  Classical as well as quantum features of the late-time evolution of
cosmological models with fluids obeying a Shan-Chen-like equation of state are
studied. The latter is of the type $p=w_{\rm eff}(\rho)\,\rho$, and has been
used in previous works to describe, e.g., a possible scenario for the growth of
the dark-energy content of the present Universe. At the classical level the
fluid dynamics in a spatially flat Friedmann-Robertson-Walker background
implies the existence of two possible equilibrium solutions depending on the
model parameters, associated with (asymptotic) finite pressure and energy
density. We show that no future cosmological singularity is developed during
the evolution for this specific model. The corresponding quantum effects in the
late-time behavior of the system are also investigated within the framework of
quantum geometrodynamics, i.e., by solving the (minisuperspace) Wheeler-DeWitt
equation in the Born-Oppenheimer approximation, constructing wave-packets and
analyzing their behavior.
