Three-dimensional lattice-Boltzmann simulations of critical spinodal decomposition in binary immiscible fluids

TL;DR

This study employs 3D lattice-Boltzmann simulations to analyze spinodal decomposition in binary fluids, revealing non-universal domain growth exponents and specific structure function behaviors that challenge existing universality claims.

Contribution

It introduces a modified Shan-Chen lattice-BGK model for 3D binary fluids and demonstrates non-universal scaling and structure function behaviors during phase separation.

Findings

Domain size grows as t^γ with 0.545 < γ < 0.717

Crossover from q^2 to q^4 in structure function at early times

Exponential growth of structure function at initial stages

Abstract

We use a modified Shan-Chen, noiseless lattice-BGK model for binary immiscible, incompressible, athermal fluids in three dimensions to simulate the coarsening of domains following a deep quench below the spinodal point from a symmetric and homogeneous mixture into a two-phase configuration. We find the average domain size growing with time as $t^\gamma$, where $\gamma$ increases in the range $0.545 < \gamma < 0.717$, consistent with a crossover between diffusive $t^{1/3}$ and hydrodynamic viscous, $t^{1.0}$, behaviour. We find good collapse onto a single scaling function, yet the domain growth exponents differ from others' works' for similar values of the unique characteristic length and time that can be constructed out of the fluid's parameters. This rebuts claims of universality for the dynamical scaling hypothesis. At early times, we also find a crossover from $q^2$ to $q^4$ in the scaled structure function, which disappears when the dynamical scaling reasonably improves at later times. This excludes noise as the cause for a $q^2$ behaviour, as proposed by others. We also observe exponential temporal growth of the structure function during the initial stages of the dynamics and for wavenumbers less than a threshold value.