Settling of spherical particles in the transitional regime

Abstract

The settling process and wall impact of large spherical particles in a stagnant, highly viscous fluid has been observed by means of high-speed shadow imaging. The particles included in this study vary in size and material properties: steel, polytetrafluorethylen (PTFE), polyoxymethylen (POM), or rubber. The corresponding terminal Reynolds numbers range from 333 to 4012, covering in principle the transitional and Newton regime for drag forces. However, most particles do not reach the terminal velocity before colliding with the impact object. Therefore, the main focus of this study is set on particle settling and collision in the transitional regime. For collision studies, the Stokes number just before impact is also relevant, and lies in the range 50<St<2250. The settling curves obtained experimentally (characterized by vertical position and vertical velocity component) are compared with numerical and analytical solutions. The latter has been derived on the basis of nominal terminal velocity and relaxation time for the Stokes and Newton regimes. The numerical model takes into account the side walls and the corresponding correction of the drag coefficient.A deviation between experimental results and analytical solution was observed in all cases where the terminal Reynolds number is larger than 300 and smaller than 1100. It appears that, in this flow regime, the settling process of the spheres is already affected at a long distance from the impact object, leading to an early but significant deceleration. Moreover, a reduced settling velocity was observed along the whole trajectory for the PTFE particles with the lowest terminal Reynolds number. All these effects are captured in the numerical model and the corresponding results agree fairly well with the experiments. There is one exception, induced by particle rotation, which is not considered in the current model. In that case, it is not possible to correctly predict the settling process. All processed datasets are available via the Mendeley Data repository Hagemeier (2020).Two additional effects have been observed during this study. First, a bright region was detected around all PTFE spheres. It finally was found to be due to total light reflection around the sphere, but, to the best of our knowledge, this peculiarity has never been reported before. Being purely optical, this does not effect the settling behavior for PTFE. On the other hand, partial absorption of liquid at the particle surface was observed for rubber, leading to a reduced sedimentation velocity. This property, already documented for homogeneous porous particles, is found here for a rubber particle with almost impermeable core.