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It is well known that suspensions of particles in a viscous fluid can affectthe rheology significantly, producing a pronounced non-Newtonian response evenin dilute suspension. However, it is unclear a priori which particle shapeslead to this behaviour. We present two simple symmetry conditions on the shapewhich are sufficient for a dilute suspension to be Newtonian for all strainsizes and one sufficient for Newtonian behavior for small strains. We alsoconstruct a class of shapes out of thin, rigid rods not found by the symmetryargument which share this property for small strains.

Particle shapes leading to Newtonian dilute suspensions