Damping Of Capillary Waves Research Articles

Anomalous Damping of Capillary Waves in Systems with Insoluble Monolayers of Alkyldimethylphosphine Oxides

Anomalously high damping of capillary waves has been discovered for systems with insoluble surface films of N-alkyldimethylphosphine oxides in the transition region from a heterogeneous to a continuous monolayer. This effect is probably caused by capillary wave scattering at two-dimensional cavities of a gaseous phase in the condensed monolayer phase (two-dimensional bubbles).

Calming the capillary waves on the surface of a bubble using an insoluble surfactant

The excess damping of capillary waves caused by a surfactant monolayer was demonstrated for the quadrupole shape mode of an isolated acoustically trapped bubble in water. A known amount of the water-insoluble surfactant stearic acid was deposited on the bubble surface from a microliter of ethanol solution. As the bubble dissolves, its surface area decreases thus compressing the monolayer. Compression rates ranged from 0.09 to 0.18 Å2 per molecule per minute for different bubbles and surfactant coverage ranged from 20 to 37 Å2 per molecule specific area. This technique was tested for accuracy and reproducibility by application to pendant bubbles and subsequent measurements of the static surface tension. Shape oscillations were induced by modulation of the ultrasonic radiation pressure and the free decay was recorded by an optical extinction technique. Local maxima in the normalized damping and frequency were observed near 26 Å2 per molecule coverage in agreement with similar studies of capillary waves on flat interfaces. An unexpected increase in the frequency was observed at high coverage and may be associated with the solidification or collapse of the monolayer. Any effects due to the presence of ethanol were shown to be negligible. [Work supported by ONR.]

Effect of an insoluble surfactant on capillary oscillations of bubbles in water: Observation of a maximum in the damping.

The excess damping of capillary waves caused by a surfactant monolayer is demonstrated to be present as well for the quadrupole shape mode of an isolated acoustically trapped bubble in water. To facilitate measurements of damping as a function of surface concentration, a method was developed for depositing a known amount of insoluble surfactant (stearic acid) on the surface of the bubble. As the bubble dissolves, the stearic acid concentration increases, and the excess damping has a pronounced local maximum near 0.26 ${\mathrm{nm}}^{2}$ per molecule specific area in agreement with capillary wave data for a flat surface. The method of depositing insoluble surfactant should be applicable to the characterization of other surface-limited processes in isolated bubbles.

Viscoelastic Properties of Dodecylammonium Chloride Monolayers

Monolayers of dodecylammonium chloride formed at the solution-air interface at different electrolyte concentrations have been investigated by dynamic surface light scattering. Pronounced maxima in the damping of capillary waves were observed at surfactant concentrations around 0.1 × CMC. These maxima occur at concentrations just above the break points in the surface tension vs concentration curves caused by first-order phase transitions from a gaseous to a liquid-expanded state. The experimental results were analyzed by comparisons with theoretical calculations based on the standard theory of light scattering due to capillary waves on liquid surfaces, and the molecular theory of the surface tension of ionic surfactant solutions presented earlier by Eriksson and Ljunggren. In this way it was possible to account satisfactorily for the observed concentration and salt dependencies of the central frequency and width of the spectral peak.

Capillary Wave Damping in Heterogeneous Monolayers

We studied capillary wave damping in heterogeneous monolayers of triglyceride at the air–water interface over a range of surface wavelengths (70–300 μm) using a light scattering technique. In addition, we studied the monolayer morphology using a Brewster angle microscope. We found that the morphology has a strong effect on the capillary wave damping. In the gas–liquid expanded (G/LE) coexistence region the monolayer forms a two–dimensional foam structure, where ‘bubbles’ of gas phase are separated by regions of liquid expanded phase. If the width of the LE regions is smaller than the wavelength of the capillary wave, the monolayer has no measurable effect on the damping of the capillary wave. When the width of the LE regions is larger than the wavelength, the capillary wave damping constant increases from its value for a clean water surface. We attribute this increase to a rise in the dynamic dilational elasticity of the heterogeneous monolayer.

Direct measurement of the spatial damping of capillary waves at liquid-vapor interfaces

We measured the spatial damping of low-frequency surface waves at air-water interfaces using a novel heterodyne light-scattering technique. For pure water the measured damping agrees well with linear hydrodynamic theory. For interfaces covered with a monolayer of pentadecanoic acid, we find a 5-fold increase in damping at a surface concentration of 2.2 molecules nm -2 , near the high-density end of the gas/liquid-expanded coexistence region. The behavior of the damping as a function of surface concentration cannot be explained by existing theories

Dynamical properties of heterogeneous surface layers. capillary wave scattering

The dynamics of a heterogeneous liquid surface constituting a two-dimensional disperse system is considered. One of the surface phases (the dispersed phase) forms circular regions of diameter comparable with the characteristic length of the mechanical disturbances within the continuous disperse medium. Inhomogeneous boundary conditions for the Navier-Stokes equations with a discontinuity on the surface phase contact line are formulated. Special attention is paid to the conditions on this line. An approximate method of solving the surface wave diffraction problem and the results for the case of transverse surface wave scattering are described. It is shown that if the wavelength is close to the dimensions of the two-dimensional dispersed particles and their concentration is sufficiently high, the energy of the scattered waves may exceed that dissipated in the vorticity layer. Thus, a new nonclassical mechanism of surfactant action on capillary wave damping is possible.

Observation of unusual effects in the damping of capillary waves on monolayer-covered surfaces

Observation of unusual effects in the damping of capillary waves on monolayer-covered surfaces

Damping of capillary waves by polymeric monolayers. Comparison with hydrodynamic theory

Etudes de l'attenuation des ondes capillaires par des couches monomoleculaires de poly(dimethylsiloxane)

Effect of surfactant concentration on the critical thicknesses of liquid films

It is shown that an increase in surfactant concentration at first causes the critical thicknesses of rupture on microscopic films to decrease but gradually a nearly constant value is reached. With films of aqueous solutions of fatty acids (valeric, caproic, caprylic and capric acids), this dependence correlates well with the effect of the surfactant concentration on the damping of capillary waves. With surfactants of the detergent type (OPE-7, OPE-20) in addition to the change of the critical thickness, the transition from rupture to formation of black spots is described, as the surfactant concentration exceedsC bl. The remarkable fact in the latter case is the independence of the critical thickness of the final state, be it rupture or formation of first or second black films. On the basis of the experimental data the assumption is put forward that the critical thickness of rupture or the critical thickness of formation of black spots is substantially affected by macroscopic non-uniformities in the film thickness. Thus the conclusion is reached that the critical thickness of an ideally plane parallel film which is the object of the theory, must be obtained by extrapolation of the measured value toward extremely small radii.

OBSERVATIONS OF LANGMUIR CIRCULATIONS IN LAKE ONTARIO1

The downwelling velocities associated with Langmuir circulations in Lake Ontario correlate well with wind speed under surface cooling. With surface heating the correlations with wind speed are poor and calculations of a stability parameter indicate a different proportionality. Observations of surface phenomena indicate that surface slicks and capillary wave damping are in operation at the point of downwelling.

Light scattering from the surface of sodium carboxymethylcellulose in water

Inelastic light scattering measurements of capillary wave frequency and damping in the kHz range for several solutions of sodium carboxymethylcellulose in redistilled water are reported. The capillary waves were thermally excited and had extremely low amplitudes. Light beating spectroscopy was used. For these solutions the capillary wave damping was very much lower than expected from hydrodynamic theory. A surface zone theory is proposed to interpret the experimental results.

Capillary waves at a gas-liquid phase interface

A first-order perturbation analysis of capillary waves at a gas-liquid phase interface is carried out. We recognize in this analysis that a surfactant may be present that will be transferred to and from the phase interface as a function of time. The Newtonian surface fluid model is used to describe the surface source of momentum and the jump momentum balance; Levich's model for surface convection has been adopted for the surface source in the jump mass balance for surfactant. We do not assume equilibrium to be instantaneously established between the surface and the substrate in the sense that the surface concentration of surfactant is not required to be a function merely of the concentration of surfactant in the bulk phase at the interface. The results indicate that the surface shear viscosity and surface dilational viscosity are equally important. To date only Mann's data for this geometry present the wavelength and damping factor as functions of frequency. Unfortunately our analysis and all other analyses presently available do not appear to be applicable to his data, because he introduced a mechanical probe in the interface. If we assume that Mann's correction for the effect of his mechanical probe is sufficient, then there appears to be a question concerning his value for surface tension. The three models studied give a much better description of his data, if one uses a value for surface tension smaller than that he reported. If we assume both that Mann has fully accounted for the presence of his mechanical probe in reporting his experimental data and that the values of surface tension he gave are in error, then we can say that the analysis presented here for the damping of capillary waves is superior to any other analysis previously available. With these assumptions, we would be encouraged to say that the use of the Newtonian surface fluid model for surface stress and the Levich model for surface convection are apparently justified in this situation. It would also seem that equilibrium is not instantaneously established between the surface and the substrate, in the sense that the surface concentration of surfactant cannot be assumed to be a function merely of the concentration of surfactant in the bulk phase at the interface. However, these conclusions must still be considered tentative in view of the scatter in Man's experimental data.

Damping of capillary waves on water by monomolecular films of linear polyorganosiloxanes

Damping of capillary waves on water by monomolecular films of linear polyorganosiloxanes

SURFACE CHEMICAL CHARACTERIZATION OF SURFACE‐ACTIVE MATERIAL IN SEAWATER

Seawater samples were collected using a technique that isolated the upper 0.15 mm of surface water. Much of their organic matter was surface‐active, slick‐forming material that was originally at the seawater‐air interface. These surface‐active molecules are of interest because of their influence on many properties of the sea surface. Determinations were made of the effect of monolayers of these materials on the surface tension, on the surface potential, on the damping of capillary waves, and on the surface viscosity. The measurements were made as functions of the area of surface occupied by the adsorbed molecules. Organic materials collected from widely different locations were surprisingly similar in their behavior, suggesting that the more strongly adsorbed, stable, film‐forming materials at the interface were chemically similar. It is suggested that the more stable components of the films are primarily polar‐nonpolar compounds containing long‐chain hydrocarbon groups, such as the high molecular weight saturated and unsaturated fatty acids and their esters.

On the damping of capillary waves by surface films : Davie J.T. and R.W. Vose, 1965. Proc. R. Soc., London, (A), 286 (1405): 218–234

On the damping of capillary waves by surface films : Davie J.T. and R.W. Vose, 1965. Proc. R. Soc., London, (A), 286 (1405): 218–234

On the damping of capillary waves by surface films

The damping of horizontal waves on a deep fluid has been measured and compared with published theoretical predictions for the following systems: (1) clean water (frequency range: 50 to 920 c/s); (2) solutions of soluble surface-active agents (frequency range 14 to 800 c/s); (3) aqueous solutions on which has been spread a monolayer of an insoluble surfaceactive agent (frequency 150 c/s). The results for clean water agree closely with the appropriate theoretical equations. Data on the damping as a function of frequency and concentration for a soluble surfaceactive agent (sodium lauryl sulphate) show a relaxational effect, due to desorption and adsorption of the film during the passage of each wave. Three other surface-active agents of different chain lengths have been studied to determine the effect of the rate of desorption on the damping at different frequencies. The results are consistent with theory. Soluble and insoluble films possessing different surface compressibilities and shear viscosities have been studied to find how these factors affect the damping at various surface pressures. Results are in excellent accord with the mathematical theory of Dorrestein (1951): the surface compressional modulus is of prime importance in damping capillary waves, and quite low values of this modulus can cause wave damping which considerably exceeds that at a completely immobile surface.