Porous materials, which are characterized by the large surface area and percolated nature crucial for transport, play an important role in many technological applications including battery, ion exchange, catalysis, microelectronics, medical diagnosis, and oil recovery. Phase separation of a mixture in such a porous structure should be strongly influenced by both surface wetting and strong geometrical confinement effects. Despite its fundamental and technological importance, however, this problem has remained elusive for a long time because of the difficulty associated with the complex geometry of pore structures. We overcome this by developing a novel phase-field model of two coupled order parameters, the composition field of a binary mixture and the density field of a porous structure. We find that demixing behavior in complex pore structures is severely affected by the topological characteristics of porous materials, contrary to the conventional belief that it can be inferred from the behavior in a simple cylindrical pore. Our finding not only reveals the physical mechanism of demixing in random porous structures but also has an impact on technological applications.
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