective approach for overcoming the need of a pre-defined dynamic contact angle law, frequently adopted as an approximate boundary condition for such simulations. Clearly, this model is mostly influential during the spreading phase for the cases of low We number impacts (We < ˜80) since for high impact velocities, inertia dominates significantly over capillary forces in the initial phase of spreading.     

Covalently Attached Liquids: Instant Omniphobic Surfaces with Unprecedented Repellency

Recent strategies to prepare “omniphobic” surfaces have demonstrated that minimizing contact angle hysteresis (CAH) is the key criterion for effectiveness. CAH is affected by chemistry and topography defects at the molecular and higher levels, thus most surfaces exhibit significant CAH. Preparative methods for stable coatings on smooth substrates with negligible CAH (<2°) for a broad range of liquids have not been reported. In this work, we describe a simple and rapid procedure to prepare omniphobic surfaces that are stable under pressure and durable at elevated temperatures. Consistent with theory, they exhibit sliding angles that decrease with liquid surface tension. Slippery omniphobic covalently attached liquid (SOCAL) surfaces are obtained through acid‐catalyzed graft polycondensation of dimethyldimethoxysilane. The smooth, stable, and temperature‐resistant coatings show extremely low CAH (≤1°) and low sliding angles for liquids that span surface tensions from 78.2 to 18.4 mN m^?1.     

Design of a superhydrophobic surface using woven structures

The relationship between surface tension and roughness is reviewed. The Cassie-Baxter model is restated in its original form, which better describes the most general cases of surface roughness. Using mechanical and chemical surface modification of nylon 6,6 woven fabric, an artificial superhydrophobic surface was prepared. A plain woven fabric mimicking the Lotus leaf was created by further grafting 1H,1H-perfluorooctylamine or octadecylamine to poly(acrylic acid) chains which had previously been grafted onto a nylon 6,6 woven fabric surface. Water contact angles as high as 168 degrees were achieved. Good agreement between the predictions based on the original Cassie-Baxter model and experiments was obtained. The version of the Cassie-Baxter model in current use could not be applied to this problem since the surface area fractions in this form is valid only when the liquid is in contact with a flat, porous surface. The angle at which a water droplet rolls off the surface has also been used to define a superhydrophobic surface. It is shown that the roll-off angle is highly dependent on droplet size. The roll-off angles of these superhydrophobic surfaces were less than 5 degrees when a 0.5 mL water droplet was applied.     

Patterned nonadhesive surfaces: superhydrophobicity and wetting regime transitions

Nonadhesive and water-repellent surfaces are required for many tribological applications. We study mechanisms of wetting of patterned superhydrophobic Si surfaces, including the transition between various wetting regimes during microdroplet evaporation in environmental scanning electron microscopy (ESEM) and for contact angle and contact angle hysteresis measurements. Wetting involves interactions at different scale levels: macroscale (water droplet size), microscale (surface texture size), and nanoscale (molecular size). We propose a generalized formulation of the Wenzel and Cassie equations that is consistent with the broad range of experimental data. We show that the contact angle hysteresis involves two different mechanisms and how the transition from the metastable partially wetted (Cassie) state to the homogeneously wetted (Wenzel) state depends upon droplet size and surface pattern parameters.     

Two-dimensional fluidics based on differential lyophobicity and gravity

We have prepared planar fluidics devices using binary chemical patterns consisting of hydrophobic "roads" on which water droplets slide easily and more hydrophobic "curbs" that direct droplet motion. Contact angle and contact angle hysteresis both control the motion of liquid droplets on surfaces. The difference between the advancing contact angles of the two regions prevents the liquid from crossing the interface between them. The low hysteresis of the roads allows facile movement. Gravity (slight tilting of samples) forces droplets to move effortlessly in defined pathways even though the difference in contact angles is not large and both regions are hydrophobic.     

Particle capture processes and evaporation on a microscopic scale in wet filters

This paper details results of an experimental study of the capture of solid and liquid aerosols on fibrous filters wetted with water. A microscopic cell containing a single fibre (made from a variety of materials) was observed via a microscope, with a high speed CCD camera used to dynamically image the interactions between liquid droplets, zeolite and PSL particles and fibres. Variable quantities of liquid irrigation were used, and the possibility for subsequent fibre regeneration after clogging or drying was also studied. It was found that drainage of the wetting liquid (water) from the fibres occurred, even at very low irrigation rates when the droplet consisted almost completely of captured particles. It was also found that the fibre was rapidly loaded with captured particles when the irrigation was not supplied. However, almost complete regeneration (removal of the collected cake) by the liquid droplets occurred shortly after recommencement of the water supply. The study also examined the capture of oily liquid aerosols on fibres wetted with water. A predominance of the barrel shaped droplet on the fibre was observed, with oil droplets displacing water droplets (if the oil and fibre combination created a barrel shaped droplet), creating various compound droplets of oil and water not previously reported in literature. This preferential droplet shape implies that whatever the initial substance wetting a filter, a substance with a greater preferential adherence to the fibre will displace the former one.     

Effects of interface mobility on the dynamics of colliding bubbles

At its core, the outcome of the collision between air bubbles is determined by the hydrodynamic interaction forces, which in turn are strongly dependent on the tangential mobility of the gas–liquid interfaces. A clean gas–liquid interface is tangentially mobile, whereas the presence of surfactant contaminants can immobilise the interface. Bubbles with mobile surfaces coalescence much easier because of the low hydrodynamic resistance to drainage of the thin liquid film separating the colliding bubbles. In this opinion, we highlight recent experimental and numerical simulations demonstrating that in addition to the expected faster coalescence, mobile-surface bubbles can produce a much stronger rebound from a mobile liquid interface compared to an immobile one. The stronger rebound is explained by the lower viscous dissipation during collisions involving mobile surfaces. The role of the surface mobility in controlling the stability of gas or liquid emulsion should be reassessed in the light of these new findings.     

Modeling contact angle hysteresis of a liquid droplet sitting on a cosine wave-like pattern surface

A liquid droplet sitting on a hydrophobic surface with a cosine wave-like square-array pattern in the Wenzel state is simulated by using the Surface Evolver to determine the contact angle. For a fixed drop volume, multiple metastable states are obtained at two different surface roughnesses. Unusual and non-circular shape of the three-phase contact line of a liquid droplet sitting on the model surface is observed due to corrugation and distortion of the contact line by structure of the roughness. The contact angle varies along the contact line for each metastable state. The maximum and minimum contact angles among the multiple metastable states at a fixed viewing angle correspond to the advancing and the receding contact angles, respectively. It is interesting to observe that the advancing/receding contact angles (and contact angle hysteresis) are a function of viewing angle. In addition, the receding (or advancing) contact angles at different viewing angles are determined at different metastable states. The contact angle of minimum energy among the multiple metastable states is defined as the most stable (equilibrium) contact angle. The Wenzel model is not able to describe the contact angle along the three-phase contact line. The contact angle hysteresis at different drop volumes is determined. The number of the metastable states increases with increasing drop volume. Drop volume effect on the contact angles is also discussed.