Mixing of Matter by a Falling Spherical Particle in a Still Liquid

The mixing of liquid mass caused by a spherical solid particle falling in a still liquid in a pipe was investigated by visualization and noninvasive concentration measurement using a photochromic dye. A spherical particle with diameter of 4.76 mm was dropped in a kerosene-paraffin mixture liquid with a photochromic dye. The photochromic dye was activated by an ultraviolet light and was subjected to the mixing by the particle wake. The falling velocity of particle was changed by using 8 different densities of particle. The effect of the particle Reynolds number on the mixing was investigated for the Reynolds number range from 10 to 2490. The effect of liquid viscosity on the mixing time was also investigated using two liquids having different viscosity. The visualized dye patterns indicated the mixing process depended strongly on the particle Reynolds number. For the Reynolds numbers higher than 300, the particle shed the vortices behind the particle and the dye was mixed isotropically by large-scale vortices. For the Reynolds numbers lower than 300, the dye was drawn straightly by a laminar wake of the particle. The concentration of the mixed dye was measured using the photochromic concentration measuring (PCM) technique to discuss the mass mixing quantitatively. The turbulent diffusion coefficient (TDC) was evaluated for the cases the dye was mixed by the vortices. It was found that the evaluated TDCs showed strong time-dependency, which was attributed to the change in scale and whirling velocity of wake vortices. The maximum TDC depended on the falling velocity regardless of the fluid viscosity. The mixing time depended strongly on the liquid viscosity. The mixing time of the TDC was suggested to be governed by the viscous decay time and expanding time of vortices in the pipe. The amount of dye drift was evaluated for the cases the particle wake was laminar. It was found that the dye drift increased sharply just after the particle passing and then saturated. The final dye drift increased gradually with increasing Reynolds number.