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We use a modified Shan-Chen, noiseless lattice-BGK model for binaryimmiscible, incompressible, athermal fluids in three dimensions to simulate thecoarsening of domains following a deep quench below the spinodal point from asymmetric and homogeneous mixture into a two-phase configuration. We find theaverage domain size growing with time as $t^\gamma$, where $\gamma$ increasesin the range $0.545 < \gamma < 0.717$, consistent with a crossover betweendiffusive $t^{1/3}$ and hydrodynamic viscous, $t^{1.0}$, behaviour. We findgood collapse onto a single scaling function, yet the domain growth exponentsdiffer from others' works' for similar values of the unique characteristiclength and time that can be constructed out of the fluid's parameters. Thisrebuts claims of universality for the dynamical scaling hypothesis. At earlytimes, we also find a crossover from $q^2$ to $q^4$ in the scaled structurefunction, which disappears when the dynamical scaling reasonably improves atlater times. This excludes noise as the cause for a $q^2$ behaviour, asproposed by others. We also observe exponential temporal growth of thestructure function during the initial stages of the dynamics and forwavenumbers less than a threshold value.Comment: 45 pages, 18 figures. Accepted for publication in Physical Review

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