A scaling theory of 3D spinodal turbulence

TL;DR

This paper introduces a new scaling theory for 3D spinodal turbulence during phase separation, incorporating multiple length scales to better align with energy conservation and turbulence principles.

Contribution

It develops a three-scale scaling framework for spinodal decomposition in the inertial regime, improving upon previous single-scale models.

Findings

Reveals the importance of three length scales in turbulence modeling.

Shows the t^{2/3} domain growth scaling is consistent with energy conservation.

Predicts a saturating Reynolds number at late times.

Abstract

A new 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. The new 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.