Clarence A. Miller

Spreading kinetics of liquid drops on solids

Abstract During spreading of a liquid drop on a solid surface, there is an initial stage where several factors can be important, then a stage where gravity and fluid viscosity are the chief factors promoting and resisting spreading, and finally a stage where intermolecular forces at the drops periphery replace gravity as the main factor causing spreading. Approximate analyses for the last two stages are developed. The results are in excellent agreement with available experimental data on spreading rates. The use of intermolecular forces acting throughout a finite region near the drops edge is superior to the use of a line force acting at the edge itself in predicting experimental spreading rates for the last stage.

The origin of flow during wetting of solids

Abstract During wetting processes a fluid interface moves along a solid surface which it contacts. This motion can occur only if flow arises near the contact line. A mechanism is proposed for the origin of such flow. Flow along the fluid interface near a solid-liquid-gas contact line is produced, for example, by the action of intermolecular forces on the liquid near the contact line. Whether flow is toward or away from the contact line depends both on the relative magnitude of liquid-liquid and liquid-solid intermolecular forces and on the size of the contact angle. A simple theoretical analysis correctly predicts that at an advancing contact line, i.e., one where liquid replaces gas in contact with the solid, the contact angle exceeds its equilibrium value and flow along the fluid interface is toward the contact line. Similar predictions are obtained for receding contact lines. The predicted variation of equilibrium contact angle for different liquids on a single solid is also consistent with experimental data.

Ultralow interfacial tensions and their relation to phase separation in micellar solutions

Interfaces having very low tensions can be produced when a micellar solution separates into a micelle-rich and a micelle-lean phase. For separation to occur under reasonable conditions, the micelles must contain enough solubilized oil or water to be about 100 A in diameter or larger. A simple model is developed to predict the conditions for phase separation and the compositions of the phases in equilibrium. Interfacial tension is calculated by adapting Cahn and Hilliards approach (J. Chem. Phys. 28 , 258 (1958)). Results show that interfacial tensions can be 10 −2 dyn/cm or lower even when the system is far from a consolute point. Predictions of the theory are in general agreement with the data of Healy et al . (Soc. Petrol. Eng. J. 16 , 147 (1976)) on low interfacial tensions in oil-water systems with a synthetic petroleum sulfonate surfactant.

Theory of drop size and phase continuity in microemulsions I. Bending effects with uncharged surfactants

Abstract A simple theory is developed using the methods of statistical thermodynamics to predict the drop size and solubilization in microemulsions containing uncharged surfactants. Its novel feature is a lattice model of the hydrocarbon region of the surfactant film at the surface of each drop. This region contains the hydrocarbon “tails” of surfactant and cosurfactant molecules, which are assumed to be fully extended, as well as oil molecules taken up by the film, which are assumed to be completely flexible. The effect of curvature is taken into account by considering this spherical region to consist of parallel lattice planes with unequal numbers of sites. With this model of the tail region and with the surfactant and alcohol polar groups taken as hard disks occupying a surface, the theory provides a simple description of bending effects on drop size. These effects are shown to be particularly important when a microemulsion phase is in equilibrium with excess oil or water. Calculations of drop size in such systems are made by minimizing system free energy with respect to drop radius and area per surfactant molecule for a given ratio of alcohol to surfactant molecules in the film. The “natural” radius of curvature is found by neglecting the free energy of drop dispersion and interaction. Then the Percus-Yevick approximation for hard spheres is used to account for dispersion effects. Our results indicate that the effect of dispersion is always to lower drop radius below its “natural” value. Calculations are made for systems containing double-chain and single-chain surfactants representative of those studied in our laboratory. The oils are straight-chain hydrocarbons and the cosurfactants straight-chain alcohols. Predicted variation of drop size and inversion behavior with surfactant, alcohol, and oil chain length, with surfactant head size, and with surfactant to alcohol ratio in the film are all in qualitative agreement with experimental results. The theory explains clearly for the first time how oil chain length affects microemulsion behavior. Basically, different oil-chain lengths lead to different free energies of mixing in the hydrocarbon region of the film and hence to different amounts of oil taken up by the film.

Spreading kinetics of a drop on a rough solid surface

Abstract The effect of surface roughness on spreading rates has been analyzed using a model in which a liquid drop spreads over the surface of a porous medium filled with the same liquid. The equations of motion in the drop are simplified with the lubrication theory approximation and then solved for both zero and small but nonzero contact angles by the method of matched asymptotic expansions. Although the largest pressure gradients and velocity gradients occur near the contact line at the drop periphery, behavior in this region is not singular as found in previous analysis of spreading on perfectly smooth surfaces. The reason no singularities exist is that flow occurs in the “porous medium” underlying the drop, i.e., the region of surface irregularities which is present for all real surfaces. Because the solution is not valid in the initial stages of spreading where experimental data on spreading rates are available, a quantitative comparison of theory and experiment cannot be made at present. The theory does, however, explain all qualitative features observed for spreading drops, e.g., the increase in spreading rate with increasing roughness and the frequent appearance of apparent contact angles significantly different from equilibrium contact angles.

Spreading kinetics of a drop on a smooth solid surface

Abstract Spreading of a drop on a perfectly smooth solid surface is analyzed using the method of matched asymptotic expansions. The analysis includes the effect of intermolecular forces near the contact line both on surface diffusion of adsorbed molecules and on flow within the liquid phase itself near the contact line. The former effect produces slip and allows the contact line to advance, while the latter effect is found to be small for most situations of interest. Equations obtained for drop shapes and spreading rates are formally similar to those found previously for rough surfaces, the main difference being that the length scale for the effective range of intermolecular forces replaces the length scale of surface irregularities in the definition of the small parameter used in the perturbation expansions. Expressions for the spreading rate are given for both zero and small but nonzero equilibrium contact angles.

Phase behavior of pH-dependent microemulsions

Abstract A model microemulsion system which exhibits pH-dependent phase behavior has been developed using oleic acid as the surfactant. Ultralow interfacial tensions were observed using an automated sessile drop technique. The effect of salinity on phase behavior can be counterbalanced by pH adjustment under appropriate conditions. Added electrolyte makes the surfactant system hydrophobic while an increase in pH can make it hydrophilic by ionizing more surfactant. Calculations based on the Gouy-Chapman theory are presented to describe the effects of pH and salinity. The study is relevant to enhanced oil recovery by chemical flooding.

SPONTANEOUS EMULSIFICATION IN OIL-WATF.R.-SURFACTANT SYSTEMS*

ABSTRACT Mixtures of several alkl-aryl sulfonates with brine were carefully contacted with oil. The mixtures contained a few percent surfactant and were either liquid crystalline phases or dispersions of liquid crystalline particles in brine. At high salinities a brine layer developed between the initial phases and an emulsion of brine drops in oil formed spontaneously at discrete sites along the surface of contact. At low salinities no emulsifixation was seen. The occurrence of emulsification only at high salinities is explained in terms of local supersaturation produced by the diffusion process.

Stability of interfaces with ion or dipole layers

Electrostatic energies of various planar and nearly planar arrays of charges and image charges, dipoles and image dipoles are calculated on the assumption of a discontinuity in dielectric constant nearby. Changes in electrostatic energy and interfacial energy are evaluated for small amplitude, wavy perturbations of a flat interface. Electrical contributions are destabilizing and, because of the discreteness of charge, marginal configurational stability occurs when total interfacial tension is still positive but small—a few dynes per centimeter or less. The effect of an adsorbed or deposited layer of ions depends strongly on how they rearrange when the interface is deformed; the generally weaker effect of a layer of dipoles depends greatly on how they reorient.

Phase behavior of dilute sodium dodecyl sulfate-hexanol-brine systems

ABSTRACT Dilute aqueous “solutions” of anionic surfactants injected during enhanced oil recovery processes usually contain liquid crystalline material. Phase behavior has been studied in a model system containing sodium chloride brine with surfactant, alcohol, and salt contents maintained below 6, 10, and 3 weight percent respectively. Pseudoternary phase diagrams at constant salinities are used to represent the results. Some interpretation of the results is given in terms of micellar shape transformations produced by changes in the relative hydrophilic and hydrophobic properties of surfactant-alcohol mixtures.