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.     

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.     

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.     

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.     

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.     

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.     

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).     

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.     

Mechanical and superhydrophobic stabilities of two-scale surfacial structure of lotus leaves

To understand why lotus leaf surfaces have a two-scale structure, we explore in this paper two stability mechanisms. One is the stability of the Cassie-Baxter wetting mode that generates the superhydrophobicity. A recent quantitative study (Zheng et al., Langmuir 2005, 21, 12207) showed that the larger the slenderness ratio of the surface structures was, the more stable the Cassie-Baxter wetting mode would be. On the other hand, it is well-known that more slender surface structures can only sustain lower critical water pressures for structure buckling, or Euler instability, while in the natural environments, the water pressure impacting on the lotus surface can reach a fairly high value (105 Pa in a heavy rain). Our analysis reveals that the two-scale structure of the lotus leaf surfaces is necessary for keeping both the structure and the superhydrophobicity stable. Furthermore, we find that the water-air interfacial tension makes the slender surface structure more instable and the two-scale structure a necessity.     

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 line and contact angle dynamics in superhydrophobic channels

The dynamics of the wetting and movement of a three-phase contact line confined between two superhydrophobic surfaces were studied using a mean-field free-energy lattice Boltzmann model. Principle features of superhydrophobic surfaces, such as trapped vapor/air between rough microstructures, high contact angles, reduced contact angle hysteresis, and low resistance to fluid flow, were all observed. Movement of the three-phase contact line over a well-patterned superhydrophobic surface displays a periodic stick-jump-slip behavior, while the dynamic contact angle changes accordingly from maximum to minimum. Two regimes were found for the flow velocity as a function of surface roughness and can be related directly to the balance between driving force and flow resistance. This work provides a better understanding of dynamic wetting and fluid flow behaviors over superhydrophobic surfaces and hence could be useful in related applications.     

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.     

Contact angle hysteresis in carbon fibers studied by wetting force measurements

The surface free energy of polyacrylonitrile carbon fibers was investigated by using the Wilhelmy technique. The difference in surface free energy between immersion and emersion was observed for the carbon fiber pyrolyzed at 2500 °C.In contrast, the hysteresis disappeared with repyrolyzation of the carbon fibers at 3000 °C. Auger electron spectroscopic analysis indicated that the surface of the latter carbon fiber (repyrolyzed at 3000 °C) consisted of the basal planes of graphite. Rough surface topography of the carbon fiber repyrolyzed at 3000 °C, as observed by scanning electron microscope, did not affect the hysteresis. Therefore, the contact angle hysteresis was attributed to the chemical adsorbants on the activation sites of the fiber surfaces, as detected by Auger electron spectroscopy.     

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.     

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.     

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.     

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.     

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.