Rheology and ordering transitions of non-Brownian suspensions in a confined shear flow: effects of external torques.

We investigate the effect of an external torque, applied in the vorticity direction, to particles in a sheared non-Brownian suspension confined by rigid walls. At volume fractions of ϕ=0.48-0.52 such suspension flows undergo an ordering transition, developing a hexagonal structure of particle strings in the velocity gradient-vorticity plane. The hexagonal structure is disturbed by negative torques, leading to an increase in the shear viscosity. Positive torque has a favorable effect on the ordered state. However, if the magnitude of the positive torque exceeds a certain threshold, the hexagonal order begins to be weakened. Due to the significant changes in suspension microstructures, rheological parameters such as the shear and vortex viscosities exhibit nonlinear responses to the external torques. On the other hand, at lower volume fractions ϕ≤0.40, where ordered structures are not developed, suspension microstructure is not sensitive to an external torque and the apparent viscosity is a linear function of the torque.