Amplitude Of Capillary Waves Research Articles

Capillary Waves at the Liquid-Vapor Interface. Widom-Rowlinson Model at Low Temperature

We have examined in detail the structure and properties of the liquid-vapor interface for the two-dimensional Widom-Rowlinson model in its low-temperature regime. Various simplifying features permit the deduction of several basic results. Included among these are (1) unambiguous definition of capillary wave modes with upper wavelength cutoff proportional to ~ 1 l ’ ~ (el = liquid density); (2) wavelength dispersion of bare surface tension; and (3) nonmonotonic intrinsic density profile (i.e., that with vanishing capillary wave amplitudes). In an Appendix we show how many of these results can be extended to the three and higher dimensional cases.

On parasitic capillary waves generated by steep gravity waves: an experimental investigation with spatial and temporal measurements

An experimental investigation of steep, high-frequency gravity waves (∼ 4 to 5 Hz) and the parasitic capillary waves they generate is reported. Spatial, as well as temporal, non-intrusive surface measurements are made using a new technique. This technique employs cylindrical lenses to magnify the vertical dimension in conjunction with an intensified, high-speed imaging system, facilitating the measurement of the disparate scales with a vertical surface-elevation resolution on the order of 10 μm. Thus, high-frequency parasitic capillary waves and the underlying gravity wave are measured simultaneously and accurately in space and time. Time series of spatial surface-elevation measurements are presented. It is shown that the location of the capillary waves is quasi-stationary in a coordinate system moving with the phase speed of the underlying gravity wave. Amplitudes and wavenumbers of the capillaries are modulated in space; however, they do not propagate with respect to the gravity wave. As capillary amplitudes are seen to decrease significantly and then increase again in a recurrence-like phenomenon, it is conjectured that resonance mechanisms are present. Measured surface profiles are compared to the theories of Longuet-Higgins (1963) and Crapper (1970) and the exact, two-dimensional numerical formulation of Schwartz & Vanden-Broeck (1979). Significant discrepancies are found between experimental and theoretical wavetrains in both amplitude and wavenumber. The theoretical predictions of the capillary wave amplitudes are much smaller than the measured amplitudes when the measured phase speed, amplitude, and wavelength of the gravity wave are used in the Longuet-Higgins model. In addition, this theory predicts larger wavenumbers of the capillaries as compared to experiments. The Crapper model predicts the correct order-of-magnitude capillary wave amplitude on the forward face of the gravity wave, but predicts larger amplitudes on the leeward face in comparison to the experiments. Also, it predicts larger capillary wavenumbers than are experimentally determined. Comparison of the measured profiles to multiple solutions of the stationary, symmetric, periodic solutions determined using the Schwartz & Vanden-Broeck numerical formulation show similar discrepancies. In particular, the assumed symmetry of the waveform about crest and trough in the numerical model precludes a positive comparison with the experiments, whose underlying waves exhibit significantly larger capillaries on their forward face than on their leeward face. Also, the a priori unknown multiplicity of numerical solutions for the same dimensionless surface tension and steepness parameters complicates comparison. Finally, using the temporal periodicity of the wave field, composite images of several successive wavelengths are constructed from which potential energy and surface energy are calculated as a function of distance downstream.

Analysis of a surface-scattering spectrometer

A general light-scattering spectrometer for measuring surface fluctuations is analyzed by using the methods of Fourier optics. Optical configurations can be designed so that the autocorrelation of the photocurrent is given by either the first- or the second-order correlation functions for the surface fluctuations. Fluctuations in capillary-wave amplitude and in surface density can be detected separately for a number of cases of practical interest. A method is proposed for unambiguous detection of capillary waves with amplitudes larger than the optical wavelength.

Effect of surface mobility on the dynamic behavior of thin liquid films

The role of various factors such as bulk and surface diffusion of surfactant, surface viscosity and, in the case of emulsions, liquid flow in the drops, in determining the surface mobility and hence the velocity of thinning and the lifetime of liquid films are discussed. It is shown that: 1) With relatively low concentrations of surfactant sol— uble in the continuous phase surface diffusion plays a dominant role. 2) The velocity of thinning of a plane—parallel emulsion film depends strongly on the partition coefficient of the surfactant: when the sur— factant is soluble: in the drops rather than in the continuous phase it has no influence on the surface mobility and the velocity of film thinning is very high. 3) With surfactant free emulsions or with surfactant sol— uble in the drops the dissipation of energy in the film is negligible so that the velocity of thinning does not depend on film viscosity. 4) Sur— face mobility increases the amplitude of capillary waves in the films but does not affect the critical thickness of rupture when surface diffusion and surface viscosity can be neglected; the allowance for the latter two effects may help in explaining the experimentally observed dependence of the critical thickness, of rupture upon surfactant concentration.

Particle Size-Amplitude Relations for the Ultrasonic Atomizer

A relationship between capillary wave amplitude and the diameter of spherical particles ejected in an ultrasonic atomizer is developed. This relationship predicts a threshold amplitude for the generation of the aerosol and is based upon a bifurcation process to reduce surface energy. The most probable size of particles is found to be a diameter of 0.36λ, where λ is the wavelength of capillary waves for the system. This result is in excellent agreement with the previously reported empirical median particle diameter of 0.34λ.