We demonstrate an
autonomous, high-throughput mechanism for sorting
of emulsion droplets with different sizes concurrently flowing in
a microfluidic Hele-Shaw channel. The aqueous droplets of varying
radii suspended in olive oil are separated into different streamlines
across the channel upon interaction with a shallow (depth ∼
700 nm) inclined guiding track ablated into the polydimethylsiloxane-coated
surface of the channel with focused femtosecond laser pulses. Specifically,
the observed differences in the droplet trajectories along the guiding
track arise due to the different scaling of the confinement force
attracting the droplets into the track, fluid drag, and wall friction,
with the droplet radius. In addition, the distance traveled by the
droplets along the track also depends on the track width, with wider
tracks providing more stable droplet guiding for any given droplet
size. We systematically study the influence of the droplet size and
velocity on the trajectory of the droplets in the channel and analyze
the sensitivity of size-based droplet sorting for varying flow conditions.
The droplet guiding and sorting experiments are complemented by modeling
of the droplet motion in the channel flow using computational fluid
dynamics simulations and a previously developed model of droplet guiding.
Finally, we demonstrate a complete separation of droplets produced
by fusion of two independent droplet streams at the inlet of the Hele-Shaw
channel from unfused daughter droplets. The presented droplet sorting
technique can find applications in the development of analytical and
preparative microfluidic protocols.