Complex Dynamics of a Model of Sheared Nematogenic Fluids

Abstract: Nonlinearities in constitutive equations of extended objects in shear flow lead to novel phenomena, {\it e.g.} "rheochaos" in solutions of wormlike micelles and "elastic turbulence" in polymer solutions. Since both phenomena involve anisotropic objects, their contributions to the deviatoric stress are likely to be similar. However, these two fields have evolved rather independently and an attempt at connecting these fields is still lacking. We show that a minimal model in which the anisotropic nature of the constituting objects is taken into account by a nematic alignment tensor field reproduces several statistical features found in rheochaos and elastic turbulence. We numerically analyse the full non-linear hydrodynamic equations of a sheared nematic fluid under shear stress and strain rate controlled situations, incorporating spatial heterogeneity only in the gradient direction. For a certain range of imposed stress and strain rates, this extended dynamical system shows signatures of \textit{spatiotemporal chaos} and \textit{transient shear banding}. In the chaotic regime the power spectra of the order parameter stress, velocity fluctuations and the total injected power show power law behavior and the total injected power shows a non-gaussian, skewed probability distribution. These dynamical features bear resemblance to \textit{elastic turbulence} phenomena observed in polymer solutions. The scaling behavior is independent of the choice of shear rate/stress controlled method.