  We report observations of the self-assembly of coated droplets into regular
clusters at the sudden expansion of a microfluidic channel. A double emulsion
consisting of a regular train of coated microdroplets was created upstream of
the channel expansion, so that the inter-drop distance, droplet length,
velocity and coating thickness could be varied by imposing different inlet
pressures, albeit not independently. Provided that the enlarged channel remains
sufficiently confined to prohibit propagation in double file, droplets can
assemble sequentially into regular linear clusters at the expansion. Droplets
join a cluster via the coalescence of their coating film with that of the group
ahead. This coalescence occurs when the droplets approach each other to within
a critical distance at the expansion, enabled by hydrodynamic interactions
within the train. Clusters comprising a finite number of droplets are obtained
because reconfiguration of the droplet assembly during coalescence increases
the distance to the following droplet. Decreasing the inter-drop distance
increases the cluster size up to a maximum value beyond which continuous
clusters form. Formalising these observations in a simple model reveals that
clusters of any size are possible but that they occur for increasingly narrow
ranges of parameter values. Our experimental observations suggests that
background experimental fluctuations limit the maximum discrete cluster size in
practice. This method of self-assembly offers a robust alternative to flow
focusing for encapsulating multiple cores in a single coating film and the
potential to build more complex colloidal building blocks by de-confining the
clusters.
