Switching liquid morphologies on linear grooves

The morphology of liquids confined to linear micrometer-sized grooves of triangular and rectangular cross section is studied for different substrate wettabilities. Depending on the wettability and exact geometry, either droplike morphologies or elongated liquid filaments represent the generic equilibrium structures on the substrate. Upon changing the apparent contact angle of aqueous drops by electrowetting, we are able to trigger the transition between elongated filaments and droplets. In the case of rectangular grooves, this transition allows us to advance liquid reversibly into the grooves while crossing a certain threshold contact angle. In triangular grooves, however, these elongated filaments undergo a dynamic instability when the contact angle returns to a value above the filling threshold. The different filling and drainage behavior is explained by specific aspects of the triangular and rectangular groove geometry.     

Anisotropic drop morphologies on corrugated surfaces

The spreading of liquid drops on surfaces corrugated with micrometer-scale parallel grooves is studied both experimentally and numerically. Because of the surface patterning, the typical final drop shape is no longer spherical. The elongation direction can be either parallel or perpendicular to the direction of the grooves, depending on the initial drop conditions. We interpret this result as a consequence of both the anisotropy of the contact line movement over the surface and the difference in the motion of the advancing and receding contact lines. Parallel to the grooves, we find little hysteresis due to the surface patterning and that the average contact angle approximately conforms to Wenzel's law as long as the drop radius is much larger than the typical length scale of the grooves. Perpendicular to the grooves, the contact line can be pinned at the edges of the ridges, leading to large contact angle hysteresis.     

Study of the advancing and receding contact angles: liquid sorption as a cause of contact angle hysteresis

Two types of experiments were used to study the behavior of both advancing and receding contact angles, namely the dynamic one-cycle contact angle (DOCA) and the dynamic cycling contact angle (DCCA) experiments. For the preliminary study, DOCA measurements of different liquids on different solids were performed using an automated axisymmetric drop shape analysis-profile (ADSA-P). From these experimental results, four patterns of receding contact angle were observed: (1) time-dependent receding contact angle; (2) constant receding contact angle; (3) 'stick/slip'; (4) no receding contact angle. For the purpose of illustration, results from four different solid surfaces are shown. These solids are: FC-732-coated surface; poly(methyl methacrylate/n-butyl methacrylate) [P(MMA/nBMA)]; poly(lactic acid) (DL-PLA); and poly(lactic/glycolic acid) 50/50 (DL-PLGA 50/50). Since most of the surfaces in our studies exhibit time dependence in the receding contact angle, a more extended study was conducted using only FC-732-coated surfaces to better understand the possible causes of decreasing receding contact angle and contact angle hysteresis. Contact angle measurements of 21 liquids from two homologous series (i.e. n-alkanes and 1-alcohols) and octamethylcyclotetrasiloxane (OCMTS) on FC-732-coated surfaces were performed. It is apparent that the contact angle hysteresis decreases with the chain length of the liquid. It was found that the receding contact angle equals the advancing angle when the alkane molecules are infinitely large. These results strongly suggest that the chain length and size of the liquid molecule could contribute to contact angle hysteresis phenomena. Furthermore, DCCA measurements of six liquids from the two homologous series on FC-732-coated surfaces were performed. With these experimental results, one can construe that the time dependence of contact angle hysteresis on relatively smooth and homogeneous surfaces is mainly caused by liquid retention/sorption. The results also suggested that the contact angle hysteresis will eventually approach a steady state, where the rate of liquid retention-evaporation or sorption process would balance out each other. If the existence of contact angle hysteresis can be attributed to liquid sorption/retention, one should only use the advancing contact angles (measured on a dry surface) in conjunction with Young's equation for surface energetic calculations.     

Retention forces and contact angles for critical liquid drops on non-horizontal surfaces

Retention forces and drop parameters are investigated for drops on the verge of sliding on vertical and inclined surfaces. Using earlier observations of drop geometry, the retentive-force factor relating surface-tension forces to contact-angle hysteresis is reliably determined. The retention force for a drop is found to be insignificantly affected by the aspect ratio of its contour. The maximum size of a drop is predicted with good accuracy, based on the two-circle method for approximating shapes of drops. The Bond number of a critical drop is found to be constant for a given surface and liquid. A general relation is proposed between the characteristic advancing and receding contact angles. The relation is supported by a large set of contact-angle data. In the absence of theta R data, the relation allows estimating the receding contact angle and the critical drop size, using only the advancing angle.     

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.     

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.     

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.     

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.     

Anisotropic wetting characteristics on submicrometer-scale periodic grooved surface

Submicrometer-scale periodic structures consisting of parallel grooves were prepared on azobenzene-containing multiarm star polymer films by laser interference. The wetting characteristics on the patterned surfaces were studied by contact angle measurements. Macroscopic distortion of water drops was found on such small-scale surface structures, and the contact angles measured from the direction parallel to the grooves were larger than those measured from the perpendicular direction. A thermodynamic model was developed to calculate the change in the surface free energy as a function of the instantaneous contact angle when the three-phase contact line (TPCL) moves along the two orthogonal directions. It was found that the fluctuations, i.e., energy barriers, on the energy versus contact angle curves are crucial to the analysis of wetting anisotropy and contact angle hysteresis. The calculated advancing and receding contact angles from the energy versus contact angle curves were in good agreement with those measured experimentally. Furthermore, with the groove depth increasing, both the degree of wetting anisotropy and the contact angle hysteresis perpendicular to the grooves increased as a result of the increase in the energy barrier. The theoretical critical value of the groove depth, above which the anisotropic wetting appears, was determined to be 16 nm for the grooved surface with a wavelength of 396 nm. On the other hand, the effect of the groove wavelength on the contact angle hysteresis perpendicular to the grooves was also interpreted on the basis of the thermodynamic model. That is, with the wavelength decreasing, the contact angle hysteresis increased due to the increase in the number of energy barriers. These results may provide theoretical evidence for the design and application of anisotropic wetting surface.     

A refractive tilting-plate technique for measurement of dynamic contact angles

The contact angle is a critical parameter in liquid interface dynamics ranging from liquid spreading on a solid surface on earth to liquid motion in partially filled containers in space. A refractive tilting-plate technique employing a scanning laser beam is developed to conduct an experimental study of a moving contact line, with the intention of making accurate measurements of the contact angle. The technique shows promise as an accurate and potentially fully automated means to determine the velocity dependence of the contact angle at the intersection of the interface between two transparent fluids with a transparent solid surface. Ray tracing calculations are included to reinforce the measurement concept. The principal experiments were conducted at speeds ranging from 0.05 to 1.00 mm/s, both advancing and receding, using an immiscible liquid pair (nonane/formamide) in contact with glass. The contact angle was found to depend for practical purposes only on the sign of the velocity and not on its magnitude for the range of velocities studied. Other observations revealed a bimodal behavior of the contact line that depends on which liquid first contacts the glass, with resulting drift in the dynamic contact angle with time.     

Dewetting of liquid filaments in wedge-shaped grooves

The dewetting of liquid filaments in linear grooves of a triangular cross section is studied experimentally and theoretically. Homogeneous filaments of glassy polystyrene (PS) are prepared in triangular grooves in a nonequilibrium state. At elevated temperatures, the molten PS restores its material contact angle with the substrate. Liquid filaments with a convex liquid-vapor interface decay into isolated droplets with a characteristic spacing depending on the wedge geometry, wettability, and filament width. This instability is driven by the interplay of local filament width and Laplace pressure and constitutes a wide class of 1D instabilities that also include the Rayleigh-Plateau instability as a special case. Our results show an accurately exponential buildup of the instability, suggesting that fluctuations have a minor influence in our system.     

Sliding behavior of liquid droplets on tilted Langmuir-Blodgett surfaces

The sliding behavior of liquid droplets on inclined Langmuir-Blodgett surfaces was investigated. The critical sliding angle defined as the tilt angle of the surface at which the drop slides down as well as the advancing and receding contact angles was measured for five different liquids on five surfaces. In addition, the contact line geometry was analyzed at critical sliding angle. The experimental relationship between the surface tension forces resulting from contact angle hysteresis and the weight of the drop was compared to theoretical predictions. Even though the shape of the drop bases was found as skewed ellipses, a model assuming parallel-sided elongated drops is shown to describe reasonably the experimental values. This result probably indicates the main influence of the capillary forces at the rear and front edges of the drop with respect to that exerted on the lateral sides.     

Electroactuation of fluid using topographical wetting transitions

The complex morphologies of liquids on topographically structured substrates are exploited for liquid actuation in open microchannels. The liquid is either confined in prefabricated grooves, thus forming elongated filaments, or gathers in macroscopic drops without invading the grooves, depending on conditions. Using the electrowetting effect, we can reversibly switch between these two states. The length of the filaments is sensitive to the ionic content of the liquid and can be described quantitatively with an electrical model considering the voltage drop along the groove.     

苯乙烯/甲基丙烯酸和苯乙烯/甲基丙烯酸(β-羟丙酯)嵌段共聚物的表面动态行为

通过测定表面动态接触角研究了两亲性的苯乙烯／甲基丙烯酸嵌段共聚物（ＰＳ ｂ ＰＭＡＡ）和苯乙烯／甲基丙烯酸（β 羟丙酯）嵌段共聚物（ＰＳ ｂ ＰＨＰＭＡ）的表面动态行为及温度、嵌段长度比等因素对其值的影响,讨论了聚合物表面当接触介质改变时链段或基团的再取向行为和表面性质     

Detachment of deposited colloids by advancing and receding air-water interfaces

Moving air-water interfaces can detach colloidal particles from stationary surfaces. The objective of this study was to quantify the effects of advancing and receding air-water interfaces on colloid detachment as a function of interface velocity. We deposited fluorescent, negatively charged, carboxylate-modified polystyrene colloids (diameter of 1 μm) into a cylindrical glass channel. The colloids were hydrophilic with an advancing air-water contact angle of 60° and a receding contact angle of 40°. After colloid deposition, two air bubbles were sequentially introduced into the glass channel and passed through the channel at different velocities (0.5, 7.7, 72, 982, and 10,800 cm/h). The passage of the bubbles represented a sequence of receding and advancing air-water interfaces. Colloids remaining in the glass channel after each interface passage were visualized with confocal microscopy and quantified by image analysis. The advancing air-water interface was significantly more effective in detaching colloids from the glass surface than the receding interface. Most of the colloids were detached during the first passage of the advancing air-water interface, while the subsequent interface passages did not remove significant amounts of colloids. Forces acting on the colloids calculated from theory corroborate our experimental results, and confirm that the detachment forces (surface tension forces) during the advancing air-water interface movement were stronger than during the receding movement. Theory indicates that, for hydrophilic colloids, the advancing interface movement generally exerts a stronger detachment force than the receding, except when the hysteresis of the colloid-air-water contact angle is small and that of the channel-air-water contact angle is large.     

Liquid drops on vertical and inclined surfaces; I. An experimental study of drop geometry

Experiments have been conducted to investigate the geometric parameters necessary to describe the shapes of liquid drops on vertical and inclined plane surfaces. Two liquids and eight surfaces have been used to study contact angles, contact lines, profiles, and volumes of drops of different sizes for a range of surface conditions. The results show the contact-angle variation along the circumference of a drop to be best fit by a third-degree polynomial in the azimuthal angle. This contact-angle function is expressed in terms of the maximum and minimum contact angles of the drop, which are determined for various conditions. The maximum contact angle, thetamax, is approximately equal to the advancing contact angle, thetaA, of the liquid on the surface. As the Bond number, Bo, increases from 0 to a maximum, the minimum contact angle, thetamin, decreases almost linearly from the advancing to the receding angle. A general relation is found between thetamin/thetaA and Bo for different liquid-surface combinations. The drop contour can be described by an ellipse, with the aspect ratio increasing with Bo. These experimental results are valuable in modeling drop shape, as presented in Part II of this work.     

Liquid Drops on an Inclined Plane: The Relation between Contact Angles, Drop Shape, and Retentive Force

Contact angle hysteresis, drop shape, and drop retention were studied with a tiltable plane. Contact liquids were water and ethylene glycol. Four polymers and silicon wafers were used as substrates. When the plane was inclined, the shape of drops distorted, exhibiting advancing and receding contact angles. Drops remained stationary until a critical angle of tilt was exceeded, and then they began to move. The difference in the advancing and receding contact angles, or contact angle hysteresis, ranged from 9° to 66°, depending on the liquid and the substrate. Roughness did not seem to influence the hysteresis as much as the chemical nature of the surfaces. Elongation and back-to-front asymmetry were greater on surfaces with high hysteresis. We found a linear correlation between the aspect ratio of drops and their contact angle hysteresis. Also, the retentive force increased with elongation of the drops.     

Wetting of real solid surfaces: new glance on well-known problems

The wetting of solid surfaces is treated. The Young and receding contact angles are experimentally unattainable values for the majority of solid surfaces. Actually, we always observe the apparent contact angle. This makes the characterization of wetting of real surfaces problematic. It is proposed in this paper to characterize wetting of real surfaces with the advancing contact angle and the minimum work of adhesion calculated according to the Dupre equation. The advancing contact angle, which depends slightly on the experimental technique used for its measurement, corresponds to the maximal solid/liquid surface tension and correspondingly to the minimal work of adhesion, calculated according to the Dupre equation.