  We investigate the nature of dissipative instability at the boundary (seen
here as tangential discontinuity) between the viscous corona and the partially
ionised prominence plasma in the incompressible limit. The importance of the
partial ionisation is investigated in terms of the ionisation fraction.
Matching the solutions for the transversal component of the velocity and total
pressure at the interface between the prominence and coronal plasmas, we derive
a dispersion relation whose imaginary part describes the evolution of the
instability. Results are obtained in the limit of weak dissipation. Using
simple analytical methods, we show that dissipative instabilities appear for
flow speeds that are lower than the Kelvin-Helmholtz instability threshold.
While viscosity tends to destabilise the plasma, the effect of partial
ionisation (through the Cowling resistivity) will act towards stabilising the
interface. For ionisation degrees closer to a neutral gas the interface will be
unstable for larger values of equilibrium flow. The same principle is assumed
when studying the appearance of instability at the interface between
prominences and dark plumes. The unstable mode appearing in this case has a
very small growth rate and dissipative instability cannot explain the
appearance of flows in plumes. The present study improves our understanding of
the complexity of dynamical processes at the interface of solar prominences and
solar corona, and the role partial ionisation can have on the stability of the
plasma. Our results clearly show that the problem of partial ionisation
introduces new aspects of plasma stability with consequences on the evolution
of solar prominences.
