Surface capillary wave

Analogous droplet-size dependence has been observed for electron transfer between ferrocene and hexacyanoferrate(III) across a droplet/water interface with the droplet radius of <5 /an, as described in Section III [80]. In this system, FeCp-X+ transfer is coupled with the electron transfer process and the physical properties of the droplet have been suggested to vary with r. However, droplet size effects on surface capillary waves analogous to those in the MT process may also govern the electron transfer process in the FeCp-X/Fe(IIl) system. 

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

The linear stability characteristics of the jet are specified by Eq. (10.4.32), where we note that (3 alpa, which may be compared with the plane capillary wave result where crlpX. This behavior is not surprising and can be deduced from dimensional arguments. Indeed, for the jet when a 1, that is, when the wavelengths are small compared with the jet radius, we have from the properties of the Bessel function that /(,( )/I (a) = 1. With f3 = io), Eq. (10.4.32) reduces to the dispersion relation o) - k crlp for stable, sustained surface capillary waves on deep water (Eq. 10.4.19). 

Surface light scattering methods from thermally induced capillary waves at the interface [139-141] or from electric-field-induced surface waves [142, 143] have appeared. The technique is limited by the viscosities of the two phases if the viscosities are too large, then the spatial damping of the surface capillary waves is too rapid to be detected by the technique. The applicability of this method for highly viscous polymeric interfaces has not been verified yet. 

For polymer surface profile evolution with time and temperature, the physics is well described by the Navier-Stokes equation, a staple tool for liquid behavior.When the film thickness is larger than the wavelength (or >s 1, wave vector C = InIX), the relaxation time of the surface capillary wave is approximated by This simple relationship... 

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 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... 

As reviewed above, there have been many QELS studies on liquid surfaces. However, until a few years ago, reports were scarce on molecular dynamics at liquid-liquid interfaces which used time courses of capillary wave frequency. Molecular collective behavior at liquid-liquid interfaces from a QELS study was first reported by Zhang et al. in 1997 [5]. 

Recently, the newly developed time-resolved quasielastic laser scattering (QELS) has been applied to follow the changes in the surface tension of the nonpolarized water nitrobenzene interface upon the injection of cetyltrimethylammonium bromide [34] and sodium dodecyl sulfate [35] around or beyond their critical micelle concentrations. As a matter of fact, the method is based on the determination of the frequency of the thermally excited capillary waves at liquid-liquid interfaces. Since the capillary wave frequency is a function of the surface tension, and the change in the surface tension reflects the ion surface concentration, the QELS method allows us to observe the dynamic changes of the ITIES, such as the formation of monolayers of various surfactants [34]. 

Dynamic surface tension has also been measured by quasielastic light scattering (QELS) from interfacial capillary waves [30]. It was shown that QELS gives the same result for the surface tension as the traditional Wilhelmy plate method down to the molecular area of 70 A. QELS has recently utilized in the study of adsorption dynamics of phospholipids on water-1,2-DCE, water-nitrobenzene and water-tetrachloromethane interfaces [31]. This technique is still in its infancy in liquid-liquid systems and its true power is to be shown in the near future. 

Ultrasonic atomization is sometimes also termed capillary-wave atomization. In its most common form, 142 a thin film of a molten metal is atomized by the vibrations of the surface on which it flows. Standing waves are induced in the thin film by an oscillator that vibrates vertically to the film surface at ultrasonic frequencies. The liquid metal film is broken up at the antinodes along the surface into fine droplets once the amplitude of the capillary wave exceeds a certain value. The most-frequent diameter of the droplets generated is approximately one fourth of the wavelength of the capillary wave,1 421 and thus decreases with increasing frequency. 

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