Spinodal decomposition of a binary magnetic fluid confined to a surface

In our previous work [J. Chem. Phys. \textbf{136}, 024502 (2012)], we reported a demixing phase transition of a two-dimensional, binary Heisenberg fluid mixture driven by the ferromagnetic interactions of the magnetic species. Here, we present a theoretical study for the \textit{time-dependent} coarsening occuring within the two-phase region in the density-concentration plane, also known as spinodal decomposition. Our investigations are based on Dynamical Density Functional Theory (DDFT). The particles in the mixture are modelled as Gaussian soft spheres on a two-dimensional surface, where one component carries a classical spin of Heisenberg type. To investigate the two-phase region, we first present a linear stability analysis with respect to small, harmonic density perturbations. Second, to capture non-linear effects, we calculate time-dependent structure factors by combining DDFT with Percus' test particle method. For the growth of the average domain size $l$ during spinodal decomposition with time $t$, we observe a power-law behavior $l\propto t^{\delta_\alpha}$ with $\delta_m\simeq 0.333$ for the magnetic species and $\delta_n\simeq 0.323$ for the non-magnetic species.