Limit cycles for the motion of finite-size particles in axisymmetric thermocapillary flows in liquid bridges

The motion of a small spherical particle of finite size in an axisymmetric thermocapillary liquid bridge is investigated numerically and experimentally. Due to the crowding of streamlines towards the free surface and the recirculating nature of the flow, advected particles visit the free surface repeatedly. The balance between centrifugal inertia and the strong short-range repulsive forces a particle experiences near the free surface leads to an attracting limit cycle for the particle motion. The existence of this limit cycle is established experimentally. It is shown that limit cycles obtained numerically by one-way-coupled simulations based on the Maxey–Riley equation and a particle–surface interaction model compare favorably with the experimental results if the thickness of the lubrication gap between the free surface and the surface of the particle is properly taken into account.