(333f) A Viscoelastic Model for Droplet Breakup in Dense Emulsions

In many models of emulsion breakup, unsteady deformations pose a problem for breakage kernels: the droplet's shape and proclivity to breakup (as well as the resultant daughter droplet distribution) depends not on the instantaneous strain rate but rather on the whole strain history. In our work, we account for this history-dependence via a viscoelastic constitutive equation for droplet shape, with strict couplings to population balance dynamics. We describe the typical shape of a droplet at different size intervals, and show how this shape changes with (1) deformation, (2) relaxation, and (3) the influx/outflux of droplets due to breakage. The last of these lets daughter droplets retain their deformation at the moment of breakup, such that polydisperse daughter droplet distributions can be realized via a cascade of binary breakage events. This partially alleviates the pressure to develop complex history-dependent daughter droplet distributions. The talk will cover (1) an overview of the model's overall structure, (2) key assumptions and approximations, and (3) predictions for both step deformations and steady shear.