  The lattice Boltzmann method (LBM) is routinely employed in the simulation of
complex multiphase flows comprising bulk phases separated by non-ideal
interfaces. LBM is intrinsically mesoscale with an hydro-dynamic equivalence
popularly set by the Chapman-Enskog analysis, requiring that fields slowly vary
in space and time. The latter assumptions become questionable close to
interfaces, where the method is also known to be affected by spurious non
hydrodynamical contributions. This calls for quantitative hydrodynamical
checks. In this paper we analyze the hydrodynamic behaviour of LBM
pseudo-potential models for the problem of break-up of a liquid ligament
triggered by the Plateau-Rayleigh instability. Simulations are performed at
fixed interface thickness, while increasing the ligament radius, i.e. in the
"sharp interface" limit. Influence of different LBM collision operators is also
assessed. We find that different distributions of spurious currents along the
interface may change the outcome of the pseudo-potential model simulations
quite sensibly, which suggests that a proper fine-tuning of pseudo-potential
models in time-dependent problems is needed before the utilization in concrete
applications. Taken all together, we argue that the results of the proposed
study provide a valuable insight for engineering pseudo-potential model
applications involving the hydrodynamics of liquid jets.
