3D Spinodal Decomposition in the Inertial Regime

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 (with scales set by viscosity, density, and surface tension), our data sets cover $1\lesssim l\lesssim {10}^5$ and $10\lesssim t\lesssim {10}^8$. We achieve Reynolds numbers approaching $350$. At $\mathrm{Re}\gtrsim 100$ we find clear evidence of Furukawa's inertial scaling ( $l\sim t^{2/3}$), although the crossover from the viscous regime ( $l\sim t$) is very broad. Though it cannot be ruled out, we find no indication that Re is self-limiting ( $l\sim t^{1/2}$) as proposed by M. Grant and K. R. Elder [Phys. Rev. Lett. 82, 14 (1999)].