Fluctuations capillary-wave

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. 

Figure 11.2. Schematic representation of the heterogeneous photo-oxidation of ferrocene by specifically adsorbed water-soluble metalloporphyrin at the water/EKlE interface. It is postulated that the distance of closest approach is determined by the onset of the solvent density profiles generated by capillary wave fluctuations.

In order to determine the thermal broadening of this new intrinsic profile, we will consider, for simplicity, a single component liquid-vapor phase equilibrium, in which the density profile of the intrinsic interface is denoted by Pj(z). The energy change due to capillary wave fluctuations is assumed to be given by ... 

M. K. Sanyal, S.K.Sinha, K. G. Huang, and B. M. Ocko, Rcrc Lett., 66, 628 (1991). X-Ray Scattering Study of Capillary-Wave Fluctuations at a Liquid Surface. 

Experimental values of interfacial widths between incompatible polymers are larger than expected and there has been considerable discussion as to the origin of this discrepancy. Capillary wave fluctuations are considered to be responsible for the diSerence between calculated and experimental results [112]. Detailed discussion of these effects can be found in Reference [107]. 

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... 

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 ... 

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. 

Recent theoretical studies indicate that thermal fluctuation of a liquid/ liquid interface plays important roles in chemical/physical properties of the surface [34-39], Thermal fluctuation of a liquid surface is characterized by the wavelength of a capillary wave (A). For a macroscopic flat liquid/liquid interface with the total length of the interface of /, capillary waves with various A < / are allowed, while in the case of a droplet, A should be smaller than 2nr (Figure 1) [40], Therefore, surface phenomena should depend on the droplet size. Besides, a pressure (AP) or chemical potential difference (An) between the droplet and surrounding solution phase increases with decreasing r as predicted by the Young-Laplace equation AP = 2y/r, where y is an interfacial tension [33], These discussions indicate clearly that characteristic behavior of chemical/physical processes in droplet/solution systems is elucidated only by direct measurements of individual droplets. 

On the other hand, a liquid/liquid interface is fluctuating thermally in the time scale of tens of picoseconds, and this induces thermal capillary waves as discussed above. Thermal capillary waves at a flat liquid/liquid interface have been studied by laser light-scattering methods, and the wavelength of the capillary wave (2) has been reported to be A 102 /im [29-31], A large... 

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