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We numerically analyse the rotation of a neutrally buoyant spheroid in ashear flow at small shear Reynolds number. Using direct numerical stabilityanalysis of the coupled nonlinear particle-flow problem we compute the linearstability of the log-rolling orbit at small shear Reynolds number, ${\rmRe}_a$. As ${\rm Re}_a \to 0$ and as the box size of the system tends toinfinity we find good agreement between the numerical results and earlieranalytical predictions valid to linear order in ${\rm Re}_a$ for the case of anunbounded shear. The numerical stability analysis indicates that there aresubstantial finite-size corrections to the analytical results obtained for theunbounded system. We also compare the analytical results to results oflattice-Boltzmann simulations to analyse the stability of the tumbling orbit atshear Reynolds numbers of order unity. Theory for an unbounded system atinfinitesimal shear Reynolds number predicts a bifurcation of the tumblingorbit at aspect ratio $\lambda_{\rm c} \approx 0.137$ below which tumbling isstable (as well as log rolling). The simulation results show a bifurcation linein the $\lambda$-${\rm Re}_a$ plane that reaches $\lambda \approx0.1275$ at thesmallest shear Reynolds number (${\rm Re}_a=1$) at which we could simulate withthe lattice-Boltzmann code, in qualitative agreement with the analyticalresults.

Numerical analysis of the angular motion of a neutrally buoyant spheroid in shear flow at small Reynolds numbers