  The low solar atmosphere is composed of mostly neutral particles, but the
importance of the magnetic field for understanding observed dynamics means that
interactions between charged and neutral particles play a very important role
in controlling the macroscopic fluid motions. As the exchange of momentum
between fluids, essential for the neutral fluid to effectively feel the Lorentz
force, is through collisional interactions, the relative timescale of these
interactions to the dynamic timescale determines whether a single-fluid model
or, when the dynamic frequency is higher, the more detailed two-fluid model is
the more appropriate. However, as many MHD phenomena fundamentally contain
multi-time-scale processes, even large-scale, long-timescale motions can have
an important physical contribution from two-fluid processes. In this review we
will focus on two-fluid models, looking in detail at two areas where the
multi-time-scale nature of the solar atmosphere means that two-fluid physics
can easily develop: shock-waves and instabilities. We then connect these ideas
to observations attempting to diagnose two-fluid behaviour in the solar
atmosphere, suggesting some ways forward to bring observations and simulations
closer together.
