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

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.

arXiv comment45 pages, 18 figures. Accepted for publication in Physical Review E

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• Steering in computational science: mesoscale modelling and simulation
• Finite-Difference Lattice Boltzmann Methods for binary fluids
• Large-scale grid-enabled lattice-Boltzmann simulations of complex fluid flow in porous media and under shear
• Coarsening dynamics of ternary amphiphilic fluids and the self-assembly of the gyroid and sponge mesophases: lattice-Boltzmann simulations
• Fragmentation and Limits to Dynamical Scaling in Viscous Coarsening: An Interrupted in situ X-Ray Tomographic Study
• Two-dimensional finite-difference lattice Boltzmann method for the complete Navier-Stokes equations of binary fluids
• Self-assembly of the gyroid cubic mesophase: lattice-Boltzmann simulations
• Detection and tracking of defects in the gyroid mesophase
• On the effect of surfactant adsorption and viscosity change on apparent slip in hydrophobic microchannels
• Structural transitions and arrest of domain growth in sheared binary immiscible fluids and microemulsions
• Stress response and structural transitions in sheared gyroidal and lamellar amphiphilic mesophases: lattice-Boltzmann simulations
• Interface dynamics of immiscible two-phase lattice-gas cellular automata: A model with random dynamic scatterers and quenched disorder in two dimensions
• Two-dimensional Cahn-Hilliard simulations for coarsening kinetics of spinodal decomposition in binary mixtures