Modeling Sheared Frictional Liquid Crystals

Recent experiments [1] on sheared suspensions of rigid rods in the dense, non-Brownian regime in rotational geometries have found that the nematic director tilts out of the shear plane into the positive vorticity direction. This state is not "flow-aligned", and may be a kind of previously unobserved kayaking state. We show that at the level of a director or second order tensor model, neither the effect of the flow curvature or Frank elasticity can account for this tilting: both fiber models like Advani-Tucker and liquid crystal models like Doi-Edwards predict stable flow-alignment at high Peclet (i.e. non-Brownian) number. To model this "vorticity tilting", we also consider another feature of dense suspensions: inter-particle contacts. We construct a Rayleighian that includes the additional dissipation due to the relative motion of frictionally contacting rods, and then minimize this to produce a modified Smoluchowski equation, which we use to calculate dynamical equations for the tensor describing rod orientations. We treat both a form of "lubricated" friction, which is proportional to the magnitude of velocity at contact, and a Coulomb-like kinetic friction, which is proportional to the direction of contact velocity.

[1] Rathee et al., Role of particle orientational order during shear thickening in suspensions of colloidal rods, Physical Review E 101, 040601 (2020)