Hydrodynamically-driven assembly of nanoparticles in an anisotropic media

Nanoparticle (NP) self-assembly in liquid crystals (LCs) depends on the elasticity of the material to form arrays with crystalline symmetry. These arrays can be tuned via the anchoring of the NP, and the orientation of the director field, effectively using the defects around the NP as sites for assembly. Additionally, confinement and hydrodynamic fields can also be used to control the assembly. Scenarios often consider one, two, or three NPs under various flow regimes and in moderate confinement. The simulations presented here use the Stark-Lubensky formalism, where the Landau-de Gennes free energy functional is coupled with the momentum balance through a Poisson-bracket formulation. To describe NP-LC suspensions, a transient three-dimensional Galerkin finite element framework was implemented to achieve a numerical solution. We show that, independent of NP anchoring, defects are displaced in the up-stream direction, ultimately forming a hedgehog defect. The assembly mechanism for a pair of NPs is modified in the large Ericksen regime, where the NPs show an unexpected non-monotonic tendency to aggregate. The modifications to the defect structure and the free energy landscape open a new avenue to the directed assembly of NPs immersed in LC under conditions far from equilibrium.