Showing papers on "Surface tension published in 1981"

The effect of surface tension on the shape of fingers in a Hele Shaw cell

Abstract: The experimental results of Saffman & Taylor (1958) and Pitts (1980) on fingering in a Hele Shaw cell are modelled by two-dimensional potential flow with surface-tension effects included at the interface. Using free streamline techniques, the shape of the free surface is expressed as the solution of a nonlinear integro-differential equation. The equation is solved numerically and the solutions are compared with experimental results. The shapes of the profiles are very well predicted, but the dependence of finger width on surface tension is not quantitatively accurate, although the qualitative behaviour is correct. A conflict between the numerics and a formal singular perturbation analysis is noted but not resolved. The stability of the steady finger to small disturbances is also examined. Linearized stability analysis indicates that the two-dimensional fingers are not stabilized by the surface-tension effect, which disagrees with the experimental observations. A possible reason for the discrepancy between theory and experiment is suggested.

Density and surface tension of 83 organic liquids

Abstract: 1920 where subscript 2 stands for the solute and 1 for the solvent: x2 is the mole fraction of the solute in the solvent; f2 is the fugacity of the solute in the gas phase. Henry’s constants for hydrogen in the three aromatic compounds were evaluated by extrapolating a plot of fH,lxHl to xH = 0. The fugacity of hydrogen in the gas phase, fw was calculated from the Soave-Redlich-Kwong equation of state (4). Figure 2 shows the plot of Henry’s constants vs. temperature. The values of

Surface tension and contact angle of a liquid–solid interface

Abstract: The contact angle between a liquid film and a solid substrate is treated in the van der Waals model used previously by the author to discuss gas adsorption on solid surfaces The model accounts for the occurrence of three types of wetting behavior, ie, complete wetting, partial wetting, and nonwetting, as well as for transitions between these different regimes According to this model, the contact angle depends on two parameters, namely the reduced temperature T/Tc, where Tc is the critical temperature of the liquid, and ew/kTc, where ew is the minimum in the liquid–solid interaction potential For high‐energy surfaces, corresponding to large ew/kTc, the contact angle decreases on increasing temperature; the opposite behavior is predicted to occur on sufficiently low‐energy surfaces With some hypotheses on how ew depends on the nature of the solid and liquid phases present, one can calculate the variation in contact angle with liquid species for a given solid at fixed temperature The theory is compare

Determination of the surface tension of surfactant solutions applying the method of Lecomte du Noüy (ring tensiometer)

Abstract: Starting from a comparative assessment of the outstanding works on the ring method (du Nouy) for the determination of the surface tension of liquids and its solutions it is shown that the application of this method to surfactant solutions can lead to substantial errors if one follows conventional conditions. These errors are mainly connected with so far unknown phenomena occurring during the raising of the ring and concerning the influence of the hydrophilic vessel wall above the solution level and the stretching of the solution surface. This is demonstrated quantitatively with surfactant solutions of different kind and concentration. These effects can be explained theoretically very simply by introducing certain assumptions on the behaviour of a surfactant adsorption layer on the inner vessel wall. Conditions leading to the elimination of these errors are given, thus enabling the application of the ring method to the determination of the surface tension of surfactant solutions.

Kinetics of silica polymerization

Abstract: The polymerization of silicic acid in dilute aqueous solutions was studied experimentally and theoretically. Two basic processes were studied: the formation of colloidal particles by homogeneous nucleation, and their further growth by deposition of dissolved silica upon them. It was found that the state of ionization of the silica surface controls the rate of polymerization. The rate of deposition of dissolved silica on the surface of amorphous silica is proportional to the surface density of ionized silanol groups. The extent of surface ionization also determines the value of the surface tension, and thus also the rate of homogeneous nucleation. Added salts accelerate both molecular deposition and homogeneous nucleation by increasing the extent of surface ionization and decreasing the solubility of silica. Except for fluoride, salt ions were found not to have any specific catalytic effect. Fluoride was confirmed to be a powerful catalyst. Aluminum and boron were found to inhibit the reaction at pH 8. A successful quantitative theory of the homogeneous nucleation of colloidal silica particles was developed. The Lothe-Pound factor was shown to be about 3.34 × 1025 (kg H2O)−1. The nucleation model and results of our data analysis are incorporated in a computer code which models the homogeneous nucleation and growth of colloidal silica particles. This code is able to reproduce much of our data to within experimental error, and may be used to generate useful predictions for conditions that are typical of geothermal brines. The concentration of “adsorbed silica” on the surface of amorphous silica was determined, and was found to increase with the concentration of dissolved silica in the ambient solution. It is probably a reaction intermediate between dissolved silica and solid amorphous silica.

Surface Tension Driven Instability in a Horizontal Liquid Layer with a Deformable Free Surface. I. Stationary Convection

Abstract: The effect of a free surface deformation on the onset of surface tension driven instability in a horizontal thin liquid layer subjected to a vertical temperature gradient is examined using linear stability theory. Assuming that the neutral state is a stationary one, the conditions under which instability sets in are determined in detail. It is shown that when the upside of the liquid layer is a free surface the free surface deformation is important only for unusually thin layers of very viscous liquids. It is also shown that when the underside of the liquid layer is a free surface the free surface deformation plays an essentially important role and the presence of a vertical temperature gradient can stabilize the layer which, in case of no temperature gradient, is always unstable.

Surface Tension Driven Instability in a Horizontal Liquid Layer with a Deformable Free Surface. II. Overstability

Abstract: The theory described in the first paper of this series [M. Takashima: J. Phys. Soc. Jpn. 50 (1981) 2745] is extended to include the possibility that surface tension driven instability in a horizontal thin liquid layer confined between a solid wall and a deformable free surface can set in as purely oscillatory motions. Linear stability theory is applied to derive a time-dependent eigenvalue relationship. Numerical computations are carried, and it is found that whichever side of the liquid layer is a free surface oscillatory modes of instability can occur when and only when the temperature of the solid wall is lower than that of the air phase.

Energy Variations in Diffusive Cavity Growth

Abstract: The assignment of boundary values for the chemical potential and the calculation of energy release rates for the growth of creep cavities along grain boundaries by self-diffusion are discussed It is assumed that the boundaries are flat and that surface and gran-boundary diffusion are the dominant transport mechanisms As matter diffuses from the void surface into and along the grain boundary, misfit residual stresses are induced to alleviate the high stress concentration ahead of the cavity apex As a result, it is shown that the contribution of strain energy terms to the chemical potential can be neglected in typical cases Also, contrary to the Griffith crack extension model, the energy dissipation incurred by diffusive removal of material from the cavity surface and deposition in the grain boundary is a major term in the energy transfers associated with cavity growth The primary energy sink in diffusive cavity growth arises from the work done by the grain-boundary normal stress when matter is inserted in the near-tip region by diffusion, and not from the loss of strain energy of matter that is removed from the cavity at its tip or from a work of bond separation Thermodynamic restrictions on the angle formed bymore » the void surfaces at their apex, where they join the grain boundary is described The derivation of boundary values for the chemical potential is carried out in a manner appropriate for arbitrarily large but elastic distortions of material near the cavity tip and, by contrast to most previous work in the area Rigorously the effects of surface tension, as distinct from surface energy, is included« less

Surface tension of natural silicate melts from 1,200°–1,500° C and implications for melt structure

Abstract: The surface tension between silicate liquid and gas has been measured for four lava compositions (limburgite to andesite) from 1,200° to 1,500° C. The magnitude of surface tension (γ) is in the range 350–370 dynes/cm. Variations found in γ as a function of liquid composition were small and had no obvious relation to liquid composition. γ was also found to vary little with furnace atmosphere — air, Ar, CO2, H2, CO and their mixtures. A relaxation time of hours to days, depending on temperature, is required before reproducible results can be obtained from originally crystalline starting material.

Viscous fluid buckling of plane and axisymmetric jets

Abstract: Experimental results are presented concerning the spontaneous oscillations observed when a high-viscosity fluid jet flows vertically against a flat surface. The two jet shapes investigated were the axisymmetric jet and the plane jet. The minimum distance from the jet orifice to the flat surface for which these oscillations are observed, termed the ‘buckling height’, was determined experimentally. The frequency of the subsequent oscillations was also determined. Both were measured as functions of fluid and flow variables. It is found that surface tension effects are the dominant factors influencing the buckling height, while the rate of oscillation is affected by both surface tension effects and by viscous, gravity and inertia effects. The major results are presented in non-dimensional form. Photographs of the buckling phenomenon are provided for representative jet geometries. It is also established experimentally that there is an upper limit to the flow Reynolds number above which buckling does not occur.

The structure and thermodynamics of a solid–fluid interface

Abstract: Two sets of molecular dynamics calculations have been performed for systems of 952 Lennard‐Jones particles placed up to surfaces with and without lattice structure. The calculations are performed for different pressures corresponding to dense fluid states at a temperature above the critical temperature. Only little lattice order is found in the interface and only in the contact layer direct up to the lattice surface. The excess thermodynamic functions, e.g., the surface tension, however, are found to be affected by the particle and lattice structure of the surface.

Effect of oxygen on the surface tension of liquid copper

Abstract: The influence of oxygen on the surface tension of liquid copper has been determined by the sessile drop technique. The surface tension of pure liquid copper at 1108 °C is found to be equal to 1.320 ± 0.015 N/m. The effect of oxygen is investigated for partial pressures of oxygen ranging from 10−13 to 5 X 10−6 atm. The surface activity of oxygen is deduced to equal 3200 ± 600 N/m and the saturation adsorption to equal 5.72 X 10"6 mole/m2, which corresponds to a saturation area of 29 ±5A2 per adsorbed oxygen atom. The adsorption of oxygen on liquid copper is consistent with the formation at the metal surface of a two-dimensional compound of stoichiometry Cu3O. It is also concluded that equivalent attractive forces operate between neighboring adsorbed atoms.

Surface Tension-like Forces Determine Bacterial Shapes: Streptococcus faecium

Abstract: The same tendency that causes soap bubbles to achieve a minimum surface area for the volume enclosed seems to account for many of the features of growth and division of bacteria, including both bacilli and cocci. It is only necessary to assume that growth takes place in zones and that only in these zones does the tension caused by hydrostatic pressure create the strain that forces the cell to increase the wall area. The stress developed by osmotic pressure creates strains that significantly lower the free energy of bond splitting by hydrolysis or transfer. We believe this is sufficient to make growing wall have some of the properties ordinarily associated with surface tension. The feature common to all bacterial cell wall growth is that peptidoglycan is inserted under strain-free conditions. Only after the covalent links have been formed are the intervening stressed peptide bonds cleaved so that the new unit supports the stress due to hydrostatic pressure. The present paper analyses the growth of Streptococcus faecium in these terms. This is a particularly simple case and detailed data concerning morphology are available. The best fit to the data is achieved by assuming that growth takes place in a narrow region near the splitting septum and that the septal material is already under tension as it is externalized and is twice as thick as the external wall throughout the development of the nascent poles. Constancy of the ratio of hydrostatic pressure to the effective surface tension, P/T, is also consistent with electron microscopic observations.

Microscopic surface tension down to molecular dimensions and microthermodynamic surface areas of molecules or clusters

Abstract: Surface tension, surface energy, and entropy of small droplets, n clusters, and of cavities in liquids for sizes down to a single molecule are obtained Rigourous relations are derived that relate microsurface properties to the usual handbook properties of bulk liquids The microvalues and their dependence on the ratio of the cluster, droplet, or cavity size to the average liquid molecular size are given for common solvents, polar and nonpolar, including alcohols, water, hydrocarbons, rare gas liquids, and liquid (or solid) metals Microscopic values are less than bulk‐planar values by around 40% for nonpolar liquids, and greater for polar liquids by around 60% The n‐cluster (or cavity) sizes ? at which the microsurface properties approach the bulk values within a desired percentage, eg, 5%, are given The ordinary, bulk thermodynamic properties of liquids are also related to new useful quantities: ’’microthermodynamic surface areas’’ of molecules from which, using the equations given, ’’experimental’’

Spreading kinetics of drops on glass

Abstract: The spreading kinetics of drops on glass was experimentally studied. The liquids used were triply distilled water, aqueous electrolytic solutions of various pH's, low alcohols, glycerine, and squalane. A wide range of parameters was covered, including temperature, humidity, volume, viscosity, surface tension, and pH. A power law dependence of the contact area on time was elucidated in the form A = kt n . The values of n and k , and their dependence on the parameters studied are presented and discussed in comparison with previous experimental data for other systems and with existing theoretical models. The effect of the primary film on the kinetics of spreading is discussed and used to explain some of the phenomena observed.

Liquid film flowing slowly down a wavy incline

Abstract: A viscous lamina of given mean thickness flows down a wavy incline. Assuming low Reynolds number and small perturbations due to the wavy striations, the velocity profiles and the free surface profile are determined. It is found that the amplitude and phase shift of the free surface depend, in a complicated manner, on the surface tension and the wave length and orientation of the wavy striations. The motion of a particle on the free surface experiences drift which is also a function of the surface tension, the amplitude, wave length and orientation of the wavy incline.

Effects of alkyl chain length on surface and micellar properties of octaethyleneglycol- n alkyl ethers

Abstract: Surface and micellar properties of a homologous series of Octaethylene glycol-n-alkyl ethers (CnE8;n = 9 to 15) have been studied in aqueous solutions by the surface tension measurements. The effects of the alkyl chain length comprising even and carbon numbers have been examined in order to evaluate the surface free energy ΔGA-W and the standard free energy ΔGm for the micellization obtained from their surface tension data. The areas per molecule and the equilibrium surface tension values at the CMC decreased with an increasing carbon number and they showed zigzag curves by the difference in even and odd carbon numbers.

Viscous buckling of thin fluid layers

Abstract: Experimental results are presented describing the buckling type of instability of thin layers of very viscous liquids subjected to linear shear flow. If the dimensionless shear stress in the layer exceeds a critical value, the layer will buckle in a manner similar to the buckling of a thin elastic plate. The stability criteria are obtained as a ratio of the destabilizing viscous stresses relative to the stabilizing surface tension and gravitational forces.

Impact of a liquid drop against a flat surface

Abstract: Lagrangian methods are used with an assumed flow field and a truncated sphere model to analyze the dynamical process of a liquid drop impacting aflat, rigid surface. The resulting differential equation for drop height as a function of time during contact is solved numerically for several values of the three parameters: Weber number of the incoming drop, ratio of the surface tension in air to that at the contact surface, and the viscosity parameter. The drop contact radius as a function of time is also calculated and compared with some experimental results in the literature.

Waves in a viscous liquid curtain

Abstract: The wave motion created by a small obstacle placed in a viscous liquid curtain which falls steadily between two vertical guide wires is studied experimentally. The disturbances introduced by the obstacle propagate in the curtain to form two distinctive stationary lines of constant phase; one corresponds to the sinuous mode and the other to the varicose mode. The observed wave motion compares very well with that predicted by the theory of Lin (1980). The observed angle between the tangent at any point on the line of constant phase and the vertical are used to infer the dynamic surface tension of a rapidly moving surface. A considerable difference between the dynamic surface tension and the usual static surface tension is found for a liquid solution. However, no measurable difference is found for a pure liquid at the flow rates used in our experiments.