  The destruction of clouds by strong shocks and hot winds is the key process
responsible for the transp orting of metals and dust from the ISM to the
ICM/IGM, and establishing the multiphase structure in and around galaxies. In
this work, we perform a detailed analysis of this process using two different
approaches for tracking the cloud material (gas and dust): the so-called
'colored' fluid, and the Lagrangian (trace) particles. We find that for the
clouds in the hot phase ($T>10^5$ K), the two methods produce significantly
different mass fractions and velocities of the cloud material. In contrast, the
two methods produce similar results for the clouds that are in the warm/cold
phases ($T < 10^5$ K). We find that the Kelvin--Helmholtz instability is
suppressed in the warm clouds of size $\sim$100 pc and metallicity $Z\gt 0.1
Z_\odot$ due to effective gas cooling. This causes a delay in the destruction
of such clouds that are interacting with the hot ICM flow. We demonstrate that
the dust particles that are evacuated from their 'parent' clouds to the hot
medium show different dynamics when compared to that of the Lagrangian (trace)
particles. Our results indicate that the dust grains swept out to the hot gas
are destroyed.
