Nonequilibrium steady states in an open system connecting two reservoirs of platelike colloidal particles are investigated by means of a recently proposed phenomenological dynamic density functional theory [M. Bier and R. van Roij, Phys. Rev. E 76, 021405 (2007)]. The platelike colloidal particles are approximated within the Zwanzig model of restricted orientations, which exhibits an isotropic-nematic bulk phase transition. Inhomogeneities of the local chemical potential generate a diffusion current which relaxes to a nonvanishing value if the two reservoirs coupled to the system sustain different chemical potentials. The relaxation process of initial states towards the steady state turns out to comprise two regimes: a smoothening of initial steplike structures followed by an ultimate relaxation of the slowest diffusive mode. The position of a nonequilibrium interface and the particle current of steady states depend nontrivially on the structure of the reservoirs due to the coupling between translational and orientational degrees of freedom of the fluid
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