Effect of gravity on critical opalescence: The turbidity

The effect of the earth's gravity on the total irradiance of light scattered from a simple fluid near its critical point is investigated. It is found that gravity modifies the results of the usual theories for the total scattering (turbidity) qualitatively in two ways. First, the total scattering at the critical point (in the Born approximation) does not diverge. Second, the turbidity does not achieve its maximum value at the critical temperature, but rather above it. For example, the turbidity of xenon with a sample height of 1 cm reaches its maximum value at about ${10}^{-2\mathrm{}}$ K° above its critical temperature. By comparing these results with those of the modified Ornstein-Zernike theory (critical exponent $\eta \ne 0$) for a uniform fluid, an apparent gravity-induced $\eta$ is defined. This is a temperature- and sample-size-dependent quantity which, when substituted for $\eta$ in the modified Ornstein-Zernike theory for a uniform fluid, produces the same turbidity as the gravity-modified classical Ornstein-Zernike theory for a nonuniform fluid. It is surprising that the apparent $\eta$ increases rapidly, until it is of order unity, within a very short temperature range near the critical point, as the critical temperature is approached from above. It is more surprising that the sudden change in the apparent $\eta$ is quantitatively commensurate, through the scaling law $\gamma =\nu (2-\eta )$, with the rapid change in the exponent $\gamma$ observed by a number of experimenters.