I. Transition regions, line tensions and contact angles in soap films

doi:10.1016/S0022-0728(72)80209-2

Journal of Electroanalytical Chemistry and Interfacial Electrochemistry

Volume 37, Issue 1, June 1972, Pages 9-22

Dedicated to Professor J. Th. G. Overbeek on the occasion of the 25th anniversary of his appointement as a Professor of Physical Chemistry.

https://doi.org/10.1016/S0022-0728(72)80209-2 Get rights and content

Summary

An analysis is given of the thickness profile of a circular soap film and its Plateau border. It shows that in principle the thickness as a function of the radial distance, h(r), for a single film, can provide details of the interaction free energy ΔF(h) over a large range of h. The transition region between film and Plateau border where h(r) rapidly changes from microscopic to macroscopic values contains most information. With a simple model of ΔF(h), the profile and extension of the transition region is calculated for some “first black” soap films.

It is shown that to complete the macroscopic description of a liquid sheet, a line tension must be introduced. A theoretical expression for this line tension is given and its physical meaning is discussed. Some values are calculated using the same ΔF (h) as before.

References (25)

H.M. Princen et al.
J. Colloid Interface Sci.
(1965)
H.M. Princen et al.
J. Colloid Interface Sci.
(1971)
A. Prins
J. Colloid Interface Sci.
(1969)
J.Th.G. Overbeek
J. Phys. Chem.
(1960)
K.J. Mysels
J. Phys. Chem.
(1964)
A. Sheludko
Adv. Colloid Interface Sci.
(1967)
J. Lyklema et al.
J. Amer. Chem. Soc.
(1965)
A. Sheludko et al.
Kolloid-Z.
(1960)
M.N. Jones et al.
Trans. Faraday Soc.
(1966)
F. Huisman et al.
J. Phys. Chem.
(1969)

A. Sheludko et al.

Trans. Faraday Soc.

(1968)

J.Th.G. Overbeek

Cited by (159)

Temperature dependence of the contact angle of water: A review of research progress, theoretical understanding, and implications for boiling heat transfer
2021, Advances in Colloid and Interface Science
Contact angle, a quantitative measure of macroscopic surface wettability, plays an important role in understanding liquid-vapor heterogeneous phase change phenomena, e.g., boiling heat transfer. The contact angles of water at elevated temperatures are of particular interest for understanding of wettability-regulated boiling heat transfer in steam-based power generation. From a more theoretical perspective, the temperature dependence of contact angle of water is also essential to estimation of several key surface thermodynamic properties, such as the solid surface tension, the surface entropy, and the heats of immersion and adsorption. Here, a comprehensive review of historical efforts in measuring the contact angles of water over a wide temperature range on a variety of solids, not limited to metallic surfaces, is presented. As suggested by the literature data, the temperature dependence of contact angle of water may be classified into three regimes: (a) low temperatures below the saturation point (i.e., 100 °C at atmospheric pressure), (b) medium temperatures up to ~170 °C, and (c) high temperatures up to 300 °C at pressurized conditions. A slightly-decreasing or nearly-invariant trend of the contact angles of water on both non-metallic and metallic surfaces was reported for the low-temperature regime. In contrast, a steeper linear decline in water contact angle was demonstrated at temperatures above 100 °C. The few experimental data available on several metallic surfaces showed that the contact angle of water either again becomes nearly temperature-independent or further decreases with temperature above 210 °C. A theoretical understanding of the temperature dependence is given based on surface thermodynamic analysis, although the exact molecular mechanisms underlying these experimental observations remain unclear. Consequently, the theoretical model for predicting the variation of the contact angle of water with temperature is not well-developed. As the critical point of water (374 °C and 22.1 MPa) is approached, the surface tension, and hence the contact angle, should become vanishingly small. However, this theoretical expectation has not yet been verified due to the lack of experimental data at such high temperatures/pressures. Finally, future research directions are identified, including a systematic exploration of the contact angle at near-critical temperatures, the effects of surface oxidation, corrosion, and deposition on contact angle during operation of boilers and reactors, and the particular effect of irradiation on contact angle in nuclear reactor applications.
Thinning and thickening transitions of foam film induced by 2D liquid–solid phase transitions in surfactant–alkane mixed adsorbed films
2020, Advances in Colloid and Interface Science
Citation Excerpt :
The dark and circular spots represent the nucleated CBF or NBF. As suggested by de Feijter and Vrij [30] and lately confirmed by other researchers [31–34], the difference in the nucleation of the two black films originate from the boundary energy between the nucleated films and their surroundings. According to the DLVO theory, the CBF and NBF are respectively corresponding to the secondary and primary minimum in the foam-film free energy vs. thickness curve.
Mixed adsorbed film of cationic surfactant and linear alkane at the air-water interface shows two-dimensional phase transition from surface liquid to surface frozen states upon cooling. This surface phase transition is accompanying with the compression of electrical double layer due to the enhancement of counterion adsorption onto the adsorbed surfactant cation and therefore induces the thinning of the foam film at fixed disjoining pressures. However, by increasing the disjoining pressure, surfactant ions desorb from the surface to reduce the electric repulsion between the adsorbed films on the both sides of the foam film. As a result, the foam film stabilized by the surfactant-alkane mixed adsorbed films showed unique thickening transition on the disjoining pressure isotherm due to the back reaction to the surface liquid films. In this review, we will summarize all these features based on the previously published papers and newly obtained results.
Temperature dependence of contact angles of water on a stainless steel surface at elevated temperatures and pressures: In situ characterization and thermodynamic analysis
2020, Journal of Colloid and Interface Science
Phase change heat transfer (e.g., boiling of water) on surfaces can be enhanced by tuning the surface wettability, which is often quantified by the contact angle and is expected to be influenced by temperature and pressure. However, the temperature (and pressure) dependence of contact angles of water on metallic surfaces remain unclear. In this study, an in situ characterization of the contact angles of water on 304 stainless steel surfaces at temperatures from room temperature to 250 °C and at pressures up to 15 MPa was performed using the sessile drop method. It was shown that three distinct regimes can be identified on the contact angle-temperature curves. A slightly-decreasing trend of the contact angles with temperature was observed below 120 °C, followed by a steeper linear decrease at higher temperatures. A further rise of the decreasing rate with temperature was observed above 210 °C. In contrast to temperature, the pressure was shown to have little effects on the contact angles. Based on the theory of surface thermodynamics, the effects of temperature (and pressure) on the contact angles were analyzed in terms of the interfacial tensions. An empirical correlation was developed to predict the contact angles as a function of temperature.
Line tensions of galena (001) and sphalerite (110) surfaces: A molecular dynamics study
2017, Journal of Molecular Liquids
We used molecular dynamics (MD) simulation to determine the line tension of two sulfide mineral surfaces, namely galena (PbS)(001) and sphalerite (ZnS)(110) at 298 K. Density functional theory (DFT) calculations were used to estimate the partial charges, and the force field parameters were derived based on the nature of the surfaces and the governing potential terms. The computed bulk structures, surface energies and water adsorption energies of the minerals using such partial charges and force field parameters agree well with experiment or DFT results. Contact angles of a series of nano-sized water clusters with different sizes were determined from the MD simulations. Line tensions and macroscopic contact angles of the two mineral surfaces were then determined using the modified Young's equation. The macroscopic contact angles (~ 84^° and 40^° for galena and sphalerite surfaces) agree well with the experimental data. The resultant line tensions are on the order of 10^− 11 J/m for both surfaces but with different signs. Here, the line tension for PbS(001) with very low wettability is positive, and for the hydrophilic ZnS(110) surface is negative. Examination of the orientation of the water molecules on the two mineral surfaces showed that the tetrahedron structure present in bulk water (order parameter (q) = 0.61) was significantly perturbed on the ZnS(110) surface (q = 0.11) compared to the PbS(001) surface (q = 0.47). In particular, the average angle between water dipole moment and the surface normal and the radial distribution functions of the water molecules show that the oxygen in water molecules tends to orient itself to the cationic sites (Zn atom) in the sphalerite surface, while such orientation to the Pb atom in the galena surface is minimal. The above results explain that the favorable interaction between water molecules and sphalerite causes the microscopic contact angles to be smaller than the macroscopic value, which in turn yields a negative line tension. On the contrary, stronger affinity of water molecules to the bulk region rather than to galena surface results in bigger microscopic contact angles compared to the macroscopic value and a positive line tension.
Modeling soft interface dominated systems: A comparison of phase field and Gibbs dividing surface models
2017, Physics Reports
The two main continuum frameworks used for modeling the dynamics of soft multiphase systems are the Gibbs dividing surface model, and the diffuse interface model. In the former the interface is modeled as a two dimensional surface, and excess properties such as a surface density, or surface energy are associated with this sharp interface. Its motion and deformation, and the time evolution of the excess fields associated with it are calculated by a set of partial differential equations (the jump balances), which have to be solved together with the mass, momentum, and energy balances of the bulk phases. A wide range of phenomena have been modeled in this framework, such as the deformation of emulsion droplets in a flow field, the effects of interfacial rheology on multiphase flows, wave phenomena in stratified flows, bubbles rising in a quiescent liquid, phase separation in immiscible mixtures, wetting phenomena, and in-plane and cross-plane mass and heat transfer.
In the diffuse interface model the interface is modeled as a three dimensional region of finite thickness, in which order parameters change continuously from their value in one bulk phase to their value in the adjoining bulk phase. The model starts from a free energy functional which contains nonlocal contributions, which to leading order are represented by a square gradient term of the order parameter. The spatial distribution of density or concentration within the interfacial region is then determined by free energy minimization. When a simple pairwise inter-particle potential is assumed, a natural extension of the van der Waals model of phase transitions is obtained. Assuming a simple constitutive relation for the diffusive material fluxes in very viscous binary mixtures, the Cahn–Hilliard theory of spinodal decomposition can be obtained. For systems where convective material fluxes cannot be neglected, a reversible body force, called Korteweg force, must be added to the Navier–Stokes equation, which is proportional to the chemical potential gradient. This force is non-zero only for systems not at equilibrium, and is responsible for the strong convection observed in phase separating mixtures, while it is absent in systems where chemical potentials are uniform. Like the Gibbs dividing surface model, the diffuse interface model has been applied to a wide range of phenomena, such as mixing and demixing in binary mixtures, buoyancy driven detachment of wall-bound droplets, droplet breakup and coalescence, Marangoni effects, and flow in nano- and microchannels.
Here we discuss the derivation of the governing equations of these two frameworks, and compare their strengths and weaknesses. We also show how these two frameworks can be combined to solve multiphase problems more effectively.
Line tension and its influence on droplets and particles at surfaces
2017, Progress in Surface Science
In this review we examine the influence of the line tension τ on droplets and particles at surfaces. The line tension influences the nucleation behavior and contact angle of liquid droplets at both liquid and solid surfaces and alters the attachment energetics of solid particles to liquid surfaces. Many factors, occurring over a wide range of length scales, contribute to the line tension. On atomic scales, atomic rearrangements and reorientations of submolecular components give rise to an atomic line tension contribution τ_atom (∼1 nN), which depends on the similarity/dissimilarity of the droplet/particle surface composition compared with the surface upon which it resides. At nanometer length scales, an integration over the van der Waals interfacial potential gives rise to a mesoscale contribution |τ_vdW| ∼ 1–100 pN while, at millimeter length scales, the gravitational potential provides a gravitational contribution τ_grav ∼ +1–10 μN. τ_grav is always positive, whereas, τ_vdW can have either sign. Near wetting, for very small contact angle droplets, a negative line tension may give rise to a contact line instability. We examine these and other issues in this review.

View all citing articles on Scopus

View full text

I. Transition regions, line tensions and contact angles in soap films

Summary

J. Colloid Interface Sci.

J. Colloid Interface Sci.

J. Colloid Interface Sci.

J. Phys. Chem.

J. Phys. Chem.

Adv. Colloid Interface Sci.

J. Amer. Chem. Soc.

Kolloid-Z.

Trans. Faraday Soc.

J. Phys. Chem.

Trans. Faraday Soc.