  We prove existence of weak solutions to a diffuse interface model describing
the flow of a fluid through a deformable porous medium consisting of two
phases. The system non-linearly couples Biot's equations for poroelasticity,
including phase-field dependent material properties, with the Cahn-Hilliard
equation to model the evolution of the solid, and is further augmented by a
visco-elastic regularization consistent with secondary consolidation. To obtain
this result, we approximate the problem in two steps, where first a
semi-Galerkin ansatz is employed to show existence of weak solutions to
regularized systems, for which later on compactness arguments allow limit
passage. Notably, we also establish a maximal regularity theory for linear
visco-elastic problems.
