  In galaxy clusters, the hot intracluster medium (ICM) can develop a striking
multi-phase structure around the brightest cluster galaxy. Much work has been
done on understanding the origin of this central nebula, but less work has
studied its eventual fate after the originally filamentary structure is broken
into individual cold clumps. In this paper we perform a suite of 30
(magneto-)hydrodynamical simulations of kpc-scale cold clouds with typical
parameters as found by galaxy cluster simulations, to understand whether clouds
are mixed back into the hot ICM or can persist. We investigate the effects of
radiative cooling, small-scale heating, magnetic fields, and (anisotropic)
thermal conduction on the long-term evolution of clouds. We find that filament
fragments cool on timescales shorter than the crushing timescale, fall out of
pressure equilibrium with the hot medium, and shatter, forming smaller
clumplets. These act as nucleation sites for further condensation, and mixing
via Kelvin-Helmholtz instability, causing cold gas mass to double within 75
Myr. Cloud growth depends on density, as well as on local heating processes,
which determine whether clouds undergo ablation- or shattering-driven
evolution. Magnetic fields slow down but don't prevent cloud growth, with the
evolution of both cold and warm phase sensitive to the field topology.
Counter-intuitively, anisotropic thermal conduction increases the cold gas
growth rate compared to non-conductive clouds, leading to larger amounts of
warm phase as well. We conclude that dense clumps on scales of $500$ pc or more
cannot be ignored when studying the long-term cooling flow evolution of galaxy
clusters.
