The role of particle inertia and particle-free-surface collisions in periodic free-surface flows is evaluated in the framework of an analytical flow model for a thermocapillary liquid bridge. Inertia and particle-free-surface collisions lead to particle accumulation, but on different time scales, and can lead to different accumulation patterns. A comparison with experimental results provides strong evidence that the experimentally observed accumulation patterns are due to particle-free-surface collisions.