Oscillating hydrodynamical jets in steady shear of nano-rod dispersions

The dynamical behavior of molecular alignment strongly affects the flow properties of nano-rod dispersions such as nematic polymers. Numerical studies have been performed for the Navier-Stokes equations with an extra stress determined by the rod orientational distribution, coupled to three different orientation models: the Doi-Hess kinetic model, the Doi-Marrucci-Greco tensor model, and the alignment tensor model. We reported spatially localized spurts in the velocity profile, which we call jets, that oscillate, i.e., the jets appear and disappear in periodic fashion [14], generalizing a similar phenomenon reported by Kupferman, Kawaguchi and Denn [2] for a model two-dimensional nematic liquid. The emergence of these oscillatory hydrodynamical jets is due to the competition of elasticity from the rod ensemble and flow coupling; the jet structures coincide with the periodic formation of a disordered phase known as an oblate defect. Here we show a parameter regime where multiple jets arise within the shear gap in the alignment tensor model, reminiscent of multiple shear banding in soft matter systems that possess both locally ordered and disordered phases such as worm-like micelles [3].