Director Dynamics Within a Boundary Layer in Contact with a Shearing Solid Surface With Non-Rigid Anchoring

Abstract

The hydrodynamics of liquid crystals within thin boundary layers in contact with solid surfaces is strongly perturbed by the director anchoring on these surfaces; that manifests by occurrence of strong gradients and backflows. Accordingly, it is legitimate to question the interpretation of rheological measurements based on flow properties in the bulk where, moreover, director and velocity gradients are often assumed to be homogeneous. This remark is enhanced by the fact that rheology probes the fluid in contact with a solid surface. On the other hand, comparison between theoretical predictions and experimental observations close to the solid surface may shed light on the nematic-solid interaction. For these reasons the director dynamics at a solid surface deserves to be analysed theoretically. We have investigated the effect of non-rigid anchoring within the frame-work of Leslie-Ericksen theory combined with Rapini-Papoular model [A. Rapini, M. Papoular, J. Phys., 30C, 4, (1969)] for which the surface energy density is characterised by an anchoring strength and a preferred orientation of the director called easy axis. Calculations have been performed for nematics enclosed between two parallel plates in relative motion. Results for aligning and tumbling low molecular weight liquid crystals are presented. They may be summarised as follows: (i) strong inhomogeneities close to the surfaces, (ii) director precession at the surface for aligning nematics under certain conditions and (iii) relaxation of the stored elastic energy for tumbling nematics.

Keywords:

• boundary layer
• Leslie-Ericksen
• nematic
• shear
• tumbling
• weak anchoring

Acknowledgments

This work was partly supported by the “Fundação para a Ciência e a Tecnologia” (Portugal) under research grant SFRH/BPD/8894/2002 to A. Véron.

Notes

¹The Leslie viscosities satisfy the Parodi relation α₂ + α₃ = α₆ − α₅.

²Note that the elastic contribution vanishes in S ₂₁ and S ₂₃.

³The profiles being symmetric with respect to the middle gap at each time (see Fig. 5) the behaviour shown by Figures 1–4 close to x ₂ = 0 arise also close to x ₂ = d.