  We simulate gravity driven dynamics of partially wetting droplets moving
along a fibre using the lattice Boltzmann method. For the so-called clamshell
morphology, we find three possible dynamic regimes upon varying the droplet
Bond number and the fibre radius: compact droplet, droplet breakup and droplet
oscillation. For small Bond numbers, in the compact droplet regime, the droplet
reaches a steady state and its velocity scales linearly with the driving body
force. A similar scaling law can also be observed for the barrel morphology.
For higher Bond numbers, in the droplet breakup regime, satellite droplets are
formed trailing the initial moving droplet. We find such droplet satellite
formation is easier with increasing fibre curvature (smaller fibre radius).
Finally, in the droplet oscillation regime, favoured in the mid-range of fibre
radius, the droplet shape periodically extends and contracts along the fibre.
