Influence of shear flow on the Fréedericksz transition in nematic liquid crystals

Within the framework of Ericksen-Leslie continuum theory we analyze the influence of shear flow on the magnetic-field-induced Fréedericksz transition in nematic liquid crystal with rodlike molecules. We consider three basic orientational configurations of a nematic planar layer in the uniform magnetic field. Conditions of rigid director coupling on the boundaries of the layer and constant shear flow gradient inside the layer are used. We exhibit some flow aligning effects for nematic liquid crystals with various ratio of rotary viscosities and investigate how unequal elastic constants (elastic anisotropy) alter the magnetic Fréedericksz transition in sheared nematics. Our calculations predict that surface boundary effects in nematic films and magnetic field action lead to existence of stationary flow regimes in the so-called nonflow aligning nematics, otherwise, surface and magnetic forces extend the range of viscous coefficient values corresponding to the flow aligning regimes. We show that imposing of shear flow on the Fréedericksz transition leads to a threshold behavior or to a “smoothing” of the transition. It depends on the orientation of the nematic layer in magnetic field and magnitudes of rotary viscous coefficients.

Figure 1

Orientation of a nematic layer between moving plates in magnetic field $\mathbf{H}$ [configuration (A)].

Figure 2

The basic types of director field deformations in static Fréedericksz transition without shear flow [configuration (A)].

Figure 3

Dependence of the angle ${\phi }_0$ of the director rotation on the reduced square of magnetic field strength $h∕h_c$ in Fréedericksz transition [configuration (A)] at isotropy of elasticity $(k=1)$. Solid line corresponds to the solutions without shear flow $(\mu =0)$; dashed line describes the director behavior of a flow aligning NLC $(\gamma =1)$ under shear flow influence $(\mu =1)$.

Figure 4

Dependence of the angle ${\phi }_0$ of the director rotation on the reduced square of magnetic field strength $h∕h_c$ in Fréedericksz transition [configuration (A)] for flow aligning NLC $(\gamma =1)$ with two values of elastic anisotropy $(k=0.7,2)$ under shear flow influence $(\mu =1)$.

Figure 5

Dependence of the angle ${\phi }_0$ of the director rotation on the reduced square of magnetic field strength $h∕h_c$ in Fréedericksz transition [configuration (A)] for flow aligning NLC with elastic isotropy $(k=1)$ and two values of reactive parameter $(\gamma =1,2)$ under shear flow influence $(\mu =1)$.

Figure 6

Dependence of the angle ${\phi }_0$ of the director rotation on the reduced square of magnetic field strength $h∕h_c$ in Fréedericksz transition [configuration (A)] for flow aligning $(\gamma =1)$ and nonflow aligning NLC $(\gamma =0.5)$ with elastic isotropy $(k=1)$ under shear flow influence $(\mu =1)$.

Figure 7

Orientation of a nematic layer between moving plates in magnetic field $\mathbf{H}$ [configuration (B)].

Figure 8

Orientation of a nematic layer between moving plates in magnetic field $\mathbf{H}$ [configuration (C)].

Figure 9

The basic types of director field deformations in static Fréedericksz transition without shear flow [configuration (C)].

Figure 10

Dependence of the angle ${\theta }_0$ of the director rotation on the reduced square of magnetic field strength $h∕h_c$ in Fréedericksz transition [configuration (C)] at isotropy of elasticity $(k=1)$. Solid lines correspond to the solutions without shear flow $(\mu =0)$; dashed lines describe the transition in flow aligning NLC $(\gamma =1)$ under shear flow influence $(\mu =1)$.

Figure 11

Dependence of the angle ${\theta }_0$ of the director rotation on the reduced square of magnetic field strength $h∕h_c$ in Fréedericksz transition [configuration (C)] for flow aligning NLC $(\gamma =1)$ with two values of anisotropy of elasticity $(k=0.7,1.3)$ at presence of shear flow $(\mu =1)$.

Figure 12

Dependence of the angle ${\theta }_0$ of the director rotation on the reduced square of magnetic field strength $h∕h_c$ in Fréedericksz transition [configuration (C)] for flow aligning $(\gamma =2)$ and nonflow aligning NLC $(\gamma =0.5)$ at presence of shear flow $(\mu =1)$ and isotropy of elasticity $(k=1)$.