  This work studies the breakup of finite-size liquid filaments, when also
including substrate effects, using direct numerical simulations. The study
focuses on the effects of three parameters: Ohnesorge number, the ratio of the
viscous forces to inertial and surface tension forces, the liquid filament
aspect ratio, and where there is a substrate, a measure of the fluid slip on
the substrate, i.e. slip length. Through these parameters, it is determined
whether a liquid filament breaks up during the evolution toward its final
equilibrium state. Three scenarios are identified: a collapse into a single
droplet, the breakup into one or multiple droplets, and recoalescence into a
single droplet after the breakup (or even possibly another breakup after
recoalescence). The results are compared with the ones available in the
literature for free-standing liquid filaments. The findings show that the
presence of the substrate promotes breakup of the filament. The effect of the
degree of slip on the breakup is also discussed. The parameter domain regions
are comprehensively explored when including the slip effects. An experimental
case is also carried out to illustrate the collapse and breakup of a
finite-size silicon oil filament supported on a substrate, showcasing a
critical length of the breakup in a physical configuration. Finally, direct
numerical simulations reveal striking new details into the breakup pattern for
low Ohnesorge numbers, where the dynamics are fast and the experimental imaging
is not available; our results therefore significantly extend the range of
Ohnesorge number over which filament breakup has been considered.
