(333g) Polydisperse Daughter Droplet Distributions from a Binary Breakage Kernel: A Viscoelastic Model for 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 this talk, we show that if this history-dependence is mediated through a viscoelastic constitutive equation for the droplet shape, then a binary breakage rule is sufficient to produce complex strain-dependent daughter droplet distributions following a step-shear deformation. This result is possible because we enforce stress continuity across the breakup process (i.e. capillary stresses from daughter droplets and parent droplets match), so the entire breakage process is interpolated as a cascade of simple binary breakage events rather than a single complex breakage event. 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.