Effects of Polydispersity on the Nonaffine Behaviors of Dense 2D Granular Systems Under Shear

We study simulations of highly polydisperse emulsions under shear flow where 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 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 and how it depends on the position in the system. 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.