Two-exponential decay of dynamic light scattering in near-critical fluid mixtures

Two hydrodynamic relaxation modes associated with mass diffusion and thermal diffusion are present in binary fluids. In near-critical binary fluids a coupling between the two modes results in two characteristic relaxation times, neither of which is associated with pure mass diffusion or pure thermal diffusion. Instead, the relaxation times are inversely proportional to two effective diffusivities $D_1$ and $D_2$, which can be detected experimentally by dynamic light scattering. The physical meaning of $D_1$ and $D_2$ changes as one considers states in the vicinity of different points on the critical locus: in the infinite-dilution limit the diffusivity $D_1$ of the slow mode is associated with the thermal diffusivity and the diffusivity $D_2$ of the fast mode with the mutual mass diffusion coefficient, while in the “incompressible” liquid-mixture limit $D_1$ is associated with the mass diffusion coefficient and $D_2$ with the thermal diffusivity. In addition we have determined the intensities (amplitudes) of these relaxation modes, which can also be measured with light scattering. We discuss the conditions at which a two-exponential decay of the dynamic correlation function can be measured. As an example we consider mixtures of methane and ethane near the vapor-liquid critical line where the two exponential decays indeed have been observed.