Robustness of self-aligning particles in simple shear flow towards rotation due to Brownian motion and hydrodynamic interactions

We show that a slender, rigid self-aligning-ring that attains an equilibrium orientation in a simple shear flow (SSF) can resist rotation against rotary Brownian motion as well as pairwise interactions with other particles under certain conditions. A self-aligning particle reaches an equilibrium orientation such that its slender dimension(s) makes an angle β_S≪1 with the velocity gradient direction of the SSF of shear rate γ. The particle wobbles around the equilibrium orientation if Pe =γ/D_r≫β_S³, where D_r is the rotational diffusivity of the particle. Using rotary Brownian Dynamics, we demonstrate that the particle tumbles if Pe≪β_s³ with a frequency smaller than that of an equivalent rotating particle of the same aspect ratio. Using slender body theory, we show that a self-aligning ring also wobbles around its equilibrium orientation due to pairwise interactions with other rings. Therefore, individual particles in a dilute suspension of self-aligning rings remain aligned near the flow vorticity plane for Pe≫β_S³ and thus the suspension has a smaller intrinsic viscosity compared to a suspension of tori of the same aspect ratio. Our result opens a new avenue to tune the rheology of particle suspensions by changing the shape of individual particles.