Tuneable rheology of suspensions of self-aligning particles

The shear rheology of suspensions is important in material manufacturing, biophysics and environmental processes. Particle geometry impacts rheology in a manner that depends on the particles’ individual rotational dynamics and interparticle interactions. In this work, we investigate the rheology of a suspension of self-aligning particles (SAPs), a class of rigid particles that, in a low Reynolds number simple shear flow, remain permanently aligned near the fluid lamellae without application of external torques. We focus on ring-shaped SAPs, which are robust against secondary effects such as perturbations to the shear flow, interparticle interactions and weak Brownian motion (Borker et al. 2024 Phys. Rev. Fluids 9 , 043301). Using dynamic simulations under a slender-body theory framework, we demonstrate that SAP suspensions generate specific viscosities an order of magnitude smaller than those generated by tumbling particles of the same aspect ratio. As a result, SAP suspensions make only modest alterations to the suspension viscosity even at $O(1)$ values of the number density n̄ non-dimensionalized by the in-plane radial extent of the ring. This reduction in the shear stress arises from persistent alignment, which suppresses the short tumbling events that dominate the rheology of conventional high-aspect ratio particles. Our results indicate a distinct hydrodynamic mechanism governing shear stresses in SAPs, including a regime near a critical aspect ratio that is dominated by dipoles per unit circumference and has no analogue in tumbling-particle suspensions. As a consequence, ring-shaped SAPs with different cross-sectional shapes impart shear stress of comparable magnitude at a given aspect ratio. In contrast to their weak contribution to shear stresses, SAP suspensions generate comparatively large normal stress differences due to the intrinsic asymmetry of their equilibrium orientation. This fundamentally differs from tumbling-particle suspensions which need collisions to generate normal stresses. Therefore, normal stresses in SAP suspensions scale linearly with n̄ and are significantly larger than the O(n̄²) normal stresses observed in tumbling-particle suspensions. Consequently, SAP suspensions exhibit non-Newtonian behaviour at lower volume fractions and may exhibit the Weissenberg effect at moderate number densities. Our findings highlight that SAPs offer access to rheological properties that are challenging to replicate in suspensions of conventional rigid particles. Overall, these findings offer new insight into tuning the bulk rheology of particle suspensions by controlling the orientational dynamics of individual particles.