Scaling theory of three-dimensional spinodal turbulence

A scaling theory for spinodal decomposition in the inertial hydrodynamic regime is presented. The scaling involves three relevant length scales, the domain size, the Taylor microscale, and the Kolmogorov dissipation scale. This allows for the presence of an inertial “energy cascade,” familiar from theories of turbulence, and improves on earlier scaling treatments based on a single length: these, it is shown, cannot be reconciled with energy conservation. This theory reconciles the $t^{2/3}$ scaling of the domain size, predicted by simple scaling, with the physical expectation of a saturating Reynolds number at late times.