Surface tension 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. 

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. 

In addition to the theories reviewed above, there are many treatments in the literature which deal with the hydraulics of wavy flow in open channels. Most of these refer to very small channel slopes (less than 5°) and relatively large water depths. Under these conditions, surface tension plays a relatively minor part and is customarily neglected, so that only gravity waves are considered. For thin film flows, however, capillary forces play an important part (K7, H2). In addition, most of these treatments consider a turbulent main flow, while in thin films the wavy flow is often... 

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. 

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]... 

Capillary waves — Capillary waves are triggered by thermal fluctuation and recovered by -> surface tension on an interface between liquid phases rather than by gravity [i]. They propagate along the interface [ii], and they distort the sharp boundary at immiscible oil water interfaces. The frequency of capillary waves, which has been determined with light scattering measurements [iii, iv], is predicted to evaluate time-dependent local surface tensions without any contact with the surface. 

Let us now briefly mention an approach that is popular among physicists, and which comes down to correlating surface tensions to capillary waves. The underlying idea is that each fluid-fluid interface is subject to a superposition of a large number of thermal waves. The amplitudes of these waves are related to the inter-facial excess energy and the number and frequencies to the interfacial excess entropy, hence the total information obtainable yields F°, and hence y. The idea dates back to Mandelstam and has been taken up by others, including Frenkel and Buff et al. . ... 

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