  Long and slender liquid filaments are produced during inkjet printing, which
can subsequently either retract to form a single droplet, or break up to form a
primary droplet and one or more satellite droplets. These satellite droplets
are undesirable since they degrade the quality and reproducibility of the
print. Existing strategies for the suppression of satellite droplet formation
includes, among others, adding viscoelasticity to the ink. In the present work,
we aim to improve the understanding of the role of viscoelasticity in
suppressing satellite droplets in inkjet printing. We demonstrate that very
dilute viscoelastic aqueous solutions (concentrations $\sim$ 0.003\% wt.
polyethylene oxide (PEO), corresponding to nozzle Deborah number $De_{n}$
$\sim$ 3) can suppress satellite droplet formation. Furthermore, we show that,
for a given driving condition, upper and lower bounds of polymer concentration
exist, within which satellite droplets are suppressed. Satellite droplets are
formed at concentrations below the lower bound, while jetting ceases for
concentrations above the upper bound (for fixed driving conditions). Moreover,
we observe that, with concentrations in between the two bounds, the filaments
retract at velocities larger than the corresponding Taylor-Culick velocity for
the Newtonian case. We show that this enhanced retraction velocity can be
attributed to the elastic tension due to polymer stretching, which builds up
during the initial jetting phase. These results shed some light on the complex
interplay between inertia, capillarity, and viscoelasticity for retracting
liquid filaments, which is important for the stability and quality of inkjet
printing of polymer solutions.
