Spinodal decomposition in homogeneous and isotropic turbulence

We study the competition between domain coarsening in a symmetric binary mixtures below the critical temperature and turbulent fluctuations. We find that the coarsening process is arrested in presence of turbulence. The physics of the process shares remarkable similarities with the behaviour of diluted turbulent emulsions and the arrest length scale can be estimated with an argument similar to the one proposed by Kolmogorov and Hinze for the maximal stability diameter of droplets in turbulence. Although in the absence of flow the microscopic diffusion constant is negative, turbulence does effectively arrest the inverse cascade of concentration fluctuations by making the low wavelength diffusion constant positive for scales above the Hinze length.