  We use a dynamical systems approach based on the method of orthonormal frames
to study the dynamics of a two-fluid, non-tilted Bianchi Type I cosmological
model. In our model, one of the fluids is a fluid with bulk viscosity, while
the other fluid assumes the role of a cosmological constant and represents
nonnegative vacuum energy. We begin by completing a detailed fixed-points
analysis of the system which gives information about the local sinks, sources
and saddles. We then proceeded to analyze the global features of the dynamical
system by using topological methods by finding the $\alpha$- and $\omega$-limit
sets. The fixed points found are a flat FLRW universe, an Einstein-de Sitter
universe, a de Sitter universe, a mixed FLRW universe with both vacuum and
non-vacuum energy, and a Kasner universe. We then find conditions for which
each equilibrium point was a saddle, sink, or source, and attempt to describe
the global and past asymptotic behaviour of the model with respect to each
fixed point. The flat FLRW universe solution we found with both vacuum and
non-vacuum energy is clearly of primary importance with respect to modelling
the present-day universe. In particular, we show that this equilibrium point is
a local sink and a saddle of the dynamical system, so there are orbits that
approach this equilibrium point in the future. Therefore, there exists a time
period for which our cosmological model will isotropize and be compatible with
present-day observations of a high degree of isotropy of the cosmic microwave
background in addition to the existence of both vacuum and non-vacuum energy.
