On the flow of liquid crystals through 90° bends

Abstract

During the processing of nematic soft solids through process flow elements (pipe bends, elbows, etc.), the constitutive behavior makes its presence felt via processing (with rheology driven effects increasing pressure drop) and the final product microstructure. This paper explores the flow and microstructure configurations of nematic liquid crystals in a pressure driven flow through 90° pipe bends with different types of wall anchoring. The governing equations of the Leslie–Ericksen theory are solved numerically in a newly developed OpenFOAM solver. We show that the bend curvature deforms the nematic axis distribution; the distortion can be driven either by elastic or hydrodynamic effects. The interaction between the nematic microstructure and flow field generates non-zero normal stresses (in the radial, azimuthal, and streamwise directions), which produce a secondary flow and increase pressure losses. The strength of the secondary flow depends on the type of wall anchoring and Ericksen number; in configurations with homeotropic anchoring, decreasing the Ericksen number increases the relative strength of the secondary flow (with respect to the mean flow velocity). Conversely, homogeneous (planar) anchoring reduces normal stresses, thus weakening the secondary flow strength. We show that as the fluid enters/leaves the bend, there is a perturbation in the transverse velocity caused by streamwise stress gradients. The perturbation magnitude depends on material properties and can be of different values at the bend exit and entrance. Finally, we show that the spatial development of the nematic field downstream of the bend exit is controlled by both material properties and the Ericksen number.