Thin film drainage: hydrodynamic and disjoining pressures determined from experimental measurements of the shape of a fluid drop approaching a solid wall

Accurate measurements of the shape of a mercury drop separated from a smooth flat solid surface by a thin aqueous film reported recently by Connor and Horn (Faraday Discuss. 2003, 123, 193-206) have been analyzed to calculate the excess pressure in the film. The analysis is based on calculating the local curvature of the mercury/aqueous interface, and relating it via the Young-Laplace equation to the pressure drop across the interface, which is the difference between the aqueous film pressure and the known internal pressure of the mercury drop. For drop shapes measured under quiescent conditions, the only contribution to film pressure is the disjoining pressure arising from double-layer forces acting between the mercury and mica surfaces. Under dynamic conditions, hydrodynamic pressure is also present, and this is calculated by subtracting the disjoining pressure from the total film pressure. The data, which were measured to investigate the thin film drainage during approach of a fluid drop to a solid wall, show a classical dimpling of the mercury drop when it approaches the mica surface. Four data sets are available, corresponding to different magnitudes and signs of disjoining pressure, obtained by controlling the surface potential of the mercury. The analysis shows that total film pressure does not vary greatly during the evolution of the dimple formed during the thin film drainage process, nor between the different data sets. The hydrodynamic pressure appears to adjust to the different disjoining pressures in such a way that the total film pressure is maintained approximately constant within the dimpled region.     

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.     

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.     

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.     

Direct measurement of the laplace pressure in a very thin liquid film

Meniscus force plays an important part in magnetic storage devices, scanning probe microscopy, and micromachines, because the meniscus force increases steeply as the clearance between solid surfaces decreases down to submicrometers. Recently increased experimental and analytical studies on the subject have been published from the point of view of mechanical engineering. Meniscus force is generated by the Laplace pressure within the thin liquid film. Investigating the Laplace pressure is a direct way to clarify the generation mechanism of meniscus force. However, no appropriate measuring method of the Laplace pressure is available for a very thin liquid film confined by solid surfaces. This paper proposes a simple method of direct measurement of the Laplace pressure for the cases. The principle of the measurement method is described. Measurement is conducted using the measuring device. Experimental results on the Laplace pressure show good agreement with the theoretical predictions.     

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.     

Phase diagrams of nonionic foam films: construction by means of disjoining pressure versus thickness curves

The thickness h of foam films can be measured as a function of the disjoining pressure Pi using a thin film pressure balance. Experimental Pi-h curves of foam films stabilized with nonionic surfactants measured at various concentrations resemble the p-V(m) isotherms of real gases measured at various temperatures (p is the pressure and V(m) is the molar volume of the gas). This observation led us to adopt the van der Waals approach for describing real gases to thin foam films, where the thickness h takes the role of V(m) and the disjoining pressure Pi replaces the ordinary pressure p. Our analysis results in a phase diagram for a thin foam film with spinodal, binodal as well as a critical point. The thicker common black film corresponds to the gas phase and the compact Newton black film for which the two surfaces are in direct contact corresponds to the dense liquid. We show that the tuning parameter for the phase behavior of the film is the surface charge density, which means that Pi-h curves should not be referred to as isotherms. In addition to the equilibrium properties the driving force for the phase transition from a common black film to a Newton black film or vice versa is calculated. We discuss how this transition can be controlled experimentally.     

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.     

Disjoining pressure and capillarity in the constrained vapor bubble heat transfer system

Using the disjoining pressure concept in a seminal paper, Derjaguin, Nerpin and Churaev demonstrated that isothermal liquid flow in a very thin film on the walls of a capillary tube enhances the rate of evaporation of moisture by several times. The objective of this review is to present the evolution of the use of Churaev's seminal research in the development of the Constrained Vapor Bubble (CVB) heat transfer system. In this non-isothermal "wickless heat pipe", liquid and vapor flow results from gradients in the intermolecular force field, which depend on the disjoining pressure, capillarity and temperature. A Kelvin-Clapeyron model allowed the use of the disjoining pressure to be expanded to describe non-isothermal heat, mass and momentum transport processes. The intermolecular force field described by the convenient disjoining pressure model is the boundary condition for "suction" and stability at the leading edge of the evaporating curved flow field. As demonstrated by the non-isothermal results, applications that depend on the characteristics of the evaporating meniscus are legion.     

Correction to the paper “the condition of mechanical equilibrium on the surface of a nonuniform thin film” [1]

The correction is introduced to the definition of the disjoining pressure of wedge-shaped film formulated in the authors’ previous publication. In refined definition, the nondiagonal pattern of pressure tensor even in cylindrical coordinates is taken into account and the disjoining pressure is introduced by analogy with the case of the transition zone of wetting meniscus. The alternative procedure of the definition of the disjoining pressure through the diagonal pressure tensor in the middle of the wedge is also considered.     

Hydrophobic forces in the foam films stabilized by sodium dodecyl sulfate: effect of electrolyte

Further studies of the hydrophobic force in foam films were carried out, including the effect of added inorganic electrolyte. We used a thin film balance of Scheludko-Exerowa type to obtain the disjoining pressure isotherms of the foam films stabilized by 10(-4) M sodium dodecyl sulfate in varying concentrations of sodium chloride. The results were compared with the disjoining pressure isotherms predicted from the extended Derjaguin-Landau-Verwey-Overbeek theory, which considers contributions from hydrophobic force in addition to those from double layer and van der Waals dispersion forces. The double layer forces were calculated from the surface potentials (psi s) obtained using the Gibbs adsorption equation and corrected for the counterion binding effect, while the dispersion forces were calculated using the Hamaker constant (A232) of 3.7 x 10(-20) J. The hydrophobic forces were calculated from the equilibrium film thickness as described previously. The predicted disjoining pressure isotherms were in good agreement with the experimental ones. It was found that the hydrophobic force is dampened substantially by the added electrolyte.     

The condition of mechanical equilibrium on the surface of a nonuniform thin film

The condition of internal mechanical equilibrium of a curved surface layer is derived, and its application to practically important cases of incomplete formation of the surface layer (as is sometimes the case, for example, in thin films) is considered. The notion of a local disjoining pressure is introduced, and the equilibrium condition for a variable-thickness thin film is obtained; this condition is valid both in the absence and in the presence of external fields. The cases of a wedge-shaped film, cylindrical film, spherical film, and transition zone of a wetting film are analyzed.__________Translated from Kolloidnyi Zhurnal, Vol. 67, No. 2, 2005, pp. 235–242.Original Russian Text Copyright © 2005 by Rusanov, Shchekin.     

Kinetics of Gas Bubble Motion in a Capillary

Two flow regimes were discovered by measuring flow rate vof water through thin capillaries containing small gas bubble. The first regime is realized at a low pressure drop P, when the main resistance to flow is created by the wetting film. The estimate of its thickness makes it possible to determine the parameters of the isotherm of the electrostatic component of the disjoining pressure corresponding to the constant charge of the film–gas interface and potential of the quartz surface, which requires the application of a new calculation procedure. As Pincreases, an advancing meniscus forms contact angle of 50°–60° due to the film rupture when it reaches critical pressure in the thinnest part near the meniscus. In this case, the rate vis controlled by the flow in the filled part of a capillary, although some additional viscous drag is also created by the film moving in front of advancing meniscus. The longer the bubble, the greater this contribution.     

Equilibrium thin liquid films

The latest results are reviewed and a number of new concepts of the thermodynamics of thin films are formulated. Current definitions of disjoining pressure and their applications for introducing disjoining pressure into thermodynamics of phase equilibria, as well as the new thermodynamic definition of the thickness of thin film, are considered. New approaches to the rigorous definition of disjoining pressure in curved films and films with nonuniform thickness, including transition zones of wetting films, are analyzed. The modulus of Gibbs’ elasticity is derived for the case of a thin film. The role of the elasticity of this type in thin films and its correlation with traditional transverse (Derjaguin) elasticity related to the disjoining pressure are explained.     

Influence of the ambient medium on the disjoining pressure of liquid metallic films

We have found the electron density of states in a thin liquid metallic film for an arbitrary form of the boundary conditions for the wavefunctions of the electrons on the film surface. Assuming a Fermi distribution of the electron energies, we have calculated the thermodynamic characteristics of the film and determined and electronic component of the disjoining pressure. It has been shown that the ambient medium and the state of the surface determine the value and the sign of the electronic component of the disjoining pressure. We have determined the conditions for which a stable state of liquid metallic films is ensured.