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Keywords:

  • complex fluids;
  • fluid mechanics;
  • microrheology;
  • particulate flows;
  • rheology

As a gift to Professor Bird, hydrodynamic interactions between two slender toroidal particles immersed in a viscous fluid are derived to extend the Rotne–Prager–Yamakawa (RPY) tensor formulation of bead-spring and bead-rod models of polymer kinetic theory to toroidal beads. As a relatively simple example of a multiply connected domain, this model geometry exhibits the special “role of the hole” and features new tensorial constructs beyond the Oseen–Burgers and Stokes quadrupoles that are encountered in the classical RPY theory. © 2014 American Institute of Chemical Engineers AIChE J, 60: 1517–1522, 2014