Shear-induced rotations in a weakly anchored nematic liquid crystal

Abstract

We analyse the instability dynamics of a nematic liquid crystal under steady plane Couette flow. Weak anchoring for molecules of the nematic at the boundaries with an easy axis perpendicular to the flow plane is assumed. Orientation of the director along the easy axis is our basic state. Previously (Tarasov et al., 2001, Liq. Cryst. 28, 833), it was found that the critical shear rate of the primary instability of the basic state strongly decreases with anchoring strength. In the present study our interest was to examine the effect of the anchoring strength on the nematic dynamics in the regime with a slightly supercritical shear rate. It was found that for weaker anchoring the director rotates more strongly and the relaxation time of the amplitude of the basic state perturbations significantly increases. Results obtained can be used for experimental measurements of the anchoring strengths.

Notes

^†MBBA material parameters at 25°C [18]. Elastic constants, 10⁻¹² N: K ₁₁=6.66, K ₂₂=4.2, K ₃₃=8.61. Viscosities, 10⁻³ N s m⁻²: α ₁=−18.1, α ₂=−110.4, α ₃=−1.1, α ₄=82.6, α ₅=77.9, α ₆=−33.6. Mass density ρ=10³ kg m⁻³.

^‡An exact value of the critical shear rate is not reported in [8], but from the presented graphs it can be estimated by interpolating the data to be about 0.14–0.15 s⁻¹. From our calculations for the parameters of this experiment (d=150 µm, MBBA material parameters [18]) it follows that the critical shear rate is ≈0.19 s⁻¹.

Twist and splay relaxation of the director. Symbols are experimental data from [8], solid and dashed lines are theoretical calculations for 90°−ϕ _m and θ _m, respectively. Rigid boundary conditions are assumed in the calculations