We report on the mobility and orientation of finite-size, neutrally buoyant prolate ellipsoids (of aspect ratio $Lambda=4$) in Taylor-Couette flow, using interface resolved numerical simulations. The setup consists of a particle-laden flow in between a rotating inner and a stationary outer cylinder. We simulate two particle sizes $ell/d=0.1$ and $ell/d=0.2$, $ell$ denoting the particle major axis and $d$ the gap-width between the cylinders. The volume fractions are $0.01%$ and $0.07%$, respectively. The particles, which are initially randomly positioned, ultimately display characteristic spatial distributions which can be categorised into four modes. Modes $(i)$ to $(iii)$ are observed in the Taylor vortex flow regime, while mode ($iv$) encompasses both the wavy vortex, and turbulent Taylor vortex flow regimes. Mode $(i)$ corresponds to stable orbits away from the vortex cores. Remarkably, in a narrow $textit{Ta}$ range, particles get trapped in the Taylor vortex cores (mode ($ii$)). Mode $(iii)$ is the transition when both modes $(i)$ and $(ii)$ are observed. For mode $(iv)$, particles distribute throughout the domain due to flow instabilities. All four modes show characteristic orientational statistics. We find the particle clustering for mode ($ii$) to be size-dependent, with two main observations. Firstly, particle agglomeration at the core is much higher for $ell/d=0.2$ compared to $ell/d=0.1$. Secondly, the $textit{Ta}$ range for which clustering is observed depends on the particle size. For this mode $(ii)$ we observe particles to align strongly with the local cylinder tangent. The most pronounced particle alignment is observed for $ell/d=0.2$ around $textit{Ta}=4.2times10^5$. This observation is found to closely correspond to a minimum of axial vorticity at the Taylor vortex core ($textit{Ta}=6times10^5$) and we explain why.
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