Effect of gravity on critical opalescence

Abstract

The effect of the earth's gravity on critical opalescence from simple fluids is investigated. By using a simple equation of state which is applicable in the critical region of fluids, we study the angular distribution of the scattered intensity, the total scattered intensity (turbidity) and the Rayleigh linewidth quantitatively in the framework of the Ornstein-Zernike theory. For the case of the scattered intensity we find that gravity modifies the results in three ways. First, the forward scattering at the critical point does not diverge. Second, the irradiance in any direction is not greatest at the critical temperature, but slightly above it. Third, the Ornstein-Zernike-Debye plots are concave downward at small scattering angles. For the case of the turbidity, we also find the removal of the divergence at the critical point and the shift of temperature from the critical temperature for the maximum turbidity. By comparing these results with those of the modified Ornstein-Zernike theory for a uniform fluid, an apparent gravity-induced exponent N is determined. It is surprising that the sudden change in the apparent N is quantitatively commensurate, through the scaling law equation gammy = V(2-N) , with the rapid change in the exponent gamma observed experimentally. For the case of the Rayleigh linewidth, the mode-mode-coupling and the decoupled-mode theories are studied in detail. It is found that under the influence of gravity, the comparison of the two theories is difficult and that the deviation from the "universal curve" of the scaled linewidth is inevitable regardless of the theory used. When the relative deviation of the scaled linewidth from its gravity-free value is plotted versus the reduced correlation length, it exhibits distinct patterns characterizing the theories used to compute it. By comparing these patterns with results of carefully controlled experiments, gravity should prove to be a useful tool for selecting a correct theory.