Dynamical properties of nematic liquid crystals subjected to shear flow and magnetic fields: Tumbling instability and nonequilibrium fluctuations

Abstract

We investigate the dynamical properties of monodomain nematic liquid crystals under shear flow and magnetic fields on the basis of the Ericksen-Leslie theory. Stable and unstable states appear depending on the magnetic field and the shear rate. The trajectory of the unstable state shows tumbling motion. The phase diagram of these states is plotted as a function of the three components of the magnetic field at a constant shear rate. The phase diagram changes depending on the viscous properties of different types of nematic liquid crystals. In this nonequilibrium steady state, we calculate the correlation function of director fluctuations and the response function, and discuss the nonequilibrium fluctuations and the modified fluctuation-dissipation relation in connection with nonconservative forces due to shear flow.

Nonequilibrium steady-state response of a nematic liquid crystal under simple shear flow and electric fields

“…The nonconservative forces also violate the fluctuation-dissipation relation (FDR). Fatriansyah et al have theoretically clarified the mechanism of the appearance of the nonconservative forces in NLCs and derived a modified FDR [7]. According to the theory, the nonconservative forces can emerge only when the director is out of the shear plane.…”

“…It should also be noted that the linear response to an external force and the correlation function of fluctuations can be defined in an NESS as well as in the ES. In an NESS of an NLC, brought about by a steady shear flow, Fatriansyah et al [7] calculated the correlation function and the response function of the director orientation on the basis of a hydrodynamic theory of NLCs, called the Ericksen-Leslie (EL) theory, and derived a modified FDT, assuming that the director is independent of position, that is, the monodomain case. In this system nonconservative forces are induced by the rotational flow, which violate the usual FDT.…”

Two-shape-tensor model for tumbling in nematic polymers and liquid crystals

“…Another important reason for introducing the tensor Q in our model, is that tumbling typically generates defects [23], indicating that the system could no longer be regarded as a monodomain [3]. It is observed in [23] that the defect structures, or textures, in a 8CB sample depends on the shear history of the sample.…”

“…Furthermore, for some compounds, these different behaviors are unexpected, since their molecular structure and their phase diagrams are very similar [2][3][4]. For example, while MBBA and 5CB always flow align in their nematic phase, other closely related molecules, respectively HBAB and 8CB, undergo a transition from flow alignment to tumbling when the temperature is decreased below a given threshold [2,3].…”

Three-dimensional observation of Brownian particles under steady shear flow by stereo microscopy

“…This symmetry breaking is caused by a nonconservative force due to the rotational component of the shear flow. Such a nonconservative force has also been demonstrated to play an important role in orientational fluctuations in sheared nematic liquid crystals [11,12]. In the case of a free particle under shear flow, however, there is no experiment to reveal the appearance of the cross-correlation owing to the experimental difficulty mentioned above.…”