The role of rolling friction in the rheology of a dense suspension of rings*

Suspensions of rigid particles in viscous liquids are common in wide-ranging contexts (e.g., mudslides, drug delivery), and very few involve spherical solid particles. However, the effect of particle shape is often neglected when modeling dense suspensions. To address this knowledge gap, we argue that studying the rheological behavior of dense suspensions of non-Brownian rings provides a platform for understanding the striking role of shape in establishing nonlinear rheology. For these ring-shaped particles, a geometric resistance to rotation is introduced between the particles in the form of a rolling friction coefficient that can be tuned and is proportional to their aspect ratio. We report on the experimental investigation of a dense suspension of non-Brownian, square cross-section ring-shaped particles of controlled mean diameter and aspect ratio that we design and mass-produce through a photolithography technique. We use a microfluidic device to show that, in the absence of density difference between the particles and solvent, the rings have a preferred alignment with their neighbors and with the flow. Our rheological characterization shows a yield stress due to many particle contacts at low shear rates, whereas, at high shear rates, we observe a shear-independent viscosity diverging at a jamming volume fraction smaller than that of spherical particles.