Spectral analysis of light scattered by liquid films. II. Light scattering in the long wavelength limit

Abstract

This paper describes what information can be obtained when the spectral distribution of light scattered by thin liquid films, like free soap films, is analyzed. To this end we have worked out the so-called long wavelength limit (i.e., when the wavelengths of the surface waves are much greater than the film thickness) of the thermal fluctuation power spectrum describing the dynamics of the interfacial displacements occurring on a film. The analysis reveals that the squeezing mode spectrum as well as the bending mode spectrum exhibit a three peak structure: two peaks shifted symmetrically around zero frequency (Brillouin doublet) and one peak centered around zero frequency (pure diffusive component). For the squeezing mode the diffusive component, which is typical for a film, is strong, whereas for the bending mode the energy contained in the Brillouin doublet is large when compared with the central peak. These observations and also the large difference in characteristic time scales, in which the two modes occur, enables one to study their features separately by means of dynamic light scattering. The width of the central peak of the squeezing mode depends on: the film thickness, the viscosity of the film liquid, the interfacial tension, and the second derivative with respect to film thickness of the free energy of film formation. The free energy used in this paper consists of a sum of electrical double layer repulsion and London–van der Waals attraction. The effect of the so-called surface elasticity on the central peak width of the squeezing mode is calculated. We also derived the thermal fluctuation power spectrum for interfacial waves when the film is suspended in a second medium. It turns out that for the bending mode the effect of the film bounding medium on the frequency shift of the Brillouin doublet is important, even if this is a low density vapor phase. The shift frequency for the bending depends on the film tension and the total mass that participates in this kind of fluctuation. The width of these shifted peaks depends mainly on the properties of the film bounding medium.