Capillary wave method

The values of surface elasticity were determined from the data about the rate of film drainage. They differed from those of surface elasticity determined by the capillary-wave method at which slight compression and expansion occurred around the equilibrium state. The authors attributed this difference to the non-equal rates of surfactant exchange with the film... 

The experimental methods for the determination of liquid viscosity are similar to those used for gases ( 8.VII F) (i) transpiration, through capillaries, (ii) torque on rotating cylinders, or the damping of oscillating solid discs or spheres, in the liquid, (iii) fall of solid spheres through the liquid, (iv) flow of liquid through an aperture in a plate, (v) capillary waves. Methods (i) and (ii) are mostly used for absolute, the others for comparative, measurements. 

Insoluble monolayers on an aqueous substrate have been investigated by means of the capillary wave method for many years. Lucassen and Hansen (1966) in their pioneering work neglected the surface viscosity and considered only pure elastic films. Subsequent studies showed that the surface elasticity of real surface films is a complex quantity, and both the equilibrium surface properties and the kinetic coefficients of relaxation processes in the films influence the characteristics of surface waves. However, it has been discovered recently that the real situation is even more complicated and the macroscopic structure of surface films influences the dependency of the damping coefficient of capillary waves on the area per molecule (Miyano and Tamada 1992, 1993, Noskov and Zubkova 1995, Noskov et al. 1997, Chou and Nelson 1994, Chou et al. 1995, Noskov 1991, 1998, Huhnerfuss et al. this issue). Some peculiarities of the experimental data can be explained, if one takes into account the capillary wave scattering by two-dimensional particles (Noskov et al. 1997). 

Noskov BA, Grigoriev DO (1996) Kinetic Study of Sodium Decyl Sulfate Solutions by the Capillary Wave Method. Langmuir 12 3399-3403... 

The capillary wave method is based on the generation of harmonic waves on the surface of a bulk volume of liquid [28], The wavelength of the ripples formed, A, is a function of the surface tension, which can be evaluated from expressions given by Kelvin ... 

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. 

Relations (5.275), (5.276) can be used for the interpretation of experimental results obtained by surface relaxation spectrometry methods, for example, by the capillary wave method. 

A preliminary kinetic investigation of the adsorption-desorption on the surfaces of other surfactant solutions by means of the capillary-wave method has shown that similar relaxation phenomena exist in these systems. Further studies of these systems will lead to a quantitative clarification of the adsorption-desorption phenomena. 

When the diffusion time has comparable magnitude with the time of formation of the electric double layer, the quasiequilibrium model is not applicable. Lucassen et al. [Ill] and Joos et al. [112] established that mixtures of anionic and cationic surfactants diffuse as a electroneutral combination in the case of small periodic fluctuations of the surface area consequently, this process is ruled by the simple diffusion equation. The e/ec ro-diffusion problem was solved by Bonfillon et al. [113] for a similar case of small periodic surface corrugations related to the capillary-wave methods of dynamic surface-tension measurement. 

One encounters the following difficulties in the interpretation of the data from the experiments with interfacial dilatation. As discussed in Ref. 58, the shear viscosity, T jh, does not influence the total stress, 67, only for interfacial flow of perfect spherical symmetry. If the latter requirement is not fulfilled by a given experimental technique, its output data will be influenced by a mixture of dissipative effects (not only -r d but also -qsh and tr). The apparent interfacial viscosity thus determined is not a real interfacial property insofar as it depends on the specific method of measurement. For example, the apparent interfacial viscosity measured by the capillary-wave methods [189-196] depends on the frequency the apparent interfacial viscosity measured by the Langmuir trough method [197,198] is a sum of the dilatational and shear viscosities ("q + -q h) for the methods employing nonspherical droplet deformation, like the spinning-drop method [199-201], the apparent surface viscosity is a complex function of the dilatational and shear interfacial viscosities. 

The capillary-wave method corresponds to small frequency fluctuations. For pure transverse wave motion, Eq. (259) leads to... 

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... 

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. 

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... 

We come to some important points in the analysis of capillary wave dynamics through the polar plot profile displayed in Fig. 4. First are the assumptions that we invoke in the analysis. Although the details will be better clarified when we come to the experimental part dealing with the SLS method, we must at this point lay down the assumptions and how they are in part justified. Throughout the entire scheme of capillary wave analysis presented here, we make the following assumptions ... 

Fig. 21. Ratio between the interface tension 7 and the simple expression for the strong segregation limit yssL in (54) as a function of inverse incompatibility. Symbols correspond to Monte Carlo results for the bond fluctuation model, the solid line shows the result of the SCF theory, and the dashed line presents first corrections to (54) calculated by Semenov. Also an estimate of the interface tension from the spectrum of capillary waves is shown to agree well with the results of the reweighting method. Adapted from Schmid and Muller [107]...

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