Modeling contact angle hysteresis on chemically patterned and superhydrophobic surfaces

We investigate contact angle hysteresis on chemically patterned and superhydrophobic surfaces, as the drop volume is quasistatically increased and decreased. We consider both two (cylindrical drops) and three (spherical drops) dimensions using analytical and numerical approaches to minimize the free energy of the drop. In two dimensions, we find, in agreement with other authors, a slip, jump, stick motion of the contact line. In three dimensions, this behavior persists, but the position and magnitude of the contact line jumps are sensitive to the details of the surface patterning. In two dimensions, we identify analytically the advancing and receding contact angles on the different surfaces, and we use numerical insights to argue that these provide bounds for the three-dimensional cases. We present explicit simulations to show that a simple average over the disorder is not sufficient to predict the details of the contact angle hysteresis and to support an explanation for the low contact angle hysteresis of suspended drops on superhydrophobic surfaces.     

Hydrophobic/superhydrophobic oxidized metal surfaces showing negligible contact angle hysteresis

The blood coagulation system relies on lipid membrane constituents to act as regulators of the coagulation process upon vascular trauma, and in particular the 2D configuration of the lipid membranes is known to efficiently catalyze enzymatic activity of blood coagulation factors. This work demonstrates a new application of a recently developed methodology to study blood coagulation at lipid membrane interfaces with the use of imaging technology. Lipid membranes with varied net charges were formed on silica supports by systematically using different combinations of lipids where neutral phosphocholine (PC) lipids were mixed with phospholipids having either positively charged ethylphosphocholine (EPC), or negatively charged phosphatidylserine (PS) headgroups. Coagulation imaging demonstrated that negatively charged SiO(2) and membrane surfaces exposing PS (obtained from liposomes containing 30% of PS) had coagulation times which were significantly shorter than those for plain PC membranes and EPC exposing membrane surfaces (obtained from liposomes containing 30% of EPC). Coagulation times decreased non-linearly with increasing negative surface charge for lipid membranes. A threshold value for shorter coagulation times was observed below a PS content of ～6%. We conclude that the lipid membranes on solid support studied with the imaging setup as presented in this study offers a flexible and non-expensive solution for coagulation studies at biological membranes. It will be interesting to extend the present study towards examining coagulation on more complex lipid-based model systems.     

A thermodynamic approach for determining the contact angle hysteresis for superhydrophobic surfaces

Contact angle hysteresis (CAH) is critical to superhydrophobicity of a surface. This study proposes a free energy thermodynamic analysis (of a 2-D model surface) that significantly simplifies calculations of free energy barrier associated with CAH phenomena. A microtextured surface with pillar structure, typical of one used in experimental studies, is used as an example. We demonstrate that the predicted CAH and equilibrium contact angles are consistent with experimental observations and predictions of Wenzel's and Cassie's equations, respectively. We also establish a criterion for transition between noncomposite and composite wetting states. The results and methodology presented can potentially be used for designing superhydrophobic surfaces.     

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.     

Slip-stick wetting and large contact angle hysteresis on wrinkled surfaces

Wetting on a corrugated surface that is formed via wrinkling of a hard skin layer formed by UV oxidation (UVO) of a poly(dimethylsiloxane) (PDMS) slab is studied using advancing and receding water contact angle measurements. The amplitude of the wrinkled pattern can be tuned through the pre-strain of the PDMS prior to surface oxidation. These valleys and peaks in the surface topography lead to anisotropic wetting by water droplets. As the droplet advances, the fluid is free to move along the direction parallel to the wrinkles, but the droplet moving orthogonal to the wrinkles encounters energy barriers due to the topography and slip-stick behavior is observed. As the wrinkle amplitude increases, anisotropy in the sessile droplet increases between parallel and perpendicular directions. For the drops receding perpendicular to the wrinkles formed at high strains, the contact angle tends to decrease steadily towards zero as the drop volume decreases, which can result in apparent hysteresis in the contact angle of over 100°. The wrinkled surfaces can exhibit high sessile and advancing contact angles (>115°), but the receding angle in these cases is generally vanishing as the drop is removed. This effect results in micrometer sized drops remaining in the grooves for these highly wrinkled surfaces, while the flat analogous UVO-treated PDMS shows complete removal of all macroscopic water drops under similar conditions. These wetting characteristics should be considered if these wrinkled surfaces are to be utilized in or as microfluidic devices.     

Droplet compression and relaxation by a superhydrophobic surface: contact angle hysteresis

In this article, the contact angle hysteresis (CAH) of acrylic glass is experimentally and theoretically studied through the compression-relaxation process of droplets by using a superhydrophobic surface with negligible CAH effect. In contrast to the existing technique in which the volume of the droplet changes during the measurement of CAH, this procedure is carried out at a constant volume of the droplet. By observing the base diameter (BD) and the contact angle (CA) of the droplet during the compression-relaxation process, the wetting behavior of the droplet can be divided into two regimes, the contact line withdrawal and the contact line pinning regimes, depending on the gap thickness (H) at the end of the compression process. During the compression process, both regimes possess similar droplet behavior; the contact line will move outward and the BD will expand while the CA remains at the advancing angle. During the relaxation process, the two regimes are significantly different. In the contact line withdrawal regime, the contact line will withdraw with the CA remaining at the receding angle. In the contact line pinning regime, however, the contact line will be pinned at the final position and the CA will decline to a certain value higher than the receding angle. Furthermore, the advancing pinning behavior can also be realized through a successive compression-relaxation process. On the basis of the liquid-induced defects model, Surface Evolver simulations are performed to reproduce the behavior of the droplet during the compression-relaxation process; both contact line withdrawal and pinning regimes can also be identified. The results of the experiment and simulation agree with each other very well.     

Influence of surfactant transport suppression on dynamic contact angle hysteresis

The influence of local and nonlocal transport processes of cetyltrimethylammonium bromide (CTAB) molecules on dynamic contact angles and contact angle hysteresis was studied in a rotating drum setup. The influence of long-range surfactant transport was analyzed by hindering selectively the surface or the bulk transport via movable barriers. With increasing hindrance of the surfactant transport, the receding contact angle decreased at all withdrawing velocities in the presence of CTAB. The control experiment with pure water was unaffected by the presence of the barriers. Dynamic contact angles are, therefore, not only influenced by short-range effects like Marangoni stresses close to the contact line, but also by long-range transport processes (like diffusion and advection) between the regions close to the receding and advancing contact lines.     

Stabilizing contact angle hysteresis of paraffin wax surfaces with nanoclay

The addition of montmorillonite clay modified with an alkylammonium salt surfactant (i.e., organoclay) to paraffin wax is found to reduce the decay in wetting properties associated with its heating in the melt. It was previously shown that holding wax in its molten form prior to characterization reduces crystallinity when the solid forms. This results in the development of microscale amorphous regions at wax surfaces, which appear to be more polar given the abundance of methylene linkages versus methyl groups. These regions are believed to impact the receding angles for more polar liquids almost exclusively. It is known that the introduction and exfoliation of a small amount of the organoclay greatly enhances the stiffness, strength, and toughness of paraffin wax. Here, it is shown that the organoclay also promotes the formation of coatings possessing fewer thermal cracks and helps maintain higher crystallinity levels. Fresh wax surfaces containing the clay are slightly rougher than those without, which produces a slight increase in hysteresis. However, the significant drops in receding angles found for paraffin wax samples cast from the melt subsequent to heating are absent.     

Impact of surface forces on wetting of hierarchical surfaces and contact angle hysteresis

The influence of the long-range surface forces on the wetting of multi-scale partially wetted surfaces is discussed. The possibility of partial wetting is stipulated by a specific form of the Derjaguin isotherm. Equilibrium of a liquid meniscus inside a cylindrical capillary is used as a model. The interplay of capillary and disjoining pressures governs the equilibrium of the liquid in the nano- and micrometrically scaled pores constituting the relief of the surface. It is shown that capillaries with a radius smaller than a critical one will be completely filled by water, whereas the larger capillaries will be filled only partially. Thus, small capillaries will show the Wenzel type of wetting behavior, while the same liquid inside the large capillaries will promote the Cassie-Baxter type of wetting. Consideration of disjoining/conjoining pressure allows explaining of the “rose petal effect”, when a high apparent contact angle is accompanied with a high contact angle hysteresis.     

Contact angle hysteresis: study by dynamic cycling contact angle measurements and variable angle spectroscopic ellipsometry on polyimide

The phenomenon of contact angle hysteresis was studied on smooth films of polyimide, a polymer type used in the microelectronic industry, by dynamic cycling contact angle measurements based on axisymmetric drop shape analysis-profile in combination with variable angle spectroscopic ellipsometry (VASE). It was found that both advancing and receding contact angles became smaller with increasing the number of cycles and are, therefore, not a property of the dry solid alone. The changes of the wetting behavior during these dynamic cycling contact angle measurements are attributed mainly to swelling and/or liquid retention. To reveal the water-induced changes of the polymer film, the polyimide surface was studied before and after the contact with a water droplet by VASE. Both the experimental ellipsometric spectrum for Delta and that for Psi as well as the corresponding simulations show characteristic shifts due to the contact with water. The so-called effective medium approximation was applied to recover information about the thickness and effective optical constants of the polymer layer from the ellipsometrically measured values of Delta and Psi. On the basis of these results, the swelling and retention behavior of the polyimide films in contact with water droplets were discussed.     

Air-facilitated three-phase contact formation at hydrophobic solid surfaces under dynamic conditions

The paper presents results documenting the mechanism of facilitation of the three-phase contact (TPC) formation due to gas entrapped during immersion of hydrophobic (Teflon) plates into distilled water and n-octanol solutions. Collisions, bouncing, the time scale of the TPC formation, and bubble attachment to Teflon plates of different surface roughness were studied using a high-speed camera. Processes occurring during the microscopic wetting film formation at the Teflon plates were monitored using the microinterferometric method (Scheludko-Exerowa cell). A strong relation between the time necessary to form a stable TPC and the roughness of the Teflon was observed. The higher the Teflon roughness was the shorter the time for the TPC formation. This effect can be attributed to two factors: (i) local differences in the thickness of the thinning intervening liquid layer (quicker attainment of rupture thickness at pillars of rough surface) and/or (ii) the presence of gas at the hydrophobic surface. Experimental findings, that (i) prolongation of the plate immersion time resulted in quicker TPC formation, (ii) white irregular and disappearing spots (air pockets) were recorded during the wetting film formation, and (iii) high n-octanol concentration caused prolongation of the time of the TPC formation, show that attachment (TPC formation) of the colliding bubble to hydrophobic surfaces was facilitated by air entrapped at the Teflon plates (and re-distributed) during their immersion into water phase. Thus, on collision instead of solid/gas wetting liquid film a thin gas/liquid/gas foam film was formed which facilitated the TPC formation.     

Fabrication of surfaces with extremely high contact angle hysteresis from polyelectrolyte multilayer

High contact angle hysteresis on polyelectrolyte multilayers (PEMs) ion-paired with hydrophobic perfluorooctanoate anions is reported. Both the bilayer number of PEMs and the ionic strength of deposition solutions have significant influence on contact angle hysteresis: higher ionic strength and greater bilayer number cause increased contact angle hysteresis values. The hysteresis values of ~100° were observed on smooth PEMs and pinning of the receding contact line on hydrophilic defects is implicated as the cause of hysteresis. Surface roughness can be used to further tune the contact angle hysteresis on the PEMs. A surface with extremely high contact angle hysteresis of 156° was fabricated when a PEM was deposited on a rough substrate coated with submicrometer scale silica spheres. It was demonstrated that this extremely high value of contact angle hysteresis resulted from the penetration of water into the rough asperities on the substrate. The same substrate hydrophobized by chemical vapor deposition of 1H,1H,2H,2H-perfluorooctyltriethoxysilane exhibits high advancing contact angle and low hysteresis.     

Modeling receding contact lines on superhydrophobic surfaces

We use mesoscale simulations to study the depinning of a receding contact line on a superhydrophobic surface patterned by a regular array of posts. For the simulations to be feasible, we introduce a novel geometry where a column of liquid dewets a capillary bounded by a superhydrophobic plane that faces a smooth hydrophilic wall of variable contact angle. We present results for the dependence of the depinning angle on the shape and spacing of the posts and discuss the form of the meniscus at depinning. We find, in agreement with ref 17 , that the local post concentration is a primary factor in controlling the depinning angle and show that the numerical results agree well with recent experiments. We also present two examples of metastable pinned configurations where the posts are partially wet.     

Surface heterogeneity and contact angle hysteresis

The effect of surface heterogeneity on contact angle hysteresis is studied by using the model of Neumann and Good of a vertical plate with horizontal heterogeneous strips. The results of this study explain well known, but not understood patterns of contact angle behaviour: On the one hand, the advancing contact angle on a carefully prepared solid surface is generally reproducible; on the other hand, even a very small amount of surface heterogeneity may cause the receding contact angle to be less reproducible and to depend on several non-thermodynamic factors.     

Predictive model for ice formation on superhydrophobic surfaces

The prevention and control of ice accumulation has important applications in aviation, building construction, and energy conversion devices. One area of active research concerns the use of superhydrophobic surfaces for preventing ice formation. The present work develops a physics-based modeling framework to predict ice formation on cooled superhydrophobic surfaces resulting from the impact of supercooled water droplets. This modeling approach analyzes the multiple phenomena influencing ice formation on superhydrophobic surfaces through the development of submodels describing droplet impact dynamics, heat transfer, and heterogeneous ice nucleation. These models are then integrated together to achieve a comprehensive understanding of ice formation upon impact of liquid droplets at freezing conditions. The accuracy of this model is validated by its successful prediction of the experimental findings that demonstrate that superhydrophobic surfaces can fully prevent the freezing of impacting water droplets down to surface temperatures of as low as -20 to -25 °C. The model can be used to study the influence of surface morphology, surface chemistry, and fluid and thermal properties on dynamic ice formation and identify parameters critical to achieving icephobic surfaces. The framework of the present work is the first detailed modeling tool developed for the design and analysis of surfaces for various ice prevention/reduction strategies.     

Ratchetlike slip angle anisotropy on printed superhydrophobic surfaces

The fabrication and properties of superhydrophobic surfaces that exhibit ratchet-like anisotropic slip angle behavior is described. The surface is composed of arrays of poly(dimethylsiloxane) (PDMS) posts fabricated by a type of 3D printing. By controlling the dispense parameters, regular arrays of asymmetric posts were deposited such that the slope of the posts was varied from 0 to 50 relative to the surface normal. Advancing and receding contact angles as well as slip angles were measured as a function of the post slope and droplet volume. Ratchetlike slip angle anisotropy was observed on surfaces composed of sloped features. The maximum slip angle difference (for a 180° tilt angle variation) was 32° for 20 μL droplets on surfaces with posts fabricated with a slope of 50°. This slip angle anisotropy is attributed to an increase in the triple contact line (TCL) length as the droplet is tilted in a direction against the post slope whereas the TCL decreases continuously when the drop travels in a direction parallel to the post slope. The increasing length of the TCL creates an increased energy barrier that accounts for the higher slip angles in this direction.     

Effect of orientation and mobility of polymer molecules at surfaces on contact angle and its hysteresis

The contact angle of a water droplet on the surface of a solid polymer or hydrogel (water-swollen three-dimensional network) depends on whether a hydrophilic moiety of the polymer molecule is oriented towards the air interface or towards the bulk of the solid, but not on the hydrophilicity of the molecule. Therefore, the short-range rotational mobility of a polymer molecule has a major influence on the apparent hydrophilicity of a polymer surface as measured by the contact angle of water. By the came principle, the abnormally large hysteresis effect observed in advancing and receding contact angles of water on some polymer surfaces can be attributed to the reorientation of hydrophilic moieties of polymer molecules at the surface. These factors are demonstrated by selected polymer surfaces with different degrees of mobility at the polymer-air interface.     

Constitutive modeling of contact angle hysteresis

We introduce a phase field model of wetting of surfaces by sessile drops. The theory uses a two-dimensional non-conserved phase field variable to parametrize the Gibbs free energy of the three-dimensional system. Contact line tension and contact angle hysteresis arise from the gradient term in the free energy and the kinetic coefficient respectively. A significant advantage of this approach is in the constitutive specification of hysteresis. The advancing and receding angles of a surface, the liquid-vapor interfacial energy and three-phase line tension are the only required constitutive inputs to the model. We first simulate hysteresis on a smooth chemically homogeneous surface using this theory. Next we show that it is possible to study heterogeneous surfaces whose component surfaces are themselves hysteretic. We use this theory to examine the wetting of a surface containing a circular heterogeneous island. The contact angle for this case is found to be determined solely by the material properties at the contact line in accord with recent experimental data.     

Contact angle hysteresis on regular pillar-like hydrophobic surfaces

A series of pillar-like patterned silicon wafers with different pillar sizes and spacing are fabricated by photolithography and further modified by a self-assembled fluorosilanated monolayer. The dynamic contact angles of water on these surfaces are carefully measured and found to be consistent with the theoretical predictions of the Cassie model and the Wenzel model. When a water drop is at the Wenzel state, its contact angle hysteresis increases along with an increase in the surface roughness. While the surface roughness is further raised beyond its transition roughness (from the Wenzel state to the Cassie state), the contact angle hysteresis (or receding contact angle) discontinuously drops (or jumps) to a lower (or higher) value. When a water drop is at the Cassie state, its contact angle hysteresis strongly depends on the solid fraction and has nothing to do with the surface roughness. Even for a superhydrophobic surface, the contact angle hysteresis may still exhibit a value as high as 41 degrees for the solid fraction of 0.563.     

Motion of liquid drops on surfaces induced by asymmetric vibration: role of contact angle hysteresis

Hysteresis of wetting, like the Coulombic friction at solid/solid interface, impedes the motion of a liquid drop on a surface when subjected to an external field. Here, we present a counterintuitive example, where some amount of hysteresis enables a drop to move on a surface when it is subjected to a periodic but asymmetric vibration. Experiments show that a surface either with a negligible or high hysteresis is not conducive to any drop motion. Some finite hysteresis of contact angle is needed to break the periodic symmetry of the forcing function for the drift to occur. These experimental results are consistent with simulations, in which a drop is approximated as a linear harmonic oscillator. The experiment also sheds light on the effect of the drop size on flow reversal, where drops of different sizes move in opposite directions due to the difference in the phase of the oscillation of their center of mass.