Anomalous mixing times in turbulent binary mixtures at high Prandtl number

A theory of turbulent binary fluid mixtures is applied to situations where the diffusive Prandtl number, P=νD, far exceeds the Reynolds number R. This regime is accessible just above the consolute point in binary mixtures, where Prandtl numbers in excess of 10⁶ have been observed. We find that sizable large-scale inhomogeneities are mixed to uniformity quite slowly, in a time of order τ=t₀PR, where t₀ is a characteristic stirring time. The spectrum of concentration fluctuations rapidly acquires a peak at wave vector k*~k₀R, where k₀^-1 is the scale of the initial inhomogeneity. Mixing times of ten minutes or more are possible.