Rheology of dilute suspensions of slender rings in presence of frictional contacts

Suspensions of slender ring-shaped particles have applications in drug delivery, catalysis, optics, and carbon capture. On a fundamental level, slender rings exhibit a large geometrical resistance to the relative rotation of neighboring particles in a shear flow. Therefore, studying the rheology and microstructure of suspensions of ring-shaped particles transforms our understanding of the role of topology on the nonlinear rheology of suspensions. In our initial study, we investigate the rheology of such non-Brownian suspensions in simple shear flow at low particle number densities. Suspension properties are computed by averaging many pairwise interactions that include hydrodynamic interactions (modelled using slender body theory) and particle contacts (modelled as short-range repulsive forces coupled with Coulombic friction). We explore particle friction coefficients ranging from 0 to 1, along with the infinite friction limit. We find that the contact contribution to the shear stress increases with the friction coefficient and is comparable to other stress contributions. Friction changes the microstructure during collisions in a manner that decreases the first normal stress difference and increases the magnitude of the second normal stress difference. Friction enhances the effective diffusivity of particles in the gradient direction and retards the diffusivity in the vorticity direction.