Particles suspended in a Newtonian fluid may lead to non-Newtonian behaviour, depending on their shape and flexibility. Particles can now be precisely engineered from linked, double-stranded DNA sequences or rods. To design functional nano-materials from these systems, it is important to predict the suspension properties for a given particle specification. We study this question theoretically, focusing on two classes of DNA particles; nano-stars and nun-chucks. Nano-stars are constructed from straight, rigid rods joined at fixed angles, to form e.g. Y-shapes. Nun-chucks are two rods linked at their ends by a flexible joint.

We determine a set of sufficient symmetry conditions on the particle shape for a dilute suspension to be Newtonian. We demonstrate these for nano-stars and further show that the lengths of their constituent rods may be engineered so that the suspension is Newtonian, despite the particles not possessing the appropriate symmetries. We present a simple geometric method to determine the magnitude of the elastic response of concentrated nano-star suspensions. We find that the linear elastic response for bent and branched particles increases proportional to the concentration cubed whereas for rods it increases only linearly. The non-linear response is also different; concentrated thin rod suspensions always shear thin, but suspensions of bent/branched particles can shear thicken, depending on the bending modulus of the particles. These properties are very sensitive to the shape of the particle. The diffusion of branched particles in concentrated suspensions is also discussed through a simple, two-dimensional model, which indicates a glass transition in these systems.

We develop a formalism describing the dynamics of the nun-chuck particles in dilute suspensions. We address problems ranging from the motion of the particles under shear flow in the absence of Brownian motions to the steady state non-linear elasticity. We discuss briefly how our approach may be extended to concentrated suspensions and the transition to liquid crystalline states for these particles.