  The breakup of a fluid jet into droplets has long fascinated natural
scientists, with early research dating back to the 19th century. Infinitesimal
perturbations to a jet grow because of surface tension, which eventually leads
to breakup of the jet into droplets (Rayleigh-Plateau instability). Although
this classical phenomenon has long been studied, it is not clear how it is
modified when the fluid is replaced by an active fluid. In this study, we
investigate instabilities of a jet of an active fluid. The active fluid is
modelled by a suspension of microswimmers that propel themselves by generating
surface tangential velocities, i.e. squirmers. The squirmers are assumed to be
bottom-heavy and heavier than the surrounding fluid, so that a downward jet of
the active fluid self-assembles under gravity. Hydrodynamic interactions
between squirmers are computed using the Stokesian dynamics method, in which
near-field hydrodynamics are accurately calculated. We find that jets of active
fluids are unstable, with different unstable modes between pullers and pushers.
For an active fluid of pullers, the jet breaks up into droplets in a varicose
manner reminiscent of a Newtonian fluid. For pushers, on the other hand, the
jet buckles and undergoes a waving (sinuous) instability. The physical
mechanisms for these two instabilities can be understood by an inspection of
the stress fields in the jets and parametric study reveals the importance of
hydrodynamic interactions in the instabilities. Although both gravity and
bottom-heaviness play an essential role in realizing the downward jet, their
influence on the instability is found to be limited. Our findings help reveal
new features of the collective properties of active fluids.
