Particles settling in nematic liquid-crystal fluids: effects of cluster behaviour

We investigate the sedimentation of spherical particles in a periodic cubic domain filled with nematic liquid crystals. Direct numerical simulations were performed over a range of particle volume fractions (0.09 % ≤ ϕ ≤ 31.6 %) to examine the influence of the elastic constant ( K ), the rotational diffusion constant ( Γ ) and surface anchoring conditions on settling dynamics. Under weak inertial conditions, the mean settling velocity exhibits a non-monotonic dependence on volume fraction, in contrast to the monotonic decrease observed in Newtonian fluids. At intermediate volume fractions (0.45 % < ϕ ≤ 9.0 %), director distortions induced by surface anchoring generate long-range elastic interactions that promote particle aggregation. Voronoi analysis confirms that clustering enhances settling through both accelerated aggregates and the entrainment of neighbouring particles. In contrast, at low volume fractions ( ϕ ≤ 0.45 %), elastic interactions are insufficient to sustain aggregation, and settling is not enhanced. At high volume fractions ( ϕ > 9.0 %), defect networks merge and occupy the interparticle voids, restricting motion and reducing the settling velocity. Anchoring conditions strongly affect aggregation: planar anchoring favours short chains or side-by-side structures via boojum defects, while homeotropic anchoring stabilises larger aggregates through Saturn-ring connections, yielding higher settling rates. Reducing the rotational diffusion constant promotes long-chain aggregation and accelerates settling, whereas moderate variations in the elastic constant have little effect on this process. These results demonstrate that defect-mediated interactions play a decisive role in the collective sedimentation dynamics of particles in nematic liquid-crystal fluids.