Dimerization of Annular Sector Particles*

We study annular sector particles (ASPs), open semi-circular rings characterized by two dimensionless numbers: the subtended opening angle and the ratio of inner and outer radii. The ASPs are placed in an annulus with a rotating, ridged ring above them. Applying a torque to this ring exerts a shear stress on the quasi-2D packing of ASPs. Within the annulus, if two ASPs are within the outer radius distance from each other they have the potential to intersect with each other. This entangled pair of ASPs is defined as a dimer. The movement of ASPs results in the formation as well as annihilation of dimers, known as dimerization and de-dimerization.
From images of the annulus and computational analysis, the location and orientation of each ASP is determined. From this information, we can identify dimers and classify them based on the dot product of ASP orientations. Opposite facing dimers, which have the ability to form chains, are defined by a negative dot product; Similar facing dimers are defined by a positive dot product. We investigate the distribution of structure types and how they evolve with shear.