  In many astrophysical systems, mixing between cool and hot temperature
gas/plasma through Kelvin-Helmholtz-instability-driven turbulence leads to the
formation of an intermediate temperature phase with increased radiative losses
that drive efficient cooling. The solar atmosphere is a potential site for this
process to occur with interaction between either prominence or spicule material
and the solar corona allowing the development of transition region material
with enhanced radiative losses. In this paper, we derive a set of equations to
model the evolution of such a mixing layer and make predictions for the
mixing-driven cooling rate and the rate at which mixing can lead to the
condensation of the coronal material. These theoretical predictions are
benchmarked against 2.5D MHD simulations. Applying the theoretical scalings to
prominence threads or fading spicules, we found that as a mixing layer grows on
their boundaries this would lead to the creation of transition region material
with a cooling time of ~100 s, explaining the warm emission observed as
prominence threads or spicules fade in cool spectral lines without the
requirement for any heating. For quiescent prominences, dynamic condensation
driven by the mixing process could restore ~18 per cent of the mass lost from a
prominence through downflows. Overall, this mechanism of thermal energy loss
through radiative losses induced by mixing highlights the importance for
considering dynamical interaction between material at different temperatures
when trying to understand the thermodynamic evolution of the cool material in
the solar corona.
