  The multiphase flow of droplets is widespread, both at the industrial and the
microscale, for both biological and non-biological applications alike. But the
ensemble interactions of such systems are inherently nonlinear and complex,
compounded by interfacial effects, making it a difficult many-body problem for
theory. In comparison, the self-assembly dynamics of solid particles in flow
have long been described and successfully exploited in the field of inertial
microfluidics, where particle crystals can be realized from inertial forces and
hydrodynamic interactions. Here, we report novel self-assembly dynamics of
liquid drops in confined microfluidic channels that contrast starkly with the
established paradigm of inertial microfluidics: higher inertia leads to better
spatial ordering. Instead, we find that the conventional straight wall channel
geometry not only fails to achieve regular spatial ordering for drops but
actually exacerbates it with increasing inertia. Conversely, an asymmetric
serpentine geometry is able to achieve long-range, periodic spatial ordering
over length scales that are at least 3 orders of magnitude greater than the
drop diameter, particularly at low inertia. Experimentally, we are able to
decouple droplet generation from ordering, enabling independent variation of
number density, confinement, inertia, and surfactant concentration. We find the
inertia-dependent emergence of preferred drop separations and show for the
first time that Marangoni effects can influence the longitudinal ordering of
multidrop arrays. These results present a largely unexplored direction for
inertial microfluidics but also show the potential of its unification with
droplet microfluidics. In particular, the utility of passively restoring
uniform drop spacing on-chip is a key requirement for the streamlined
integration of incubation and drop-by-drop interrogation capabilities.

Fluid Dynamics;Applied Physics