Stick-slip of the three-phase line in measurements of dynamic contact angles

Contact angles of a series of n-alkanes (i.e., n-heptane to n-hexadecane) are studied on two functionalized maleimide copolymers (i.e., poly(ethene-alt-N-(4-(perfluoroheptylcarbonyl)aminobutyl)maleimide) (ETMF) and poly(octadecene-alt-N-(4-(perfluoroheptylcarbonyl)aminobutyl)maleimide) (ODMF)). On the homogeneous ETMF films, all liquids show a smooth motion of the three-phase line. In contrast, on ODMF surfaces that are found to consist of mainly fluorocarbons and small patches of hydrocarbons, short-chain n-alkanes show a stick-slip pattern. By increasing the chain length of the probe liquids, stick-slip is reduced significantly. The phenomenon is discussed in the framework of the Cassie equation. It is found that the upper limit of contact angles in the stick-slip pattern is given by the advancing angle that would be obtained on the pure fluorocarbon surface, whereas the lower limit of the stick-slip pattern is given by the Cassie angle.     

Thermodynamic modeling of contact angles on rough, heterogeneous surfaces

Theoretical modelling for contact angle hysteresis carried out to date has been mostly limited to several idealized surface configurations, either rough or heterogeneous surfaces. This paper presents a preliminary study on the thermodynamics of contact angles on rough and heterogeneous surfaces by employing the principle of minimum free energy and the concept of liquid front. Based on a two-dimensional regular model surface, a set of relations were obtained, which correlate advancing, receding and system equilibrium contact angles to surface topography, roughness and heterogeneity. It was found that system equilibrium contact angles (theta(ES)) can be expressed as a function of surface roughness factor (delta) and the Cassie contact angle (theta(C)): costheta(ES) = deltacostheta(C). This expression can be reduced to the classical Wenzel equation.: theta(ES) = theta(W) for rough but homogeneous surfaces, and the classical Cassie equation theta(ES) = theta(C) for heterogeneous but smooth surfaces. A non-dimensional parameter called surface feature factor (omega) was proposed to classify surfaces into three categories (types): roughness-dominated, heterogeneity-dominated and mixed-rough-heterogeneous. The prediction of advancing and receding contact angles of a surface is dependent on which category the surface belongs to. The thermodynamic analysis of contact angle hysteresis was further extended from the regular model surface to irregular surfaces; consistent results were obtained. The current model not only agrees well with the models previously studied by other researchers for idealized surfaces, but also explores more possibilities to explain the reported experimental results/observations that most existing theories could not explain.     

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.     

Vapour adsorption and contact angles on hydrophobic solid surfaces

To test the effects of vapour adsorption on contact angle measurements, contact angles of high-vapour-pressure liquids and low-vapour-pressure liquids on a hydrophobic solid surface (FC721) were measured by using the axisymmetric drop shape analysis-profile (ADSA-P) technique. Details of the surface preparation and the experiments are presented. By plotting the experimental data in terms of _1v cos vs. _1v, this study shows that the vapour adsorption on a fluorocarbon surface, FC721, is negligible.     

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.     

Models of adsorption at a line of three-phase contact

Two model density distributions at a line of three-phase contact for which the adsorptions are readily calculated are analyzed. One of them provides a numerical illustration of a recently found surprising fact about the thermodynamics of adsorption at such contact lines. A form of the line analogue of the Gibbs adsorption equation is conjectured, and it is noted that the conjecture is in principle testable by computer simulation and by experiment.     

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.     

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.     

Simulation analysis of contact angles and retention forces of liquid drops on inclined surfaces

A simulation study of liquid drops on inclined surfaces is performed in order to understand the evolution of drop shapes, contact angles, and retention forces with the tilt angle. The simulations are made by means of a method recently developed for dealing with contact angle hysteresis in the public-domain Surface Evolver software. The results of our simulations are highly dependent on the initial contact angle of the drop. For a drop with an initial contact angle equal to the advancing angle, we obtain results similar to those of experiments in which a drop is placed on a horizontal surface that is slowly tilted. For drops with an initial contact angle equal to the mean between the advancing and the receding contact angles, we recover previous results of finite element studies of drops on inclined surfaces. Comparison with experimental results for molten Sn-Ag-Cu on a tilted Cu substrate shows excellent agreement.     

On the role of the three-phase contact line in surface deformation

Viscoelastic braking theories developed by Shanahan and de Gennes and by others predict deformation of a solid surface at the solid-liquid-air contact line. This phenomenon has only been observed for soft smooth surfaces and results in a protrusion of the solid surface at the three-phase contact line, in agreement with the theoretical predictions. Despite the large (enough to break chemical bonds) forces associated with it, this deformation was not confirmed experimentally for hard surfaces, especially for hydrophobic ones. In this study we use superhydrophobic surfaces composed of an array of silicon nanostructures whose Young modulus is 4 orders of magnitude higher than that of surfaces in earlier recorded viscoelastic braking experiments. We distinguish between two cases: when a water drop forms an adhesive contact, albeit small, with the apparent contact angle θ < 180° and when the drop-surface adhesion is such that the conditions for placing a resting drop on the surface cannot be reached (i.e., θ = 180°). In the first case we show that there is a surface deformation at the three-phase contact line which is associated with a reduction in the hydrophobicity of the surface. For the second case, however, there cannot be a three-phase contact line associated with a drop in contact with the surface, and indeed, if we force-place a drop on the surface by holding it with a needle, no deformation is detected, nor is there a reduction in the hydrophobic properties of the surface. Yet, if we create a long horizontal three-phase contact line by partially immersing the superhydrophobic substrate in a water bath, we see a localized reduction in the hydrophobic properties of the surface in the region where the three-phase contact line used to be. The SEM scan of that region shows a narrow horizontal stripe where the nanorods are no longer there, and instead there is only a shallow structure that is lower than the nanorods height and resembles fused or removed nanorods. Away from that region, either on the part of the surface which was exposed to bulk water or the part which was exposed to air, no change in the hydrophobic properties of the surface is observed, and the SEM scan confirms that the nanorods seem intact in both regions.     

Indirect methods to measure wetting and contact angles on spherical convex and concave surfaces

In this work, a method was developed for indirectly estimating contact angles of sessile liquid drops on convex and concave surfaces. Assuming that drops were sufficiently small that no gravitational distortion occurred, equations were derived to compute intrinsic contact angles from the radius of curvature of the solid surface, the volume of the liquid drop, and its contact diameter. These expressions were tested against experimental data for various liquids on polytetrafluoroethylene (PTFE) and polycarbonate (PC) in the form of flat surfaces, spheres, and concave cavities. Intrinsic contact angles estimated indirectly using dimensions and volumes generally agreed with the values measured directly from flat surfaces using the traditional tangent method.     

Expansion of three-phase contact line after rupture of thin non-symmetrical liquid films

Summary Rate of expansion of three-phase contact perimeter at monolayers of octadecyl amine (substrate:quartz) of different numbers was investigated and the results were discussed on the basis of a theory for dimple formation. Correlations between adsorption density of surfactant at the liquid/gaseous interface, velocity of three-phase contact perimeter and induction time are presented.

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Zusammenfassung Es wurde die Ausbreitungsgeschwindigkeit des Dreiphasenkontaktperimeters auf Monoschichten von Octadecylamin (Substrat:Quarz) unterschiedlicher Zahl untersucht und die Ergebnisse auf Grundlage einer Theorie zur Dimplebildung diskutiert. Korrelationen zwischen der Adsoptionsdichte an Tensid an der Grenzfläche flüssig/Gas, der Geschwindigkeit des Dreiphasenkontaktperimeters und der Induktionszeit werden aufgezeigt.

     

Expansion of three-phase contact line after rupture of thin non-symmetrical liquid films

Summary One of the important stages in the process of interaction between a particle and a gas bubble in the liquid phase is the expansion of three-phase contact perimeter immediately after rupture of the thin liquid film. The rate of expansion for the system flat quartz surface/liquid dodecylamine hydrochloride solution is determined by use of a high-speed camera. The results were discussed on the basis of a theory on hydrodynamics of thin liquid films.

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Zusammenfassung Ein wichtiger Vorgang bei der Wechselwirkung von Gasblase und Teilchen in flüssiger Phase ist die Bewegung des Dreiphasenkontaktperimeters sofort nach dem Zerreißen des dünnen Flüssigkeitsfilmes, deren Geschwindigkeit für das System ebene Quarzoberfläche/wäßrige Dodecylaminhydrochloridlösung mittels Zeitlupenkamera gemessen wurde. Die Ergebnisse werden auf Grundlage einer Theorie zur Hydrodynamik dünner Flüssigkeitsfilme diskutiert.

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With 2 figures     

Contact angles on spherical surfaces

In this paper, we explore the influence of curved surfaces on contact angles. Small liquid drops were deposited at the apex of spheres. Liquid was added to advance the contact line (or withdrawn to cause recession). As drop volume increased, the contact line advanced outward and downward. With the addition of each increment of liquid, the contact line encountered a steeper slope and showed progressively larger apparent advancing contact angles. Observed apparent contact angles could be explained in terms of intrinsic contact angles and surface orientation. We found that if curvature and geometry were correctly accounted for, the classic Gibbs relation held. The experimental approach and analysis used here for estimating intrinsic wettability from curved surfaces could easily be integrated into automated contact angle measurement systems.     

The dynamic nature of contact angles as measured by atomic force microscopy

Atomic force microscopy appears to be a useful tool for determining the contact angle for small particles. It is shown in this paper that the contact angle of a spherical polyethylene particle changes with the speed of the AFM piezoelectric translator. Such dynamic behavior of the contact angle and other uncertainties such as the position of the three-phase contact on the particle surface during bubble-particle interaction make it difficult to decide whether or not the AFM single-particle contact angle can be used to describe the hydrophobic state of the particle surface.     

Geometric view of the thermodynamics of adsorption at a line of three-phase contact

We consider three fluid phases meeting at a line of common contact and study the linear excesses per unit length of the contact line (the linear adsorptions Lambda(i)) of the fluid's components. In any plane perpendicular to the contact line, the locus of choices for the otherwise arbitrary location of that line that makes one of the linear adsorptions, say Lambda(2), vanish, is a rectangular hyperbola. Two of the adsorptions Lambda(2) and Lambda(3) then both vanish when the contact line is chosen to pass through any of the intersections of the two corresponding hyperbolas Lambda(2)=0 and Lambda(3)=0. There may be two or four such real intersections. It is found most surprisingly, and confirmed in a numerical example, that Lambda(1(2,3)), the adsorption of component 1 in a frame of reference in which the adsorptions Lambda(2) and Lambda(3) are both 0, depends on which intersection of the hyperbolas Lambda(2)=0 and Lambda(3)=0 is chosen for the location of the contact line. This implies that what had long been taken to be the line analog of the Gibbs adsorption equation is incomplete; there must be additional, previously unanticipated terms in the relation, consistent with the invariance of the line tension to choice of location of the contact line. It is then not Lambda(1(2,3)) by itself but a related expression containing it that must be invariant, and this invariance is also confirmed in the numerical example. The presence of the additional terms in the adsorption equation is further confirmed and their origin clarified in a mean-field density-functional model. The supplemental terms vanish at a wetting transition, where one of the contact angles goes to 0.     

Growth of giant two-dimensional crystal of protein molecules from a three-phase contact line

A novel method to fabricate a two-dimensional (2D) crystal of protein molecules has been developed. The method enables us to control both the position of nucleation and the direction of the crystal growth. The crystal obtained using a protein molecule, ferritin, was found to be composed of a number of densely packed single crystal domains with an unprecedentedly large size of approximately 100 microm(2). This method also reveals characteristic behavior of the spatiotemporal evolution of the crystal; for example, "fusion" of the crystal domains, which is never observed in an ordinary crystal composed of atoms or ions, was demonstrated. Our approach could have potential in fabricating extraordinarily large and highly ordered nanoparticle arrays of organic or inorganic materials.