Shape analysis based critical Eotvos numbers for buoyancy induced partial detachment of oil drops from hydrophilic surfaces

Removal of oil drops from solid surfaces immersed in an aqueous medium is of interest in many applications. It has been shown that drop shape analysis can be used to predict conditions at which the stability limit of a lighter than water oil drop on a solid surface immersed in an aqueous bath is reached (Adv. Colloid Interface Sci. 98 (2002) 265). However the above analysis is restricted to cases where the contact angle made by the drop is below 90degrees and when the surface conditions result in a 'pinned' contact line. In this paper, it is shown that drop shape analysis can be used to predict the critical conditions at which drop stability limit is reached for drop contact angles of 90degrees and above, which is encountered with 'hydrophilic' surfaces. This critical condition can predict the occurrence of partial oil drop detachment, before complete removal due to 'roll-up', which occurs when the hydrophilic surface is adequately smooth which prevents 'pinning' of the contact line. The critical conditions at which partial drop detachment occurs can also be approximately predicted from simple force balances. It has been shown (Adv. Colloid Interface Sci. 98 (2002) 265) that for contact angles less than 90degrees, the critical limit based on shape analysis appears to resolve the differences that arise due to alternate expressions for capillary retention force. This paper shows that even for contact angles above 90degrees, the critical conditions predicted from the shape analysis resolves the differences in the predictions from the alternate force balances. Drop shape analysis used in this paper is based on the 'Arc-length' form of Young-Laplace or 'drop shape' equation, which is different from the 'Y vs X' form of the above equation that is used in Adv. Colloid Interface Sci. 98 (2002) 265. The above drop shape equation is solved by a fourth order Runge-Kutta technique and it is shown that for angles less than 90degrees, the two forms of the drop shape equation, predict almost identical values of the critical Eotvos number. This paper highlights the competing effects of interfacial tension lowering induced drop instability and 'roll-up', a term that is used to describe the retraction of the contact line of an oil drop on a surface, in being the primary c ause for drop detachment.     

Validity of the "sharp-kink approximation" for water and other fluids

The contact angle of a liquid droplet on a solid surface is a direct measure of fundamental atomic-scale forces acting between liquid molecules and the solid surface. In this work, the validity is assessed of a simple equation, which approximately relates the contact angle of a liquid on a surface to its density, its surface tension, and the effective molecule-surface potential. This equation is derived in the sharp-kink approximation, where the density profile of the liquid is assumed to drop precipitously within one molecular diameter of the substrate. It is found that this equation satisfactorily reproduces the temperature-dependence of the contact angle for helium on alkali metal surfaces. The equation also seems be applicable to liquids such as water on solid surfaces such as gold and graphite, on the basis of a comparison of predicted and measured contact angles near room-temperature. Nevertheless, we conclude that, to fully test the equation's applicability to fluids such as water, it remains necessary to measure the contact angle's temperature-dependence. We hypothesize that the effects of electrostatic forces can increase with temperature, potentially driving the wetting temperature much higher and closer to the critical point, or lower, closer to room temperature, than predicted using current theories.     

Kinetics of wetting of liquid on a solid surface

To consider a sessile drop on an ideal solid surface in equilibrium with a vapor phase, the classic Young equation was given. The derivation of the Young equation was based on both the mechanics and the energy knowledge. According to the constant volume of the liquid in the wetting process of the liquid on a smooth and homogeneous solid surface and the low energy law, Young equation was ob-tained through the mathematic method in this paper. The previous work indicated that the contact angle θ was a function...     

Effect of temperature on the surface free energy of amorphous carbon films

Diamond-like carbon (DLC) and tetrahedral amorphous carbon (ta-C) have attracted much attention recently for biomedical and antifouling applications due to their excellent biocompatibility and inherent nonstick properties. It has been demonstrated that the solid surface free energy is a dominant factor in cellular or fouling adhesion. However, few data for the surface free energy of DLC and ta-C coatings at temperatures in the range 37-95 degrees C are available. In this study DLC and ta-C coatings on stainless steel 304 sheets were prepared using an unbalanced magnetron sputtering system and a filtered cathodic vacuum arc system, respectively. The contact angles of water, diiodomethane and ethylene glycol on the coated surfaces at temperatures in the range 20-95 degrees C were measured using a Dataphysics OCA-20 contact angle analyzer. The surface free energy of the coatings and their components (e.g., dispersion, polar or acid/base portions) were calculated using various methods. The experimental results showed that the total surface free energy and dispersive surface free energy of the ta-C coatings, DLC coatings, stainless steel 304 and titanium decreased with increasing surface temperature, while the acid-base SFE component increased with increasing temperature.     

Contact angle and film pressure: study of a talc surface

Talc samples in both sheet and powder form are studied by adsorption calorimetry and adsorption isotherm techniques. A model is used to determine the solid surface energy, the solid surface tension and the dispersive, acidic, and basic components of these terms. These results are introduced in an approximate equation relating adsorption to contact angle data. Experimental contact angles are in correct agreement with this approach. The Neumann equation of state is used to fit the data and discussed. It appears as a numerical form of the general equation taking into account gas adsorption and film pressure. Behaviors of talc in contact with liquids do not appear very different whether the solid is in sheet or powder form.     

The surface energy of montmorillonite

By combining the relation that describes pair interaction in binary mixtures with the Young equation, a formula is obtained for calculating the surface energy of montmorillonite as a function of the surface pressure, the surface tension of water, and the liquid/solid contact angle. The formula is an equation of an inverted parabola, which could be represented by a polynomial function. Roots of the polynomial gave one real value of 205.066+/-2.764 mJm(-2) for the surface energy of montmorillonite. The value obtained is of the expected magnitude and probably is better than those obtained by previous approaches.     

Factors influencing the contact angle value. The contact angle,as a characteristic of the properties of solid surfaces

A survey of publications concerning the properties of solids in relation to wetting phenomena is presented. Factors influencing the contact angle value as well as problems of objective approach to research into wetting phenomena are discussed. Peculiarities of the direct and reverse processes during the formation of the solid—liquid—vapor three-phase contact and the inevitability of contact angle hysteresis for polar solids and liquids are analyzed. It is suggested that contact angle hysteresis is due to high energy of the interaction between the liquid and the solid and hence a long relaxation time of the three-phase contact system. Specific features of the response of a solid surface to all surface processes (“chemomechanics”) is discussed. Cleaning of solid surfaces as well as surface preparation for repeated measurements is considered. It is shown that good reproducibility of results is possible if conditions for sample preparation are met. The results of determination of the activation energy for wetting of glass surface with water are presented. The influence of the structure of solids (their hardness) on the contact angle values is demonstrated. Inevitability of the presence of different-type active sites characterized by different dissociation constants (pK_a) on the surface of solids is discussed. The pK_a values and content of these surface sites obtained from potentiometric titration and wetting data are estimated. The estimates thus obtained are in reasonable agreement with each other and can thus be used in practical applications. However, potentiometric titration is currently inappropriate for evaluating the content of individual surface sites as well as the surface charge.     

Electrowetting of nonwetting liquids and liquid marbles

Transport of a water droplet on a solid surface can be achieved by differentially modifying the contact angles at either side of the droplet using capacitive charging of the solid-liquid interface (i.e., electrowetting-on-dielectric) to create a driving force. Improved droplet mobility can be achieved by modifying the surface topography to enhance the effects of a hydrophobic surface chemistry and so achieve an almost complete roll-up into a superhydrophobic droplet where the contact angle is greater than 150 degrees . When electrowetting is attempted on such a surface, an electrocapillary pressure arises which causes water penetration into the surface features and an irreversible conversion to a state in which the droplet loses its mobility. Irreversibility occurs because the surface tension of the liquid does not allow the liquid to retract from these fixed surface features on removal of the actuating voltage. In this work, we show that this irreversibility can be overcome by attaching the solid surface features to the liquid surface to create a liquid marble. The solid topographic surface features then become a conformable "skin" on the water droplet both enabling it to become highly mobile and providing a reversible liquid marble-on-solid system for electrowetting. In our system, hydrophobic silica particles and hydrophobic grains of lycopodium are used as the skin. In the region corresponding to the solid-marble contact area, the liquid marble can be viewed as a liquid droplet resting on the attached solid grains (or particles) in a manner similar to a superhydrophobic droplet resting upon posts fixed on a solid substrate. When a marble is placed on a flat solid surface and electrowetting performed it spreads but with the water remaining effectively suspended on the grains as it would if the system were a droplet of water on a surface consisting of solid posts. When the electrowetting voltage is removed, the surface tension of the water droplet causes it to ball up from the surface but carrying with it the conformable skin. A theoretical basis for this electrowetting of a liquid marble is developed using a surface free energy approach.     

Selenocysteine versus cysteine reactivity: a theoretical study of their oxidation by hydrogen peroxide

The cysteine and selenocysteine oxidation by H2O2 in vacuo and in aqueous solution was studied using the integrated molecular orbital + molecular orbital (IMOMO) method combining the quadratic configuration method QCISD(T) and the spin projection of second-order perturbation theory PMP2. It is shown that including in the model system of cysteine (selenocysteine) residue up to 20 atoms has significant consequences upon the calculated reaction energy barrier. On the other hand, it is demonstrated that free cysteine and selenocysteine have very similar reaction energy barriers, 77-79 kJ mol(-1) in aqueous solution. It is thus concluded that the high experimental reaction rate constant reported for the oxidation of the selenocysteine residue in the glutathione peroxidase (GPx) active center is due to an important interaction between selenocysteine and its molecular environment. The sensitivity of the calculated energy barrier to the dielectric constant of the molecular environment observed for both cysteine and selenocysteine as well as the catalytic effect of the NH group emphasized in the case of cysteine supports this hypothesis.     

Low voltage electrowetting using thin fluoroploymer films

This paper investigates the nonideal electrowetting behavior of thin fluoroploymer films. Results are presented for a three phase system consisting of: (1) an aqueous water droplet containing sodium dodecyl sulfate (SDS), (2) phosphorous-doped silicon topped with SiO2 and an amorphous fluoroploymer (aFP) insulating top layer on which the droplet is situated, and (3) a dodecane oil that surrounds the droplet. The presented measurements indicate that the electrowetting equation is valid down to a 6 nm thick aFP film on a 11 nm thick SiO2. At this dielectric thickness, a remarkable contact angle change of over 100 degrees can be achieved with an applied voltage less than 3 V across the system. The data also shows that for this water/surfactant/oil system, contact angle saturation is independent of the electric field, and is reached when the surface energy of the solid-water interface approaches zero.     

Surfactant and electric field strength effects on surface tension at liquid/liquid/solid interfaces

We performed a series of experiments designed to elucidate the effects of the presence of sodium dodecyl sulfate (SDS) surfactant and an applied electrical field on the wetting behavior in a system containing a sessile droplet of phenylmethyl polysiloxane (PMPS) oil on a polished stainless steel surface submersed in aqueous solution. The voltage difference ranged from -3 to +3 V, which is at least 3 orders of magnitude smaller than from comparable recent work. We report the measured equilibrium contact angle of the droplet as a function of surfactant concentration and field strength. We then modeled the system. We solved the Laplace equation to obtain the 3D field within our system. We expanded the three surface tensions (oil droplet-aqueous solution (oa), oil droplet-metal surface (os), and aqueous solution-metal surface (as)) in a Taylor series with respect to surfactant concentration and local field strength. We use these three surface tensions in Young's equation to obtain the theoretical contact angle of the organic droplet. We demonstrate that the large changes in contact angle due to the simultaneous presence of small concentrations of surfactant and small voltage differences can be accounted for by changes in the oa and as surface tensions.     

Surface films and metallurgy related to lubrication and wear

The nature of the tribological surface is identified and characterized with respect to adhesion, friction, wear, and lubricating properties. Surface analysis is used to identify the role of environmental constituents on tribological behavior. The effect of solid to solid interactions for metals in contact with metals, ceramics, semiconductors, carbons, and polymers is discussed. The data presented indicate that the tribological surface is markedly different than an ideal solid surface. The environment is shown to affect strongly the behavior of two solids in contact. In certain instances, the environment can dominate surface characteristics. With metals in contact with metals, adhesion is found to be related to the cohesive binding energy. Strong adhesive bonding occurs for metals in contact with ceramics, semiconductors, carbons, and polymers. Bond strength at the interface is, with some exceptions, stronger than the bond strength of the cohesively weaker of the two materials. Many different surface properties of metals and alloys influence tribological performance. These include (1) surface energy, (2) crystallographic orientation, (3) amorphous versus the crystalline state, (4) grain boundaries, (5) texturing of the surface, (6) crystal structure, and (7) order-disorder transformations. At sufficiently high loads or sliding velocities, metals or alloy surfaces are shown to undergo recrystallization effecting tribological properties. The chemical valency, d-valence-bond characteristics, of metal surfaces affect adhesion, friction, and wear. The greater the percent d-bond character, the lower the friction and wear. The ideal tensile and shear strengths of simple transition metals correlate with friction coefficients. Results presented also show that small amounts of alloying elements in base metals can alter markedly adhesion, friction, and wear by segregating to the solid surface.     

Work of Adhesion of a Sessile Drop to a Clean Surface

According to the Young-Dupré equation, as interpreted by Bangham and Razouk, the work of adhesion of a sessile drop to a smooth solid surface is given by WS(V)L = gammaL (1 + cos θ), where θ is the equilibrium contact angle measured at equilibrium of the system with the saturated vapor of the liquid, and WS(V)L is the work of adhesion of that drop to the solid surface which is in equilibrium with that vapor and may contain an adlayer of the vapor. For calculation of WSL, the work of adhesion of a sessile drop to a clean solid surface, the equation WSL = gammaL (1 + cos θ) + Pie is generally used (although Bangham and Razouk never proposed it). Pie is the negative of the free energy of formation of the adlayer, sometimes called the spreading pressure. In the present work it is shown that the latter equation cannot be accurate. Copyright 1999 Academic Press.     

The Neumann and Young equations for nematic contact lines

The Neumann and Young equations for three-phase nematic contact lines have been derived using the momentum balance equation and classical liquid crystal physics theories. The novel finding is the presence of bending forces, originating from the anchoring energy of nematic interfaces, and acting on the contact line. The classical Neumann triangle or tensile force balance becomes in the presence of a nematic phase the Neumann pentagon, involving the usual three tensile forces and two additional bending forces. The Young equation that describes the static contact angle of a fluid in contact with a rigid solid is again a tensile force balance along the solid, but for nematics it also involves an additional bending force. The effects of the bending forces on contact angles and wetting properties of nematic liquid crystals are thoroughly characterized. It is found that in terms of the spreading coefficient, bending forces enlarge the partial wetting window that exists between dewetting and spontaneous spreading. Bending forces also affect the behaviour of the contact angle, such that spreading occurs at contact angles greater than zero and dewetting at values greater than pi. Finally, the contact angle range in the partial wetting regime is always less than pi.     

The Neumann and Young equations for nematic contact lines

The Neumann and Young equations for three-phase nematic contact lines have been derived using the momentum balance equation and classical liquid crystal physics theories. The novel finding is the presence of bending forces, originating from the anchoring energy of nematic interfaces, and acting on the contact line. The classical Neumann triangle or tensile force balance becomes in the presence of a nematic phase the Neumann pentagon, involving the usual three tensile forces and two additional bending forces. The Young equation that describes the static contact angle of a fluid in contact with a rigid solid is again a tensile force balance along the solid, but for nematics it also involves an additional bending force. The effects of the bending forces on contact angles and wetting properties of nematic liquid crystals are thoroughly characterized. It is found that in terms of the spreading coefficient, bending forces enlarge the partial wetting window that exists between dewetting and spontaneous spreading. Bending forces also affect the behaviour of the contact angle, such that spreading occurs at contact angles greater than zero and dewetting at values greater than pi. Finally, the contact angle range in the partial wetting regime is always less than pi.     

Problems of contact angle and solid surface free energy determination

The current general problems of formulation and determination of surface free energy are discussed. So far several theories and approaches have been proposed, but formulation of surface and interfacial free energy, as regards its components, is still a very debatable issue. However, as long as no method for determination of real surface free energy quantities is known, even relative values charged with many simplified assumptions are useful for better understanding of the wetting processes. In this paper special focus is concentrated on powdered solids for which direct measurement of the contact angles is not possible. For such solids the porous layer imbibition techniques are most frequently applied. Then, using the wicking results the contact angle is calculated from Washburn's equation. However, such a procedure leads to overestimated contact angle values in comparison to those measured directly on smooth surfaces of the same solid, if such surface can be obtained at all. As a consequence, the solid surface free energy components calculated via such overestimated contact angles are significantly lower than those obtained from contact angles measured directly. Methodologies to avoid this problem are also described.     

Physical significance of contact angles

Summary The physical significance of contact angles has been interpreted on the basis of a model derived from known surface energy relationships. The degrees of non-spreading and spreading have been expressed in terms of the magnitude of contact angles. On the basis of the physical picture, hysteresis of contact angle has been calculated from the experimental values of equilibrium contact angle and surface tension of the liquid. It has been suggested that it is not necessary to assume that hysteresis of contact angles is due to surface roughness of solids. The picture also explains why apparent contact angle on a non-flat solid surface is more than that on a flat solid.With 2 figures and 1 table     

Contact angle interpretation in terms of solid surface tension

Recent experimental (low-rate) dynamic contact angles for 14 solid surfaces are interpreted in terms of their solid surface tensions. Universality of these experimental contact angle patterns is illustrated; other reasons that can cause data to deviate from the patterns are discussed. It is found that surface tension component approaches do not reflect physical reality. Assuming solid surface tension is constant for one and the same solid surface, experimental contact angle patterns are employed to deduce a functional relationship to be used in conjunction with the Young equation to determine solid surface tensions. The explicit form of such a relation is obtained by modifying Berthelot’s rule together with experimental data; essentially constant solid surface tension values are obtained, independent of liquid surface tension and molecular structure. A new combining rule is also derived based on an expression similar to one used in molecular theory; such a combining rule should allow a better understanding of the molecular interactions between unlike solid–liquid pairs.     

Double-layer interaction between parallel solid cylinders partially immersed in an oil/water interface

We consider two identical, parallel, infinitely long solid cylinders at a given separation, lying flat on a plane oil/water interface and both immersed to the same extent in the oil and water phases. The part of the surface of each cylinder in contact with the aqueous phase is charged, forming an electric double layer in a symmetrical aqueous binary electrolyte. The electrical potential in the overlapping electric double layers in the aqueous phase satisfies the Poisson-Boltzmann equation. The potentials within the uncharged interiors of the solid cylinders and in the oil phase satisfy Laplace's equation. The equations for the three potentials are solved simultaneously using the finite element method with Galerkin weighted residuals. The double-layer interaction per unit length of the cylinders is then calculated. Of the numerical results obtained, three deserve special mention. First, a short-range double-layer repulsion, decaying exponentially with separation between the two cylinders, acts through the aqueous electrolyte medium, whereas in the case of an uncharged oil/water interface a weaker, but much longer-ranging, repulsive interaction acts through the oil medium. Second, reasonable estimates of the short-range interaction between cylinders in a planar interface can be obtained from the Derjaguin approximation for thin double layers. Third, in addition to the repulsive force between the cylinders parallel to the oil/water interface, a force normal to the interface acts on the cylinders in the direction of the aqueous electrolyte phase.     

Contact angle interpretation: re-evaluation of existing contact angle data

We have recently shown that static contact angles measured by conventional goniometer techniques could be meaningless in the context of the Young equation. There is an abundance of contact angles in the literature that are of unknown status. Here, we explored whether one should completely neglect the literature contact angle data. Existing static contact angles for 34 different types of solid surfaces from Zisman and co-workers were evaluated in terms of their solid surface tensions using experimental contact angle patterns. A fortran computer program was implemented to automate these procedures. It was found that literature contact angles do not have to be discarded completely; they can be used to determine solid surface tensions, with caution. The surface tensions for the 34 solid surfaces from Zisman et al. are also reported.