3D Spinodal Decomposition in the Inertial Regime

TL;DR

This study uses lattice Boltzmann simulations to analyze late-stage coarsening in 3D binary fluids, confirming inertial scaling at high Reynolds numbers and challenging previous viscous regime hypotheses.

Contribution

The paper provides extensive 3D simulation data demonstrating inertial scaling in binary fluid coarsening, with Reynolds numbers up to 350, and clarifies the crossover from viscous to inertial regimes.

Findings

Inertial scaling l ~ t^{2/3} observed at Re > 100

Broad crossover from viscous to inertial regimes

No evidence supporting Re self-limiting l ~ t^{1/2}

Abstract

We simulate late-stage coarsening of a 3D symmetric binary fluid using a lattice Boltzmann method. With reduced lengths and times l and t respectively (scales set by viscosity, density and surface tension) our data sets cover 1 < l < 10^5, 10 < t < 10^8. We achieve Reynolds numbers approaching 350. At Re > 100 we find clear evidence of Furukawa's inertial scaling (l ~ t^{2/3}), although the crossover from the viscous regime (l ~ t) is very broad. Though it cannot be ruled out, we find no indication that Re is self-limiting (l ~ t^{1/2}) as proposed by M. Grant and K. R. Elder [Phys. Rev. Lett. 82, 14 (1999)].