  We study microfluidic self digitization in Hele-Shaw cells using pancake
droplets anchored to surface tension traps. We show that above a critical flow
rate, large anchored droplets break up to form two daughter droplets, one of
which remains in the anchor. Below the critical flow velocity for breakup the
shape of the anchored drop is given by an elastica equation that depends on the
capillary number of the outer fluid. As the velocity crosses the critical
value, the equation stops admitting a solution that satisfies the boundary
conditions; the drop breaks up in spite of the neck still having finite width.
A similar breaking event also takes place between the holes of an array of
anchors, which we use to produce a 2D array of stationary drops in situ.
