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We present a density-functional study of a binary phase-separating mixture ofsoft core particles immersed in a random matrix of quenched soft core particlesof larger size. This is a model for a binary polymer mixture immersed in acrosslinked rigid polymer network. Using the replica `trick' forquenched-annealed mixtures we derive an explicit density functional theory thattreats the quenched species on the level of its one-body density distribution.The relation to a set of effective external potentials acting on the annealedcomponents is discussed. We relate matrix-induced condensation in bulk to thebehaviour of the mixture around a single large particle. The interfacialproperties of the binary mixture at a surface of the quenched matrix display arich interplay between capillary condensation inside the bulk matrix andwetting phenomena at the matrix surface.Comment: 20 pages, 5 figures. Accepted for Phys. Rev.

Soft core fluid in a quenched matrix of soft core particles: A mobile mixture in a model gel