  Microfluidics encompasses a wide variety of subfields that can often be
combined or applied independently of one another. Two such areas are droplet
microfluidics and inertial microfluidics. The former has seen growing use due
to the advantage of droplets being individual reactors, allowing for
compartmentalized chemical synthesis, single-molecule assays, as well as
single-cell sequencing. Inertial microfluidics on the other hand has largely
been focused on utilizing fluid inertia and the hydrodynamic forces that arise
to focus, order, and sort particles, such as beads and cells. However, such
principles have seen far less direct application to droplet manipulation, owing
to a lack of physical studies on the longitudinal inertial self-assembly of
liquid droplets, which has limited the potential unification of these fields.
This study investigates how the parameters of channel geometry (asymmetric
serpentine vs straight), number density, confinement, inertia, and Marangoni
forces independently affect the self-assembly of droplet trains. Interestingly,
we find that the traditional straight wall geometry fails to achieve uniform
spatial ordering while the asymmetric serpentine is able to establish
long-range ordering in continuous drop trains over distances that are at least
3 orders of magnitude greater than the drop diameter. Such ordering is also
achievable at low flow rates, which is particularly well-suited to droplet
microfluidic applications, such as ensuring sufficient time for on-chip
incubation and for individual drop screening or sorting. These insights further
the understanding of complex multiphase fluid dynamics and could enable more
streamlined and integrated droplet microfluidic platforms.
