Transition to centrifuging granular flow in rotating tumblers: A modified Froude number

Centrifuging of granular material in a partially filled rotating circular tumbler occurs when particles are flung outward to form a ring of particles at the periphery of the tumbler rotating as a solid body. The critical rotation speed for centrifuging was studied experimentally in a quasi-two-dimensional tumbler as a function of particle diameter, tumbler fill fraction and interstitial fluid. A qualitative numerical study using the discrete element method was also conducted to obtain a better understanding of the impact of friction on the transition. Experimental results show that the critical rotational speed for dry systems is not affected by the particle diameter unless the fill fraction is above 75%, where endwall friction begins to play a significant role. The critical speed is proportional to (1 - φ) ^(-1/4), where φ represents the tumbler fill fraction. The angle of repose, which represents inter-particle friction, also affects the transition to centrifuging. Finally, the interstitial fluid, or rather the density difference between the particles and the interstitial fluid, affects the measured critical speed. Correction terms for the critical rotational speed are proposed to more accurately characterize the transition to centrifuging for granular flow in rotating tumblers, resulting in a modified Froude number.