Wave, capillary

The subject of surface viscosity is a somewhat complicated one it has been reviewed by several groups [95,96], and here we restrict our discussion to its measurement via surface shear and scattering from capillary waves. 

Another approach to measurement of surface tension, density, and viscosity is the analysis of capillary waves or ripples whose properties are governed by surface tension rather than gravity. Space limitations prevent more than a summary presentation here readers are referred to several articles [123,124]. 

Capillary waves may be generated mechanically by means of an oscillating bar, and for this case one writes the solutions to Eqs. IV-25 and IV-26 in the form... 

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 correction due to the temperature gradient in the capillary wave peak heights is the corresponding fractional difference, which can be obtained by evaluating A(<7, = w. The result is simple ... 

It can be shown that this fonn leads to an unphysical dispersion relation for capillary waves t/,7 -- f/", rather... 

In this brief review of dynamics in condensed phases, we have considered dense systems in various situations. First, we considered systems in equilibrium and gave an overview of how the space-time correlations, arising from the themial fluctuations of slowly varying physical variables like density, can be computed and experimentally probed. We also considered capillary waves in an inliomogeneous system with a planar interface for two cases an equilibrium system and a NESS system under a small temperature gradient. 

The fluctuations of the local interfacial position increase the effective area. This increase in area is associated with an increase of free energy Wwhich is proportional to the interfacial tension y. The free energy of a specific interface configuration u(r,) can be described by the capillary wave Hamiltonian ... 

Laoasse M D, Grest G S and Levine A J 1998 Capillary-wave and ohain length effeots at polymer/polymer interfaoes Phys. Rev. Lett. 80 309... 

R. Evans. The role of capillary wave fluctuations in determining the liquid-vapor interface. Analysis of the van der Waals model. Mol Phys 42 1169-1196, 1981. 

According to the capillary wave approximation , a rough interface is characterized by a width that diverges logarithmically with its transverse dimensions ... 

In the past five years, it has been demonstrated that the QELS method is a versatile technique which can provide much information on interfacial molecular dynamics [3 9]. In this review, we intend to show interfacial behavior of molecules elucidated by the QELS method. In Section II, we present the principle and the experimental apparatus of the QELS along with the historical background. The dynamic collective behavior of molecules at liquid-liquid interfaces was first obtained by improving the time resolution of the QELS method. In Section III, we show the molecular collective behavior of surfactant molecules derived from the analysis of the time courses of capillary wave frequencies. Since the... 

II. QUASI-ELASTIC LASER SCATTERING METHOD A. Capillary Waves... 

Capillary waves occur spontaneously at liquid surfaces or liquid liquid interfaces due to thermal fluctuations of the bulk phases. These waves have been known as surface tension waves, ripples, or ripplons for the last century, and Lamb described their properties in his book Hydrodynamics in 1932 [10]. Before that, William Thomson (Lord Kelvin) mentioned these waves in some of his many writings. 

Here we briefly present the relevant theory of capillary waves. The thermally excited displacement (r, t) of the free surface of a liquid from the equilibrium position normal to the surface can be Fourier-decomposed into a complete set of surface modes as... 

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