An exponential decay relationship between micro-flotation rate and back-calculated induction time for potential flow and mobile bubble surface

Flotation researchers have long hypothesised that particles have inherently different flotation rates under the same operating conditions because they have different induction times in the flotation cell. The relationship between flotation rate constant and induction time, however, has yet to be explored. Here we analysed the relationship between micro-flotation rate and back-calculated induction time for galena and sphalerite particles. The floatability of the particles was controlled by depression with potassium chromate (galena) and activation with copper sulphate (sphalerite). The bubble rise velocity vs. size in the micro-flotation experiments was determined by high speed video microscopy and followed the prediction for bubbles with the fully mobile air–water interface. Therefore, the theoretical analysis of the micro-flotation results was carried out, based on the potential flow model for water flow around a mobile bubble surface. The relationship between micro-flotation rate constant and back-calculated induction time was found to rapidly decay exponentially. In this model, flotation rate constant is highly sensitive to induction time. For example, a doubling or tripling of induction time results in an order-of-magnitude decrease in flotation rate constant.

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► Flotation rate determined for galena and sphalerite using a micro-flotation cell.
► Mineral floatability controlled by depression and activation.
► Fully mobile bubble surface confirmed by bubble rise velocity vs. size.
► Micro-flotation results analysed using the models with a mobile bubble surface.
► Micro-flotation rate constant vs. calculated induction time decayed rapidly exponentially.