We simulate the phase separation of a binary mixture that is deeply quenched into the unstable range of its phase diagram. The mixture is described through the diffuse-interface model and the governing equations are integrated in 2D and 3D in a periodic box and in a channel using a pseudo-spectral method. Spinodal decomposition patterns for critical and off-critical mixtures are studied, revealing the scaling laws of the characteristic lengthscale and composition of single-phase microdomains, together with their dependence on the Peclet number. Comparison between 2D and 3D results reveals that 2D simulations capture, even quantitatively, the main features of the phenomenon. However, while the agreement between 2D and 3D simulations is excellent when the mixture is confined in a periodic box, it appears to be less pronounced in a channel-like geometry.
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