Showing papers on "Surface tension published in 1979"

Liquids on solid surfaces: static and dynamic contact lines

Abstract: A contact line is formed at the intersection of two immiscible fluids and a solid. That the mutual interaction between the three materials in the immediate vicinity of a contact line can significantly affect the statics as well as the dynamics of an entire flow field is demonstrated by the behavior of two immiscible fluids in a capillary. It is well known that the height to which a column of liquid will rise in a vertical circular capillary with small radius, a, whose lower end is placed into a bath, is given by (2(j/apg) cos (), where (j is the surface tension of the air/liquid interface, f) is the static contact angle as measured from the liquid side of the contact line, p is the density, and g is the magnitude of the accelera­ tion due to gravity.! Thus, depending on the value of the contact angle, e, which is a direct consequence of the molecular interactions among the three materials at the contact line, the height can take on any value within the interval [ 2(J/apg, 2(J/apg]. In a sense, the influence of the contact angle is indirect: the contact angle, in capillaries with small radii, controls the radius of curvature of the meniscus which, in turn, regulates the pressure in the liquid under the meniscus. It is this pressure that determines the height of the column. In a similar manner, the dynamic contact angle can influence the rate of displacement of tbe meniscus through the capillary. The pressure drop

Translation of J. D. van der Waals' “The thermodynamik theory of capillarity under the hypothesis of a continuous variation of density”

Abstract: Van der Waals justifies the choice of minimization of the (Helmholtz) free energy as the criterion of equilibrium in a liquid-gas system (Sections 1–4). If densityρ is a function of heighth then the local free energy density differs from that of a homogeneous fluid by a term proportional to (d 2 ρ/dh 2); the extra term arises from the energy not from the entropy (Section 5). He uses this result to show howρ varies withh (Section 6), how this variation leads to a stable minimum free energy (Section 7), and to calculate the capillary energy or surface tensionσ (Section 9). Near the critical pointσ varies as (τ k -τ)3/2, whereτ k is the critical temperature (Section 11). The paper closes with short discussions of the thickness of the surface layer (Section 12), of the difficulty of assuming thatρ varies discontinuously with height (Section 14), and of the possible effect of derivatives of higher order than (d 2 ρ/dh 2) on the free energy and surface tension (Section 15).

Mechanics of Secondary Hydrocarbon Migration and Entrapment

Abstract: The mechanics of secondary hydrocarbon migration and entrapment are well-understood physical processes that can be dealt with quantitatively in hydrocarbon exploration. The main driving force for secondary migration of hydrocarbons is buoyancy. If the densities of the hydrocarbon phase and the water phase are known, then the magnitude of the buoyant force can be determined for any hydrocarbon column in the subsurface. Hydrocarbon and water densities vary significantly. Subsurface oil densities range from 0.5 to 1.0 g/cc; subsurface water densities range from 1.0 to 1.2 g/cc. When a hydrodynamic condition exists in the subsurface, the buoyant force of any hydrocarbon column will be different from that in the hydrostatic case. This effect can be quantified if the potentiome ric gradient and dip of the formation are known. The main resistant force to secondary hydrocarbon migration is capillary pressure. The factors determining the magnitude of the resistant force are the radius of the pore throats of the rock, hydrocarbon-water interfacial tension, and wettability. For cylindrical pores, the resistant force can be quantified by the simple relation: Pd = (2^ggr cos ^THgr)/R, where Pd is the hydrocarbon-water displacement pressure or the resistant force, ^ggr is interfacial tension, cos ^THgr is the wettability term, and R is radius of the largest connected pore throats. Radius of the largest connected pore throats can be measured indirectly by mercury capillary techniques using cores or drill cuttings. Subsurface hydrocarbon-water interfacial tensions range from 5 to 35 dynes/cm for oil-water systems an from 70 to 30 dynes/cm for gas-water systems. Migrating hydrocarbon slugs are thought to encounter water-wet rocks. The contact angle of hydrocarbon and water against the solid rock surface as measured through the water phase, ^THgr, is thus assumed to be 0°, and the wettability term, cos ^THgr, is assumed to be 1. A thorough understanding of these principles can aid both qualitatively and quantitatively in the exploration and development of petroleum reserves.

Interfacial free energy and the hydrophobic effect.

Abstract: Interfacial free energies demonstrate clearly that the antipathy between hydrocarbon and water rests on the strong attraction of water for itself. However, the unfavorable free energy associated with this antipathy, per unit area of contact between bulk hydrocarbon and water, is about 3-fold larger than a similar figure derived from solubility data per unit area of contact between a single dissolved hydrocarbon molecule and water. The discrepancy illustrates the difficulty in applying macroscopic concepts such as “interfacial surface” at the molecular level and can be formally resolved, at least qualitatively, by the predicted effect of surface curvature on surface tension.

The motion of bubbles in a vertical temperature gradient

Abstract: The motions of air bubbles in a viscous silicone oil in response to buoyancy and Marangoni forces have been studied. The Marangoni forces are produced by establishing a temperature gradient in the oil which generates a surface tension gradient over the bubbles. From the thermal gradients required to balance the buoyancy and Marangoni forces, the temperature dependence of the surface tension, γ′, is found to be −0.055 mJ/m 2 s. This is in agreement with an independent measurement of γ′ using the pendant drop technique.

Direct experimental verification of the Kelvin equation for capillary condensation

Abstract: THE thermodynamic properties of liquids trapped in microscopic pores or existing as very small, highly curved droplets are described by the Kelvin equation1. This equation forms the basis of critical nucleation theory2 and has been used in interpreting such diverse phenomena as adhesion3, the enhanced solubility of small particles2 and the retention and flow of liquids in porous materials4–6. The validity of the application of the Kelvin equation to such highly curved interfaces (where the mean radius of curvature can be in the range 1–100 nm) has been questioned1,4, but has never been tested by direct experiment. We have used multiple beam interferometry to observe the formation of capillary condensed liquid between crossed cylinders of molecularly smooth mica. We report here that the Kelvin equation is obeyed by cyclohexane menisci with mean radius of curvature as low as 4 nm. We further conclude that the application of the laws of thermodynamics, and the concept of a bulk surface tension, are valid in principle for such highly curved interfaces.

Skins of varying permeability: A stabilization mechanism for gas cavitation nuclei

Abstract: Numerous experiments suggest that bubble formation in water is initiated by preexisting gas nuclei. This is unexpected since gas phases larger than the order of 1 μm in radius ought to rise to the surface of a standing liquid, whereas smaller ones should dissolve rapidly via the outward diffusion of gas that results from surface tension. Several mechanisms for stabilizing gas nuclei have been proposed, but in each case there is experimental evidence to the contrary. In this article, a model is investigated in which stability is maintained by surface‐active skins of varying gas permeability. Data on ultrasonic cavitation and on bubble formation by counter‐diffusion indicate that such skins, if they exist, must be initially permeable. Quantitative comparisons with bubble counts obtained recently from supersaturated gelatin lead to the further conclusion that nuclear skins become effectively impermeable if the static pressure is raised rapidly by a sufficiently large amount. The surface area, length, and ene...

Numerical solution of the exact equations for capillary-gravity waves

Abstract: A numerical method is presented for the computation of two-dimensional periodic progressive surface waves propagating under the combined influence of gravity and surface tension. The dynamic boundary equation is used in its exact nonlinear form. The procedure involves a boundary-integral formulation coupled with a Newtonian iteration. Solutions of high accuracy can be achieved over much of the range of wavelengths and heights including limiting waves. A number of different continuous families of solutions have been produced, all of which ultimately exhibit closed bubbles at their troughs. The so-called critical wavelengths are less important than have been previously assumed; the number of possible wave forms does increase with increasing wavelength, however.

Liquid surfaces: theory of surface tension

Abstract: The theory of equilibrium liquid surfaces is reviewed from the macroscopic (thermodynamic) and microscopic (statistical) points of view. Although emphasis is placed on the surface tension, other surface thermodynamic quantities are treated, especially the contact angle and work of adhesion. The Gibbs scheme is used to describe the surface thermodynamics. The equivalent hydrostatic approach, the curvature dependence of the surface tension and its relation to other surface quantities are presented. The effect of solid surface topology on the contact angle is discussed, together with the controversial Young's equation. Good's and Fowkes' theories are described and criticised from the statistical point of view. The surface tension theories for simple liquids (Kirkwood and Buff), simple metals (Evans) and solid-fluid interphases (Navascues and Berry) are deduced from a single statistical mechanical formalism. The van der Waals theory of the liquid vapour interphase is presented. Thermodynamic perturbation theory for the interphase (Toxvaerd, Abraham) and the analysis of the free energy density as a functional of the interphase density (Yang, Flemming and Gibbs) are discussed.

Valence state at the surface of rare-earth metals

Abstract: The valence state of a rare-earth metal surface is investigated by using general properties of the surface tension of metals. Thereby it is concluded that samarium is likely to have a divalent or partly divalent surface on top of its trivalent bulk phase, which agrees with recent spectroscopic observations. Also californium metal is discussed from this point of view. Finally, the position of the 4f level in a bulk gold atom as compared to its position in a surface gold atom is briefly discussed.

On the location of surface of tension in the planar interface between liquid and vapour

Abstract: The structure of the interface of an argon-like fluid in equilibrium with its own vapour at 110 K is studied using the Monte Carlo method. The two components P N(z) and P T(z) (normal and tangential) of the pressure tensor P(r) for the planar interface are determined in the simulation. The normal component is a constant along the direction perpendicular to the surface (the z-direction) and is equal to the hydrostatic pressure. The tangential component varies across the surface. The surface tension γ, and the surface of tension z s are determined. The location of the surface of tension is compared with the location of the Gibbs equimolar dividing surface, and the results are used to determine the curvature dependence of the surface tension for spherical droplets. The results are compared with theory.

Surface thermodynamics of leukocyte and platelet adhesion to polymer surfaces

Abstract: Adhesion of leukocytes and platelets to solid substrates of different surface tensions and hence different wettability is studied from a thermodynamic point of view. A simple thermodynamic model predicts that cellular adhesion should increase with increasing surface tension of the solid substrate if the surface tension of the medium in which the cells are suspended is lower than the surface tension of the cells. If the surface tension of the suspending medium is higher than that of the cells, the opposite behavior is predicted. These predictions are borne out completely by neutrophil adhesion tests, where the surface tension of the aequeous suspending medium is varied by addition of dimethyl sulfoxide (DMSO). Platelet adhesion experiments also confirm these predictions, the only difference being that surface tensions of the suspending medium above that of the platelets cannot be realized, owing to exudation of surface active solutes from the platelets. Utilization of the thermodynamic prediction that cellular adhesion should become independent of the surface tension of the substrate when the surface tensions of the cells and that of the suspending medium are equal leads to a value of the surface tension of neutrophils of 69.0 erg/cm2,† in excellent agreement with the value obtained from contact angles measured on layers of cells.

Polymer polarity and surfactant adsorption

Abstract: The effect of polymer polarity on surfactant adsorption from aqueous solution is discussed. The analysis assumes that surfactant adsorption at the polymer–water interface follows a Langmuir-type adsorption isotherm and the free energy of adsorption is controlled by the interfacial tension of the interface. Saturation adsorption given by the area per molecule of surfactant at the critical micelle concentration (CMC) of the surfactant is related to the polymer–water interfacial tension and the polarity of the polymer surface, calculated from the polar and dispersion contributions to the polymer surface energy. Available data on the area per molecule of sodium lauryl sulfate on various polymer surfaces have been used to test satisfactorily the above analysis. The analysis is used to interpret some of the observations relating to surfactant adsorption encountered in the emulsion polymerization of polar monomers and particle size determination of latexes by the soap titration method. Further, potential utility of such area per molecule data to characterize the nature of polymer surfaces is also discussed.

Convergence and disintegration of liquid jets induced by an electrostatic field

Abstract: Liquid jets are formed by application of an electrostatic field to insulating liquids, which are prepared to have specific conductivities of 10−12–10−7 Ω−1 cm−1 with the ionic additive and viscosity of 0.73–10.2 cP with the silicone intermediate. Convergence of the jets is studied in relation to the specific conductivity. Liquids with specific conductivities between 10−10 and 10−7 Ω−1 cm−1 form fine threads of liquid followed by successive disintegration to many fine droplets. Contribution of the charge term to the disintegration is estimated to be negligible in the axisymmetric mode of disturbance. The explanation is supported by the fact that the measured drop frequency is very well correlated with the theoretical result by Weber, who analyzed the distintegration process in terms of surface tension and viscosity. The coefficient of correlation is 0.98, and the gradient of regression line is 0.97.

Thermodynamic studies of cellular adhesion.

Abstract: Cellular adhesion of granulocytes and of platelets to solid substrates of different surface tensions has been studied from a thermodynamic aspect. A simple thermodynamic model predicts that cellular adhesion should increase as the surface tension of the solid substrate increases provided that the surface tension of the liquid medium in which the cells are suspended is lower than the surface tension of the cells themselves. If, however, the surface tension of the liquid medium is higher than the surface tension of the cells, then a decrease in cell adhesion with increasing substrate surface tension can be predicted. These predictions are completely substantiated by granulocyte adhesion tests in which the surface tension of the suspending liquid medium is varied through the addition of different volumes of dimethyl sulfoxide (DMSO). Platelet adhesion experiments also confirmed these predictions, the only difference being that it is not possible to obtain a suspending liquid medium with a surface tension higher than that of platelets themselves, as a consequence of the exudation of surface active substances by the platelets.

Repulsive van der Waals forces. I. Complete dissociation of antigen-antibody complexes by means of negative van der Waals forces.

Abstract: When two types of particles and/or macromolecules with different inter- facial free energies are immersed (or dissolved) in a liquid medium with an interfacial free energy intermediate between those of the particles or macro- molecules, the net van der Waals forces between these particles or molecules are repulsive. Thus by lowering the interfacial free energy (proportional to the surface tension) of their liquid medium, antigen-antibody (Ag-Ab) complexes of the van der Waals type can be readily dissociated, as could be demonstrated with the antigen 3-azopyridine (P3) coupled to rabbit serum albumin (P3A) and rabbit anti-P3 antiserum. As surface tension lowering agents, ethylene glycol (EG) and dimethyl sulfoxide (DMSO) were principally used. Prevention of the formation of P3A-anti-P3 complexes could be effected with the addition of less EG or DMSO than was needed for the dissociation of the precipitate, once formed. The reasons for this effect are discussed. P3A-anti-P3 complexes dissociated with EG, re-...

Repulsive van der Waals Forces. II. Mechanism of Hydrophobic Chromatography

Abstract: When two materials with different interfacial free energies are immersed in a liquid with an interfacial free energy intermediate between those of the two materials, the net van der Waals forces between these two materials are repulsive. Thus by lowering the interfacial free energy of the liquid medium, solutes or particles previously adsorbed onto low energy surfaces can be readily eluted from such surfaces. This is demonstrated by the coupling to and subsequent elution from Octyl Sepharose and Phenyl Sepharose of serum and other proteins. The elution of all proteins commenced when the surface tension of the eluting liquid was decreased to a point just below that of the protein in question. The eluted serum proteins successively emerged from the column in the exact decreasing order of their own interfacial free energies. In hydrophobic chromatography, coupling is favored when the van der Waals forces between solutes (or particles) and ligand are attractive (and maximum, frequently through the ad...

The density profile and surface tension of a Lennard-Jones fluid from a generalized van der Waals theory

Abstract: We present results of calculations of the equilibrium density profile and surface tension for the liquid-vapour interface of a Lennard-Jones 12-6 fluid. These calculations are based on a ‘microscopic’ version of the van der Waals theory of the interface. At high temperatures our results are in fairly good agreement with those from computer simulations. Near the triple point, however, the calculated density profiles appear to be too broad and the corresponding surface tensions are about 50 per cent larger than the results of the simulations.