On some relations between advancing, receding and Young's contact angles

Problems of experimental determination and theoretical verification of equilibrium contact angles are discussed basing on the literature data. A relationship between the advancing and receding contact angles versus the equilibrium contact angle is described and then verified using the literature contact angles determined on paraffin wax and polypropylene. Using the proposed relationship and experimentally determined equilibrium contact angles, obtained by plotting the advancing and receding contact angles versus the contact angle hysteresis or by applying vibration of the system liquid drop/solid surface, it is found that the same value of the surface free energy for paraffin wax is calculated from the contact angles of water and ethylene glycol. However, in the case of polypropylene some inconsistency appears between the equilibrium contact angles of the probe liquid used and the calculated surface free energy. More experimental data of the equilibrium contact angle are needed to verify further the relationship.     

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.     

Line energy and the relation between advancing, receding, and young contact angles

The line energy associated with the triple phase contact line is a function of local surface defects (chemical and topographical); however, it can still be calculated from the advancing and receding contact angles to which those defects give rise. In this study an expression for the line energy associated with the triple phase contact line is developed. The expression relates the line energy to the drop volume, the interfacial energies, and the actual contact angle (be it advancing, receding, or in between). From the expression we can back calculate the equilibrium Young contact angle, theta0, as a function of the maximal advancing, thetaA, and minimal receding, thetaR, contact angles. To keep a certain maximal hysteresis between advancing and receding angles, different line energies are required depending on the three interfacial energies and the drop's volume V. We learn from the obtained expressions that the hysteresis is determined by some dimensionless parameter, K, which is some normalized line energy. The value of K required to keep a constant hysteresis (thetaA-thetaR) rises to infinity as we get closer to theta0 = 90 degrees.     

Replacing the solid needle by a liquid one when measuring static and advancing contact angles

In general, the optical determination of static and advancing contact angle is made on drops applied or extended, respectively, onto a substrate through the use of thin solid needles. Although this method is used extensively, this way of dosing can be time consuming, cumbersome and if not performed meticulously can lead to erroneous results. Herein, we present an alternative way of applying drops onto substrates using a liquid jet produced by a liquid pressure dosing system acting as a “liquid needle”. We performed a comparative static contact angle study on 14 different surfaces with two different liquids (water and diiodomethane) utilizing two different ways of dosing: the conventional solid and a novel liquid needle-based technique. We found, for all but one sample, that the obtained results on μl size drops were comparable within the experimental error bars provided the liquid needle is thin enough. Observed differences are explained by the special characteristics of either way of dosing. In addition, we demonstrate how the liquid pressure-based dosing system facilitates high-speed optical advancing contact angle measurement by expanding a drop from 0.1 to 22 μl within less than 1.2 s but yet providing constant contact angle versus drop base diameter curves. The obtained results were compared with data from tensiometric dynamic Wilhelmy contact angle measurements. These data, in conjunction with sequences of live images of the dosing process of the liquid pressure dosing system, illustrate how this system can replace the solid needle by a liquid needle.     

Dynamic contact angles and hysteresis under electrowetting-on-dielectric

By designing and implementing a new experimental method, we have measured the dynamic advancing and receding contact angles and the resulting hysteresis of droplets under electrowetting-on-dielectric (EWOD). Measurements were obtained over wide ranges of applied EWOD voltages, or electrowetting numbers (0 ≤ Ew ≤ 0.9), and droplet sliding speeds, or capillary numbers (1.4 × 10(-5) ≤ Ca ≤ 6.9 × 10(-3)). If Ew or Ca is low, dynamic contact angle hysteresis is not affected much by the EWOD voltage or the sliding speed; that is, the hysteresis increases by less than 50% with a 2 order-of-magnitude increase in sliding speed when Ca < 10(-3). If both Ew and Ca are high, however, the hysteresis increases with either the EWOD voltage or the sliding speed. Stick-slip oscillations were observed at Ew > 0.4. Data are interpreted with simplified hydrodynamic (Cox-Voinov) and molecular-kinetic theory (MKT) models; the Cox-Voinov model captures the trend of the data, but it yields unreasonable fitting parameters. MKT fitting parameters associated with the advancing contact line are reasonable, but a lack of symmetry indicates that a more intricate model is required.     

Water contact angles and hysteresis of polyamide surfaces

The wetting behavior of a series of aliphatic polyamides (PAs) has been examined. PAs with varying amide content and polyethylene (PE) were molded against glass to produce surfaces with similar roughness. After cleaning, chemical composition of the surfaces was verified with X-ray photoelectron spectroscopy. Advancing and receding contact angles were measured from small sessile water drops. Contact angles decreased with amide content while hysteresis increased. Hysteresis arose primarily from molecular interactions between the contact liquid and the solid substrates, rather than moisture absorption, variations in crystallinity, surface deformation, roughness, reorientation of amide groups, or surface contamination. Free energies of hysteresis were calculated from contact angles. For PE, which is composed entirely of nonpolar methylene groups, free energies were equivalent to the strength of dispersive van der Waals bonds. For PAs, free energies corresponded to fractional contributions from the dispersive methylene groups and polar amide groups.     

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.     

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.     

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.     

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.     

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.     

The dynamic contact angle I. Dependence of the receding contact angle on velocity in the surfactant-containing three-phase system

Spontaneous three-phase contact (tpc) motion is investigated in order to determine the dependence of the static contact angle on tpc velocity in surfactant-containing systems after recession. To interpret the experimental results, the molecular-kinetic sitechanging theory and the hydrodynamic theory were considered. It is shown that, especially at very high tpc velocities, the experimental results are not thoroughly described by these theories. The deviations are explained as a surfactant transfer from the liquid/gas to the solid/gas interface which, under insufficient afterdiffusion, leads to an increase in surface tension and to a changed surface rheology. This mechanism could be governed by a model.     

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.     

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.     

Drops sitting on a tilted plate: receding and advancing pinning

The wetting behavior of a liquid drop sitting on an inclined plane is investigated experimentally and theoretically. Using Surface Evolver, the numerical simulations are performed based on the liquid-induced defect model, in which only two thermodynamic parameters (solid-liquid interfacial tensions before and after wetting) are required. A drop with contact angle (CA) equal to θ is first placed on a horizontal plate, and then the plate is tilted. Two cases are studied: (i) θ is adjusted to the advancing CA (θ(a)) before tilting, and (ii) θ is adjusted to the receding CA (θ(r)) before tilting. In the first case, the uphill CA declines and the downhill CA remains unchanged upon inclination. When the tilted drop stays at rest, the pinning of the receding part of the contact line (receding pinning) and the depinning of the advancing part of the contact line (advancing depinning) are observed. The free energy analysis reveals that upon inclination, the reduction of the solid-liquid free energy dominates over the increment of the liquid-gas free energy associated with shape deformation. In the second case, the downhill CA grows and the uphill CA remains the same upon inclination. Advancing pinning and receding depinning are noted for the tilted drop at rest. The free energy analysis indicates that upon inclination, the decrease of the liquid-gas free energy compensates the increment of the solid-liquid free energy. The experimental results are in good agreement with those of simulations.     

Contact angles and their hysteresis as a measure of liquid-solid adhesion

The wetting behavior of a series of aliphatic polyamides was examined. Polyamides and polyethylene were molded against glass to produce smooth surfaces. After cleaning, chemical composition of the surfaces was verified with X-ray photoelectron spectroscopy. Advancing and receding contact angles were measured from small sessile water drops. Contact angles decreased with amide content while contact angle hysteresis increased. Wetting free energies calculated from contact angles were equal to those from dewetting, suggesting that contact angle hysteresis did not arise from surface anomalies, but from hydrogen bonding between water and the amide groups in the polyamide surfaces.     

Drops down the hill: theoretical study of limiting contact angles and the hysteresis range on a tilted plate

The limiting inclination angle (slip angle), for which a two-dimensional water drop may be at equilibrium on a chemically heterogeneous surface, is exactly calculated for a variety of cases. The main conclusion is that, in the cases studied, the contact angles at the upper and lower contact line do not always simultaneously equal the receding and advancing contact angles, respectively. On a hydrophobic surface, the lowest contact angle (at the upper contact line) tends to be approximately equal to the receding contact angle, while the highest contact angle (at the lower contact line) may be much lower than the advancing contact angle. For hydrophilic surfaces, the opposite is true. These conclusions imply that the hysteresis range cannot in general be measured by analyzing the shape of a drop on an inclined plane. Also, the limiting inclination angle cannot in general be calculated from the classical equation based only on the advancing and receding contact angles.     

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.     

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.