  We investigate the effect of dust on the scaling properties of galaxy
clusters based on hydrodynamic N-body simulations of structure formation. We
have simulated five dust models plus a radiative cooling and adiabatic models
using the same initial conditions for all runs. The numerical implementation of
dust was based on the analytical computations of Montier and Giard (2004). We
set up dust simulations to cover different combinations of dust parameters that
put in evidence the effects of size and abundance of dust grains. Comparing our
radiative plus dust cooling runs to a purely radiative cooling simulation we
find that dust has an impact on cluster scaling relations. It mainly affects
the normalisation of the scalings (and their evolution), whereas it introduces
no significant differences on their slopes. The strength of the effect depends
critically on the dust abundance and grain size parameters as well as on the
cluster scaling. Indeed, cooling due to dust is effective at the cluster regime
and has a stronger effect on the "baryon driven" statistical properties of
clusters such as $L_{\rm X}-M$, $Y- M$, $S-M$ scaling relations. Major
differences, relative to the radiative cooling model, are as high as 25% for
the $L_{\rm X}-M$ normalisation, and about 10% for the $Y-M$ and $S-M$
normalisations at redshift zero. On the other hand, we find that dust has
almost no impact on the "dark matter driven" $T_{\rm mw}-M$ scaling relation.
The effects are found to be dependent in equal parts on both dust abundances
and grain sizes distributions for the scalings investigated in this paper.
Higher dust abundances and smaller grain sizes cause larger departures from the
radiative cooling (i.e. with no dust) model.
