Thin disks falling in air

Abstract

We experimentally investigate the settling of millimetre-sized thin disks in quiescent air. The range of physical parameters is chosen to be relevant to plate crystals settling in the atmosphere: the diameter-to-thickness aspect ratio is$\chi =25\unicode{x2013}60$, the Reynolds numbers based on the disk diameter and fall speed are$Re=O(10^2)$and the inertia ratio is$I^*=O(1)$. Thousands of trajectories are reconstructed for each disk type by planar high-speed imaging, using the method developed by Baker & Coletti (J. Fluid Mech., vol. 943, 2022, A27). Most disks either fall straight vertically with their maximum projected area normal to gravity or tumble while drifting laterally at an angle$<20^\circ$. Two of the three disk sizes considered exhibit bimodal behaviour, with both non-tumbling and tumbling modes occurring with significant probabilities, which stresses the need for a statistical characterization of the process. The smaller disks (1 mm in diameter,$Re=96$) have a stronger tendency to tumble than the larger disks (3 mm in diameter,$Re=360$), at odds with the diffused notion that$Re=100$is a threshold below which falling disks remain horizontal. Larger fall speeds (and, thus, smaller drag coefficients) are found with respect to existing correlations based on experiments in liquids, demonstrating the role of the density ratio in setting the vertical velocity. The data supports a simple scaling of the rotational frequency based on the equilibrium between drag and gravity, which remains to be tested in further studies where disk thickness and density ratio are varied.