  We study the dynamics of a bulk viscosity model in the Eckart approach for a
spatially flat Friedmann-Robertson-Walker (FRW) universe. We have included
radiation and dark energy, assumed as perfect fluids, and dark matter treated
as an imperfect fluid having bulk viscosity. We also introduce an interaction
term between the dark matter and dark energy components. Considering that the
bulk viscosity is proportional to the dark matter energy density and imposing a
complete cosmological dynamics, we find bounds on the bulk viscosity in order
to reproduce a matter-dominated era (MDE). This constraint is independent of
the interaction term. Some late time phantom solutions are mathematically
possible. However, the constraint imposed by a MDE restricts the interaction
parameter, in the phantom solutions, to a region consistent with a null value,
eliminating the possibility of late time stable solutions with $w<-1$. From the
different cases that we study, the only possible scenario, with bulk viscosity
and interaction term, belongs to the quintessence region. In this latter case,
we find bounds on the interaction parameter compatible with latest
observational data.
