Spinodal decomposition of a binary magnetic fluid confined to a surface

In our previous work [J. Chem. Phys. 136, 024502 (2012)], we reported a demixing phase transition of a quasi-two-dimensional, binary Heisenberg fluid mixture driven by the ferromagnetic interactions of the magnetic species. Here, we present a theoretical study for the time-dependent coarsening occurring 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 modeled 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 nonlinear 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∝t^{δ_{α}} with δ_{m}≃0.333 for the magnetic species and δ_{n}≃0.323 for the nonmagnetic species.