In sheared highly polydisperse emulsions, large droplets cause trouble for smaller droplets

We study experiments and simulations of highly polydisperse emulsions under shear flow. By highly polydisperse, we mean with the largest droplet diameters being as much as ten times the smallest diameters. We quantify non-affine motion in these highly polydisperse samples -- motion where droplets move with displacements distinctly different from their neighbors, or different from the overall imposed shear flow. The largest droplets typically move affinely, as if they are in a simple effective fluid formed by the other droplets. In contrast, the smallest droplets are often forced to move non-affinely by the larger droplets. We quantify how the non-affine motion diminishes as a function of droplet size and distance from the larger particles. We further show how the behavior depends on the overall droplet size distribution; in general, the largest droplets are always the troublemakers. Our main conclusion is that highly polydisperse samples behave qualitatively differently than weakly polydisperse samples.