Wave motion capillary waves

The scattering techniques, dynamic light scattering or photon correlation spectroscopy involve measurement of the fluctuations in light intensity due to density fluctuations in the sample, in this case from the capillary wave motion. The light scattered from thermal capillary waves contains two observables. The Doppler-shifted peak propagates at a rate such that its frequency follows Eq. IV-28 and... 

The dilational rheology behavior of polymer monolayers is a very interesting aspect. If a polymer film is viewed as a macroscopy continuum medium, several types of motion are possible [96], As it has been explained by Monroy et al. [59], it is possible to distinguish two main types capillary (or out of plane) and dilational (or in plane) [59,60,97], The first one is a shear deformation, while for the second one there are both a compression - dilatation motion and a shear motion. Since dissipative effects do exist within the film, each of the motions consists of elastic and viscous components. The elastic constant for the capillary motion is the surface tension y, while for the second it is the dilatation elasticity e. The latter modulus depends upon the stress applied to the monolayer. For a uniaxial stress (as it is the case for capillary waves or for compression in a single barrier Langmuir trough) the dilatational modulus is the sum of the compression and shear moduli [98]... 

Wave length of monochromatic light Mean free path of molecules Mean free path of particles in Brownian motion Capillary conductivity (Gardner)... 

The surface motion of the sea takes place on a variety of scales from mm capillary waves to mesoscale eddies. At low wind conditions it seems that there are some scales that dominate with regard to slick-formation. They give rise to long filamentary structures observed on optical- as well as SAR-images of the sea surface, where they have a transverse dimension of the order of 100 m and longitudinal coherence for several kilometres (Scully-Powers 1986). 

Capillary Waves. At a liquid surface, capillary waves will always form, due to heat motion and induced by vibration. On a film, symmetrical... 

Capillary Ripples Surface or interfacial waves caused by perturbations of an interface. When the perturbations are caused by mechanical means (e.g., barrier motion), the transverse waves are known as capillary ripples or Laplace waves, and the longitudinal waves are known as Marangoni waves. The characteristics of these waves depend on the surface tension and the surface elasticity. This property forms the basis for the capillary wave method of determining surface or interfacial tension. 

Goren, S. Gavis, J. Transverse wave motion on a thin capillary jet of a viscoelastic liquid. Phys. Fluids 4, 575-579 (1961). 

Lucassen-Reynders and Lucassen (Lucassen 1968, Lucassen-Reynders and Lucassen 1969) have derived the dispersion relation for a liquid surface in the presence of a surface film. They showed that periodic disturbance of such a film-covered surface results in a surface tension that varies from point to point on the surface because of the fluctuations in surface concentration. Consequently, in addition to a transverse stress being developed, a finite tangential surface stress is also present. The solution to this dispersion equation has two roots, one of which corresponds to the capillary waves (transverse motion) and one of which corresponds to longitudinal or dilational waves derived from the transverse stress. The dispersion relation (D( o)) obtained for a film at the interface between two media is... 

DAMPING OF CAPILLARY WAVE MOTION BY INSOLUBLE SURFACTANTS... 

Mass transfer across a fluid interface is enhanced by convection in the vicinity of the interface. One source of such convection is wave motion. An increase in the rate of damping of waves can thus be expected to reduce mass transfer rates. As we shall now show, surfactants can cause a significant increase in the damping of capillary waves at a liquid-gas interface. 

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