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.     

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.     

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.     

Effects of contact angle hysteresis on ice adhesion and growth on superhydrophobic surfaces under dynamic flow conditions

In this paper, the icephobic properties of superhydrophobic surfaces are investigated under dynamic flow conditions using a closed-loop low-temperature wind tunnel. Superhydrophobic surfaces were prepared by coating aluminum and steel substrate plates with nano-structured hydrophobic particles. The superhydrophobic plates, along with uncoated controls, were exposed to a wind tunnel air flow of 12 m/s and ?7 °C with deviations of ±1 m/s and ±2.5 °C, respectively, containing micrometer-sized (～50 μm in diameter) water droplets. The ice formation and accretion were observed by CCD cameras. Results show that the superhydrophobic coatings significantly delay ice formation and accretion even under the dynamic flow condition of highly energetic impingement of accelerated supercooled water droplets. It is found that there is a time scale for this phenomenon (delay in ice formation) which has a clear correlation with contact angle hysteresis and the length scale of the surface roughness of the superhydrophobic surface samples, being the highest for the plate with the lowest contact angle hysteresis and finest surface roughness. The results suggest that the key for designing icephobic surfaces under the hydrodynamic pressure of impinging droplets is to retain a non-wetting superhydrophobic state with low contact angle hysteresis, rather than to only have a high apparent contact angle (conventionally referred to as a “static” contact angle).     

Influence of the dynamic contact angle on the characterization of porous media

It has been shown recently that the classical Lucas-Washburn equation, often used to model the dynamics of liquid penetration into porous media, should be modified to take account of the dynamic contact angle between the liquid and the pore. Here we show how neglect of this effect can lead to significant errors in estimation of the effective pore radius.     

Bioadhesion to solids: contact angle hysteresis effect

It was recently reported that the ease of removal of sporelings of green seaweed Ulva under shear stress from the polymer surfaces was found to be linearly and positively correlated with contact angle and wetting hysteresis, i.e., the higher the hysteresis, the greater the removal. Motivated by this report, we examined the relationship between the bioadhesion of blood platelets and proteins with contact angle hysteresis of solid substrates using the data of published papers. It was determined that there is a linear and positive relationship between the contact angle hysteresis and bioadhesion of both blood platelets and γ-globulin protein contacting the solid substrates, i.e., the higher the hysteresis, the greater the bioadhesion. The reasons are discussed and it is proposed that testing the effect of CAH on the adhesion strengths of biomaterials on surfaces is useful in order to gain a better insight on the bioadhesion mechanism.     

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.     

Static contact angle hysteresis on smooth, homogeneous solid substrates

A theory of contact angle hysteresis on smooth, homogeneous solid substrates is developed in terms of shape of disjoining/conjoining pressure isotherm and quasi-equilibrium phenomena. It is shown that all contact angles, θ, in the range θ _r?<?θ?<?θ _a, which are different from the unique equilibrium contact angle θ?≠?θ _e, correspond to the state of slow “microscopic” advancing or receding motion of the liquid if θ _e ?<?θ?<?θ _a or θ _r?<?θ?<?θ _e, respectively. This “microscopic” motion almost abruptly becomes fast “macroscopic” advancing or receding motion after the contact angle reaches the critical values θ?=?θ _a or θ _r?=?θ, correspondingly. The values of the static receding, θ _r, and static advancing, θ _a, contact angles in cylindrical capillaries were calculated earlier, based on the shape of disjoining pressure isotherm. It is shown that an advancing contact angle of a droplet on a solid substrate depends on the drop volume and is not a unique characteristic of the liquid–solid system. The suggested mechanism of contact angle hysteresis has direct experimental confirmation.     

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.     

Effect of contact angle hysteresis on the measurement of capillary forces

We conduct experimental investigations of macroscopic capillary forces between two flat rigid substrates characterized by their advancing and receding contact angles with water. Our results exhibit excellent agreement with theoretical predictions obtained by the numerical solution of the capillary equation. On the basis of this comparison, we use the measurements of the capillary force to investigate the phenomenon of contact angle hysteresis. We present examples of force measurements for surfaces that display low, moderate, and high contact angle hysteresis and compare results for a larger variety of substrates. Finally, we show that for the case of water, the role of viscosity is insignificant within the range of force and velocity measured in the present work.     

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.     

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.     

Anomalous contact angle hysteresis of a captive bubble: advancing contact line pinning

Contact angle hysteresis of a sessile drop on a substrate consists of continuous invasion of liquid phase with the advancing angle (θ(a)) and contact line pinning of liquid phase retreat until the receding angle (θ(r)) is reached. Receding pinning is generally attributed to localized defects that are more wettable than the rest of the surface. However, the defect model cannot explain advancing pinning of liquid phase invasion driven by a deflating bubble and continuous retreat of liquid phase driven by the inflating bubble. A simple thermodynamic model based on adhesion hysteresis is proposed to explain anomalous contact angle hysteresis of a captive bubble quantitatively. The adhesion model involves two solid–liquid interfacial tensions (γ(sl) > γ(sl)′). Young’s equation with γ(sl) gives the advancing angle θ(a) while that with γ(sl)′ due to surface rearrangement yields the receding angle θ(r). Our analytical analysis indicates that contact line pinning represents frustration in surface free energy, and the equilibrium shape corresponds to a nondifferential minimum instead of a local minimum. On the basis of our thermodynamic model, Surface Evolver simulations are performed to reproduce both advancing and receding behavior associated with a captive bubble on the acrylic glass.     

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.     

Surface free energy of a solid from contact angle hysteresis

Nature of contact angle hysteresis is discussed basing on the literature data (Colloids Surf. A 189 (2001) 265) of dynamic advancing and receding contact angles of n-alkanes and n-alcohols on a very smooth surface of 1,1,2,-trichloro-1,2,2,-trifluoroethane (FC-732) film deposited on a silicon plate. The authors considered the liquid absorption and/or retention (swelling) processes responsible for the observed hysteresis. In this paper hysteresis is considered to be due to the liquid film left behind the drop during retreating of its contact line. Using the contact angle hysteresis an approach is suggested for evaluation of the solid surface free energy. Molecular spacing and the film structure are discussed to explain the difference in n-alkanes and n-alcohols behaviour as well as to explain the difference between dispersion free energy gamma(s)(d) and total surface free energy gamma(s)(tot) of FC-732, as determined from the advancing contact angles and the hysteresis, respectively.     

From substrate disorder to contact angle hysteresis, and back

Based on Monte Carlo simulation of the contact line as a long-range elastic model, we develop tools relating substrate traps, trapping time and trapping length. We demonstrate the possibility of retrieving some information on the substrate topography from measurements of contact line motion, near the threshold in forced spreading or near the advancing angle in spontaneous spreading.     

The modified Cassie’s equation and contact angle hysteresis

In this paper, we derive a modified Cassie’s equation for wetting on chemically patterned surfaces from a homogenization approach. The derivation reveals that effective contact angle is a local average of the static contact angle along the contact line which describes all possible equilibrium states including the local minimum of the free energy of the system. The usual Cassie’s state which corresponds to the global minimum is only a special case. We then discuss the contact angle hysteresis on chemically patterned surfaces.     

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.     

On the role of energy barriers in determining contact angle hysteresis

The thermodynamic model of contact angles on rough, heterogeneous surfaces developed by Long et al. [J. Long, M.N. Hyder, R.Y.M. Huang and P. Chen, Adv. Colloid Interface Sci. 118 (2005) 173] was employed to study the role of energy barriers in determining contact angle hysteresis. Major energy barriers corresponding to metastable states and minor energy barriers corresponding to secondary metastable states were defined. Distributions of major and/or minor energy barriers as a function of apparent contact angle for various surfaces were obtained. The reproducibility of contact angle measurement, the effect of vibrational energy on contact angle hysteresis and the "stick-slip" phenomenon were discussed. Quantitative relations between contact angles and vibrational energy were obtained. It was found that receding contact angles are normally poorly reproducible for hydrophilic surfaces, but for extremely hydrophobic surfaces, advancing contact angles may have a poor reproducibility. When the vibrational energy available to a system increases, the measured advancing contact angle will decrease while the receding angle will increase until both reach a common value: the system equilibrium angle. This finding not only agrees well with the experimental observations in system equilibrium contact angle measurements, but also lays a theoretical foundation for such measurements. A small vibrational energy may result in a "stick-slip" phenomenon.     

Effect of dynamic contact angle on capillary rise phenomena

Capillary rise experiments of different liquids in glass capillaries and in columns of packed powders were carried out. The analysis of this rise was performed according to the classical Washburn’s equation in which the calculation of a constant term is needed in order to be able to determine contact angle of the considered liquid on the capillary wall or powders. However, it was observed that this constant term apparently varies as a function of the liquid used, in contradiction with Washburn’s approach. A more fundamental study of alkane rise into glass capillaries was carried out showing that this apparent variation is due to the variation of contact angles, which can take large values (up to 60°) as a function of velocity of the liquid front, although their expected value is 0°. Therefore, in the case of powders, different approaches to determine the real constant term with respect to particle size are proposed. Consequently, the use of Washburn’s equation for the determination of contact angles of liquids on these powders is also discussed.