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Fluid phase separation inside a static periodic field: an effectively two-dimensional critical phenomenon

When a fluid with a bulk liquid-vapor critical point is placed inside a static external field with spatial periodic oscillations in one direction, the bulk critical point splits into two new critical points and a triple point. This phenomenon is called laser-induced condensation [Mol. Phys. Vol. 101, Pg. 1651 (2003)], and it occurs when the wavelength of the field is sufficiently large. The critical points mark the end of two coexistence regions, namely between (1) a vapor and stacked-fluid phase, and (2) a stacked-fluid and liquid phase. The stacked-fluid or "zebra" phase is characterized by large density oscillations along the field direction. We study the above phenomenon for a mixture of colloids and polymers using density functional theory and computer simulation. The theory predicts that the vapor-zebra and liquid-zebra surface tensions are extremely small. Most strikingly, however, is the theoretical finding that at their respective critical points, both tensions vanish, but not according to any critical power law. The solution to this apparent paradox is provided by the simulations. These show that the field divides the system into effectively two-dimensional slabs, stacked on top of each other along the field direction. Inside each slab, the system behaves as if it were two-dimensional, while in the field direction the system resembles a one-dimensional Ising chain.