  When processing dense emulsions, complex flows stretch and deform droplets to
the point of breakup, changing the droplet size distribution and the mechanical
properties of the final product. For steady homogeneous flows, a droplet's
shape and proclivity to breakup can be inferred from a Capillary number,
comparing the strain rate with the typical shape relaxation time. More
generally, a droplet's shape depends on its whole history of deformation, and
this distinction can be salient under conditions relevant to industrial
processing. Here, we develop a coupled population balance and droplet shape
evolution model (STEPB) with a breaking rate determined by the droplet's shape.
In a first application of the STEPB model, we consider droplet breakup during
relaxation of step shear, where we predict non-trivial strain-dependent final
daughter droplet distributions. We also compare predictions from STEPB against
experimental observations in steady flow conditions, illuminating key
weaknesses in the model due to neglected terms.
