  Dust grain dynamics in molecular clouds is regulated by its interplay with
supersonic turbulent gas motions. The conditions under which dust grains
decouple from the dynamics of gas remain poorly constrained. We first aim to
investigate the critical dust grain size for dynamical decoupling, using both
analytical predictions and numerical experiments. Second, we aim to set the
range of validity of two fundamentally different numerical implementations for
the evolution of dust and gas mixtures in turbulent molecular clouds. We
carried out a suite of numerical experiments using two different schemes.
First, we used a monofluid formalism in the terminal velocity approximation
(TVA) on a Eulerian grid. Second, we used a two-fluid scheme, in which the dust
dynamics is handled with Lagrangian super-particles, and the gas dynamics on a
Eulerian grid. The monofluid results are in good agreement with the theoretical
critical size for decoupling. We report dust dynamics decoupling for Stokes
number St>0.1, that is, dust grains of $s>4~\mu$m in size. We find that the TVA
is well suited for grain sizes of 10 $\mu$m in molecular clouds, in particular
in the densest regions. However, the maximum dust enrichment measured in the
low-density material where St>1 is questionable. In the Lagrangian dust
experiments, we show that the results are affected by the numerics for all dust
grain sizes. At St<<1, the dust dynamics is largely affected by artificial
trapping in the high-density regions, leading to spurious variations of the
dust concentration. At St>1, the maximum dust enrichment is regulated by the
grid resolution used for the gas dynamics. The results of previous similar
numerical work should therefore be revisited with respect to the limitations we
highlight in this study. Dust enrichment of submicron dust grains is unlikely
to occur in the densest parts of molecular clouds.
