Flow of transversely isotropic fluid in curved pipes

We study a fully developed creeping flow of nematic liquid crystals in curved pipe with circular cross-section. A special limit zero Deborah number and an infinite Ericksen is considered, so the orientation director are described by transversely isotropic fluid (TIF) model. Analytical solutions obtained expanding governing equation small curvature ?, defined as ratio radius to bend. show that presence bend alters microstructure axial velocity profile. The additional non-Newtonian stress generates secondary flow, which consists two counter-rotating vortices. Two mechanisms responsible for motion identified (1) combination normal stresses (2) asymmetry distribution. relative strength direction those framework model quantified through parameter q. For all considered this paper, dominates, thus controlling opposite induced inertia. Finally, we quantify contribution viscous dissipation shearing increases losses power consumption without contributing throughput.