Diffusing droplet model for Rayleigh linewidth studies on critical fluids

Measurements of the intensity autocorrelation of light scattered from diffusing micropheres suspended in a normal fluid show that if the particle radii satisfy the condition $l\lesssim {\lambda }_0$ where ${\lambda }_0$ is the wavelength of the incident light, and if the suspension is polydisperse (a finite-width particle-size distribution), the experimental diffusion constant displays a dependence upon the scattered wave number $k$ which is qualitatively the same as that for a critical fluid system in the nonhydrodynamic ($k\xi \gtrsim 1$) regime. These experimental observations have led us to propose a model of a critical fluid in which the order-parameter fluctuations are considered as spherical molecular clusters, or droplets, performing Brownian motion in a normal host fluid. The droplets are assumed to have a Gaussian index of refraction spacial profile, and a particle-size distribution $N\left(l\right)\mathrm{}$ characterizing the suspension determined from the requirement that the scattered light intensity be of the modified Ornstein-Zernike form. In a first approximation, the droplets are assumed to diffuse without changing size for times of the order of the characteristic diffusion time. The intensity-autocorrelation function of light scattered by our model system of diffusing droplets is evaluated, and the effective Rayleigh linewidth is found to agree to within a constant factor of order 1 with the ansatz for the critical part of the Rayleigh linewidth chosen by Perl and Ferrell. The resulting line-shape function is nearly Lorentzian, except in the wings where experimental detection of a departure from Lorentzian behavior becomes extremely difficult. Our droplet-size distribution is very similar to that which results from the static droplet model of Fisher which has been applied successfully to describe static critical phenomena in fluids below the critical temperature. In the diffusing droplet model, the $k$ dependence of the diffusion constant extracted from light-scattering measurements on critical fluids is seen to be an artifact introduced by the light-scattering process, and introduces no new physical information concerning the critical fluid behavior which is not contained in the droplet-size distribution function.