Squeezing a drop of nematic liquid crystal with strong elasticity effects

The One Drop Filling (ODF) method is widely used for the industrial manufacture of liquid crystal devices. Motivated by the need for a better fundamental understanding of the reorientation of the molecules due to the flow of the liquid crystal during this manufacturing method, we formulate and analyze a squeeze-film model for the ODF method. Specifically, we consider a nematic squeeze film in the asymptotic regime in which the drop is thin, inertial effects are weak, and elasticity effects are strong for four specific anchoring cases at the top plate and the substrate (namely, planar, homeotropic, hybrid aligned nematic, and π-cell infinite anchoring conditions) and for two different scenarios for the motion of the top plate (namely, prescribed speed and prescribed force). Analytical expressions for the leading- and first-order director angles, radial velocity, vertical velocity, and pressure are obtained. Shear and couple stresses at the top plate and the substrate are calculated and are interpreted in terms of the effect that flow may have on the alignment of the molecules at the plates, potentially leading to the formation of spurious optical defects ("mura").