  Phase separation is a fundamental phenomenon that produces spatially
heterogeneous patterns in soft matter. In this Lecture Note we show that phase
separation in these materials generally belongs to what we call "viscoelastic
phase separation", where the morphology is determined by the mechanical balance
of not only the thermodynamic force (interface tension) but also the
viscoelastic force. The origin of the viscoelastic force is dynamic asymmetry
between the components of a mixture, which can be caused by either a size
disparity or a difference in the glass transition temperature between the
components. We stress that such dynamic asymmetry generally exists in soft
matter. The key is that dynamical asymmetry leads to a non-trivial coupling
between the concentration, velocity, and stress fields. Viscoelastic phase
separation can be explained by viscoelastic relaxation in pattern evolution and
the resulting switching of the relevant order parameter, which are induced by
the competition between the deformation rate of phase separation and the
slowest mechanical relaxation rate of a system. We also discuss an intimate
link of viscoelastic phase separation, where deformation fields are
spontaneously generated by phase separation itself, to mechanical instability
(or fracture) of glassy material, which is induced by externally imposed strain
fields. We propose that all these phenomena can be understood as
mechanically-driven inhomogeneization in a unified manner.
