Banded spatiotemporal chaos in sheared nematogenic fluids

Complex Dynamics of a Model of Sheared Nematogenic Fluids

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 reproduc…

Shear banding in nematogenic fluids with oscillating orientational dynamics

We investigate the occurrence of shear banding in nematogenic fluids under planar Couette flow, based on mesoscopic dynamical equations for the orientational order parameter and the shear stress. We focus on parameter values where the sheared homogeneous system exhibits regular oscillatory orientational dynamics, whereas the equilibrium system is either isotropic (albeit close to the isotropic--nematic transition) or deep in its nematic phase. The numerical calculations are restricted to spatial variations in shear gradient direction. We find several new types of shear banded states characteri…

Dynamics of a sheared twist bend nematic liquid crystal

We study the flow behaviour of a twist-bend nematic $(N_{TB})$ liquid crystal. It shows three distinct shear stress ($σ$) responses in a certain range of temperatures and shear rates ($\dotγ$). In Region-I, $σ\sim\sqrt{\dotγ}$, in region-II, the stress shows a plateau, characterised by a power law $σ\sim{\dotγ}^α$, where $α\sim0.1-0.4$ and in region-III, $σ\sim\dotγ$. With increasing shear rate, $σ$ changes continuously from region-I to II, whereas it changes discontinuously with a hysteresis from region-II to III. In the plateau (region-II), we observe a dynamic stress fluctuations, exhibitin…

致热流体流变学中时空混沌的途径

Routes to spatiotemporal chaos in the rheology of nematogenic fluids

为了理解在最近的实验中观察到的“流变混沌”在各种定向流体中，我们数值研究的运动方程的无痕对称序参量的时空演化的剪切致热流体。特别是，我们建立，通过决定性的数值试验，不规则的振荡行为中看到的参数空间的区域中，不稳定的流动对齐，实际上是时空混沌。我们勾勒出该模型的动力学相图，并研究了通向混沌态的途径。我们发现在这个系统中的时空混沌是通过{ \em spatiotemporal不稳定性}的机制产生的，层流区域的宽度也是幂律分布的，就像H. Chaté和P. Manneville，Phys. Rev. Lett. { \bf 58}，112（1987）.此外，带大小的直方图的演变示出了一个不断增长的长度尺度，从混沌向流动对齐的阶段。最后，我们建议可能的实验，可以观察到有趣的行为在这里讨论。

湍流动力学中的时空流变混沌

Spatiotemporal rheochaos in nematic hydrodynamics

受剪切蠕虫状胶束中流变混沌的观察的启发[Bandyopadhyay等人，Lett，84 2022，（2000）; Europhys. Lett. 56，447（2001）; Pramana 53，223（1999）]研究了剪切流体中流体动力学速度场和序参量场的耦合非线性偏微分方程。在一个合适的参数范围内，我们发现不规则的，动态剪切带，并建立决定性的数值试验，我们观察到的模型中的混沌是时空的性质。

Concentration banding instability of a sheared bacterial suspension

We demonstrate a novel shear-induced mechanism for growth of concentration fluctuations in a bacterial suspension. Using a linear stability analysis, a homogeneously sheared suspension is shown to support exponentially growing layering perturbations in the shear-rate and bacterial concentration. Non-linear simulations show that the instability eventually leads to gradient-banded velocity profiles, with a local depletion of bacteria at the interface between the bands. Our results show that long-ranged hydrodynamic interactions are sufficient to explain recent observations of shear-bands in bact…