Abstract
Thermally excited waves at the interface between two fluids contain information about the structure and tension at this interface. A surface light-scattering technique based on photon correlation spectroscopy has been developed to probe the dynamics of these interfacial waves for microemulsions. The interfacial tension (IFT) as measured by this nonperturbing technique is consistent with the values obtained by conventional methods. We have studied the temperature and salinity dependence of sigma (IFT) in a three-phase microemulsion system, and found that sigma epsilon, where epsilon is the reduced variable and with and representing the critical values of temperature and salinity, respectively. Furthermore, the correlation length, L, in the microemulsion phase has also been measured by dynamic light scattering. In the two-phase regions it was observed that, in accordance with the scaling law predictions. Thus, the scaled salinity and temperature parameters influence the IFT through their effect on the correlation length in the bulk microemulsion phase. phase. Introduction
The tension and the structure of a fluid interface have been well studied subjects for those who are interested in thermodynamics, surface properties, hydrodynamics, and a host of practical applications, including properties, hydrodynamics, and a host of practical applications, including chemical EOR. About 100 years ago, van der Waals recognized the special relation between the vanishing of interfacial (surface) tension and the critical point transitions in fluids and fluid mixtures. This relation linked the bulk properties of liquids to their interfacial behavior. More recent investigations into the structure and the tension of the critical interface have shown that van der Waals was qualitatively correct. It was also recognized by Mandelstam in 1913 that a vanishing IFT would lead to increasing amplitude in the spontaneous thermal fluctuation on the interface. This prediction could be understood in the following manner. Interface fluctuations are produced by the random thermal motions of fluid molecules. Consequently, these fluctuations cause the interface to deviate from a planar surface, which corresponds to the minimum free-energy state of the system. The lower the IFT, the easier it is for the interfacial area to increase by producing large amplitudes in fluctuations. Mathematically, we can describe these fluctuations by their Fourier components, each corresponding to a particular normal mode of the surface wave (capillary wave), subjected to the boundary conditions of the container. After the invention of optical mixing spectroscopy, Katyl and Ingard first demonstrated that the surface tension of a free liquid could be measured by light scattering. Huang and Webbs then took advantage of the vanishing IFT and density difference in a binary liquid mixture near the critical point, to develop a correlation spectroscopy. This technique analyzed the scattered light from the diverging interfacial capillary waves on the critical interface. This method allows one to determine extremely low IFT's in the range of 10 -5 to 10 -6 mN/m [10 -5 to 10 -6 dyne/cm] without perturbing the system. The advantages of determining IFT by using an optical probe over the conventional means involving direct or indirect measurements of the mechanical restoring forces are higher sensitivity and complete equilibrium of the surface under study. Furthermore, optical techniques can be used to study fluids at elevated pressures and temperatures. This optical technique was used to study the relation between the IFT of a microemulsion and its bulk properties. Scaling concepts have been used to interpret the data. Even though the scaling laws were developed to describe the critical phenomena, there is evidence to show that these are relevant and useful concepts, especially for the understanding of low-tension microemulsion systems.
Light Scattering From Interfacial Capillary Waves
Capillary waves are described by the solutions of the linearized Navier-Stokes equation in a uniform gravitational field, subject to boundary conditions at the fluid interface and infinity. The restoring forces are the gravitational force and the IFT. Interfacial and bulk shear viscosity provide the damping mechanism. A detailed derivation of the dispersion relation can be found in Ref. 14. The major conclusion is that for a low tension interface, the normal modes that can be easily probed by visible light are over damped waves with time constant, given by the expression
............................(1)
SPEJ
p. 203
Method of discrete singularities in problems of filler vibrations in fuel tanks under overloads and at low gravity
