Nonflat equilibrium liquid shapes on flat surfaces

The hydrostatic pressure in thin liquid layers differs from the pressure in the ambient air. This difference is caused by the actions of surface forces and capillary pressure. The manifestation of the surface force action is the disjoining pressure, which has a very special S-shaped form in the case of partial wetting (aqueous thin films and thin films of aqueous electrolyte and surfactant solutions, both free films and films on solid substrates). In thin flat liquid films the disjoining pressure acts alone and determines their thickness. However, if the film surface is curved then both the disjoining and the capillary pressures act simultaneously. In the case of partial wetting their simultaneous action results in the existence of nonflat equilibrium liquid shapes. It is shown that in the case of S-shaped disjoining pressure isotherm microdrops, microdepressions, and equilibrium periodic films exist on flat solid substrates. Criteria are found for both the existence and the stability of these nonflat equilibrium liquid shapes. It is shown that a transition from thick films to thinner films can go via intermediate nonflat states, microdepressions and periodic films, which both can be more stable than flat films within some range of hydrostatic pressure. Experimental investigations of shapes of the predicted nonflat layers can open new possibilities of determination of disjoining pressure in the range of thickness in which flat films are unstable.     

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.     

黑膜厚度与膜表面张力关系的研究

用微干涉测量技术直接测定楔压等温线,研究了电解质浓度对阳离子表面活性剂TTAB在浓度大于cmc时形成黑膜厚度的影响及膜表面张力与溶液表面张力之间的差别.结果显示,黑膜厚度取决于楔压和电解质浓度,随着楔压的增加,液膜厚度减少至一定程度后几乎保持不变,表明黑膜类型的转化是阶跃式的,而电解质屏蔽了液膜两个表面电荷层间的排斥作用,故电解质浓度增加,液膜厚度变小.由楔压等温线得出的膜表面张力的结果说明一般黑膜的表面张力与溶液的表面张力并无明显差别.     

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.     

Wetting and surface forces

In this review we discuss the fundamental role of surface forces, with a particular emphasis on the effect of the disjoining pressure, in establishing the wetting regime in the three phase systems with both plane and curved geometry. The special attention is given to the conditions of the formation of wetting/adsorption liquid films on the surface of poorly wetted substrate and the possibility of their thermodynamic equilibrium with bulk liquid. The calculations of contact angles on the basis of the isotherms of disjoining pressure and the difference in wettability of flat and highly curved surfaces are discussed. Mechanisms of wetting hysteresis, related to the action of surface forces, are considered.     

Stable drop shapes under disjoining pressure. II. Multiplicity and stability

The stability of the contact line region as affected by the disjoining pressure has been analyzed by solving the augmented Young-Laplace equation. Because of the results in Part I (Zhang, X., Neogi, P., and Ybarra, R. M., J. Colloid Interface Sci.), we have concentrated on obtaining multiple solutions for the same set of conditions. As many as five solutions were obtained: drops that end in a thin film with uniform thickness and where the film shape oscillates, drops that end with microscopic contact angles, as well as uniform thin films of two different thicknesses. The results of linear stability analysis were used to show that most cases were unstable to infinitesimal disturbances. Only two stable drop shapes for the particular disjoining pressure investigated are stable, a thin film of constant thickness and a thin drop that ends in a film of same thickness. Both multiplicity and stability have been discussed here for the first time and shed considerable light on the role of the attractive and repulsive forces.     

Untersuchungen des spaltdruckes dünner filme, deren entwicklung, ergebnisse und zu lösende aktuelle probleme

Considered is the development of the notions of the equilibrium disjoining pressure, beginning from its first experimental discovery for the films between solid surfaces, wetting or free. Considered is also the role of the disjoining pressure in the thermodynamics of liquid films, which is regarded as the main thermodynamic characteristic of the latter. The application of the notion of the disjoining pressure to the hydrodynamics of thin films has been mentioned. Considered are the components of the disjoining pressure, dependent upon the dispersion forces, ionic-electrostatic forces, and upon the structural peculiarities of boundary layers. In conclusion, one has considered the importance of the disjoining pressure for the stability of colloids.     

Stability of triglyceride liquid films on hydrophilic and hydrophobic glasses

Wetting and dewetting of solid surfaces by oily fluids were investigated in terms of the stability of the liquid film formed between an air bubble and the solid surface. With the objective of understanding how molecules with low polarity but relatively complex molecular structure behave at the solid/liquid interface, three liquid triglycerides with different chain length and saturation were chosen, namely, tributyrin, tricaprylin, and triolein. Tributyrin and tricaprylin exist in milkfat while triolein is present in vegetable oils. The stability of the liquid films may be inferred from the shape of the disjoining pressure isotherms, which represent the dependence of the disjoining pressure on the film thickness. Disjoining pressure isotherms for films of the three triglycerides on hydrophilic and hydrophobic glasses were obtained using a recently developed apparatus, based on the interferometric technique. The experimental curves are compared with the theoretical predictions of London-Hamaker. The deviations between theory and experiment are interpreted in terms of a structural component of the disjoining pressure. All triglycerides form metastable films on both hydrophilic and hydrophobic glasses which means that for disjoining pressures higher than a critical value, pi(c), a wetting transition occurs and the film ruptures. The mechanisms for film rupture are discussed and a correlation between film stability and the apolar (Lifshitz-van der Waals) and the polar components of the spreading coefficient is proposed.     

Investigation of the isotherms of the disjoining pressure of wetting films of binary nonionic solutions by the ellipsometric method

The paper deals with an experimental investigation into the influence of the second component on the thicknesses of the wetting films of a nonionic solvent. A technique has been developed for the production of pure, smooth, thin glass substrates for wetting liquid films.

The use of these glass substrates enabled us to exclude the influence on the experimental results of such noncontrollable factors as roughness and pollution of the substrate surface. The isotherms of the disjoining pressure of wetting films of a number of two-component mixtures of nonionic liquids on glass substrates were experimentally determined. The film thicknesses were measured by an ellipsometric method; the disjoining pressure for the film was preset by adjusting the pressure of solvent vapours. The results obtained demonstrate a qualitative agreement with the theory of the adsorption component of disjoining pressure developed by Derjaguin and Churaev.

It is also shown that even very small additions of a polar substance to a nonpolar solvent may cause a marked change in the thickness of films. In addition to adopting the theory of the adsorption component of disjoining pressure, certain assumptions are made about the formation of the structural component resulting from the addition of a polar component to quantitatively describe the results obtained. The contribution of the adsorption and structural components of disjoining pressure to the stability of films of solution is estimated.     

Stable drop shapes under disjoining pressure. I. A hierarchical approach and application

The contact line region as affected by the disjoining pressure has been analyzed under the assumption that it can sustain only two types of profiles. Disjoining pressure represents the extra potential in thin films that always exists in the contact angle region where a liquid drop or a wedge thins to meet the solid substrate and in turn affects the contact angle as well as the film profile. It is shown here that the integration of the augmented Young-Laplace equation to yield the above types of drop profiles under the action of disjoining pressure leads to the usual conditions of equilibrium as well as the condition of stability in the same analysis. Other inequality constraints are obtained where the stability condition does not apply. The fact that stability condition coexists with the conditions of equilibrium is pursued to show in one case that the stability modifies half of the predicted outcomes in the drop shapes. In addition, exceptions to the rule are found, which are physically meaningful, and a scale-dependent equilibrium is reported for the first time.     

Hydrophobicity effects in the condensation of water films on quartz

The surface forces of thin water films condensed onto crystalline quartz plates have been investigated by ellipsometric measurements of film thickness as a function of disjoining pressure. Quartz substrates ranging from fully hydroxylated (contact angle − 0°) to completely dehydroxylated (contact angle − 45°) were used and the results obtained related to the theoretically predicted van der Waals and electrostatic forces present in the system. Water films on fully hydroxylated quartz are much thicker than expected, whereas films on fully dehydroxylated quartz are close to the Lifschitz prediction of dispersion forces. As the extent of dehydroxylation decreases, the adsorption isotherm approaches that obtained on fully hydroxylated quartz.     

Wetting–dewetting films: The role of structural forces

The liquid wetting and dewetting of solids are ubiquitous phenomena that occur in everyday life. Understanding the nature of these phenomena is beneficial for research and technological applications. However, despite their importance, the phenomena are still not well understood because of the nature of the substrate's surface energy non-ideality and dynamics. This paper illustrates the mechanisms and applications of liquid wetting and dewetting on hydrophilic and hydrophobic substrates. We discuss the classical understanding and application of wetting and film stability criteria based on the Frumkin–Derjaguin disjoining pressure model. The roles of the film critical thickness and capillary pressure on the film instability based on the disjoining pressure isotherm are elucidated, as are the criteria for stable and unstable wet films. We consider the film area in the model for the film stability and the applicable experiments. This paper also addresses the two classic film instability mechanisms for suspended liquid films based on the conditions of the free energy criteria originally proposed by de Vries (nucleation hole formation) and Vrij–Scheludko (capillary waves vs. van der Waals forces) that were later adapted to explain dewetting. We include a discussion of the mechanisms of nanofilm wetting and dewetting on a solid substrate based on nanoparticles' tendency to form a 2D layer and 2D inlayer in the film under the wetting film's surface confinement. We also present our view on the future of wetting–dewetting modeling and its applications in developing emerging technologies. We believe the review and analysis presented here will benefit the current and future understanding of the wetting–dewetting phenomena, as well as aid in the development of novel products and technologies.     

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.     

Instabilities of nematic liquid crystal films

We discuss instabilities exhibited by free surface nematic liquid crystal (NLC) films of nanoscale thickness deposited on solid substrates, with a focus on surface instabilities that lead to dewetting. Such instabilities have been discussed extensively; however, there is still no consensus regarding the interpretation of experimental results, appropriate modeling approaches, or instability mechanisms. Instabilities of thin NLC free surface films are related to a wider class of problems involving dewetting of non-Newtonian fluids. For nanoscale films, the substrate–film interaction, often modeled by a suitable disjoining pressure, becomes relevant. For NLCs, one can extend the formulation to include the elastic energy of the NLC film, leading to an ‘effective’ disjoining pressure, playing an important role in instability development. Focusing on thin film modeling within the framework of the long-wave asymptotic model, we discuss various instability mechanisms and outline problems where new research is needed.     

On the calculation of disjoining pressure isotherms for nonaqueous films

A review of the methods of London and Hamaker and of Lifshitz for calculating disjoining pressure isotherms of nonaqueous liquid films is presented. The disjoining pressure isotherms for films of n-octane and of three triglycerides (tributyrin, tricaprylin, and triolein) on glass were calculated using both methods. The disjoining pressure isotherms for films on silanized glass were calculated using only the London-Hamaker approach. The refractive indices and static dielectric constants, necessary for the calculations, were measured. The silanized glass was considered to be the original glass covered by a layer with the same characteristic frequency as the underlying glass and a smaller limiting value of the dielectric constant epsilon(0). The limiting dielectric constant epsilon(0) and the thickness of the surface layer were taken as adjustable parameters. The disjoining pressure isotherms indicate that all films are stable on glass. In contrast, the stability of the films formed on silanized glass was found to depend mainly on the value of epsilon(0) and, less strongly, on the thickness of the surface layer. The stability of the films decreased with the decrease of epsilon(0) and, for each value of epsilon(0), was maximal for the thinnest surface layer.     

Thermodynamics of exogenous nanophases in metal melts

The conditions of the stability of heterophase disperse systems obtained by the exogenous introduction of nanosized solid phases in metal melts were considered by assuming the formation of thick and thin elastic films and disjoining pressure at the contact boundary of particles of disperse phase. The introduced criteria are expressed in the measured interface characteristics, i.e., surface tension and contact angles. The prospects for using a series of compounds of the Periodic system??s IV?CVI group metals as exogenous modifiers of nickel-based alloys are assessed on the basis of our experimental data.     

Molecular simulation of fluid-solid interfaces at nanoscale

The equilibrium states of vapor and liquid coexistent phases in contact with a solid surface are studied at the nanoscale by molecular dynamics simulations for a temperature close to the fluid triple point. The characteristics of the solid-fluid interfaces are determined when the interaction strength between the fluid and the solid varies in order to go from a situation of complete drying to that of complete wetting. From the vapor-liquid density profiles of liquid drops lying on the substrate surface or menisci of liquid films confined in slit pores, the contact angles made by the vapor-liquid interface with the solid are computed. The angle values are similar for the drops and the films. They are also in good qualitative agreement with the estimates obtained through the Young's relation from the surface tensions associated with the vapor-solid, liquid-solid, and vapor-liquid interfaces. However, at this scale, the uncertainties inherent to the angle computation and, to a lesser extent, to size effects seem to preclude that the quantitative agreement between the angle estimates obtained from the interface geometry and calculated from the Young's relation can be better than few degrees.     

Effect of hydrophobicity on the stability of the wetting films of water formed on gold surfaces

We have developed a methodology that can be used to determine disjoining pressures (Π) in both stable and unstable wetting films from the spatial and temporal profiles of dynamic wetting films. The results show that wetting films drain initially by the capillary pressure created by the changes in curvature at the air/water interface and subsequently by the disjoining pressure created by surface forces. The drainage rate of the film formed on a gold surface with a receding contact angle (θ(r)) of 17° decreases with film thickness due to a corresponding increase in positive Π, resulting in the formation of a stable film. The wetting film formed on a hydrophobic gold with θ(r)=81° drains much faster due to the presence of negative Π in the film, resulting in film rupture. Analysis of the experimental data using the Frumkin-Derjaguin isotherm suggests that short-range hydrophobic forces are responsible for film rupture and long-range hydrophobic forces accelerate film thinning.