**3. Conclusions**

414 Radioisotopes – Applications in Physical Sciences

Non-floatable Floatable

> Floatable Model

<sup>0</sup> <sup>500</sup> <sup>1000</sup> <sup>1500</sup> <sup>0</sup>

Time, s

Also, the function must be bounded by physical limits (e.g. the fraction of floatable mineral at zero rate constant must be zero). From these results the gamma model structure was selected for the plant flotation rate. Using the methodology to estimate the Gamma function parameters of the floatability distribution, the model fit shown in Fig. 28 was obtained.

<sup>0</sup> <sup>500</sup> <sup>1000</sup> <sup>1500</sup> <sup>0</sup>

Time, s

Plant results from two industrial cell operations showed that the flotation rate, predicted by the Gamma model, follow a rather normal distribution. The same result was observed in laboratory batch tests. The methodology has the advantage that allows the estimation of the flotation rate distribution of a single industrial cell under continuous operation. This was performed by generating a transient response, by means of floatable and non-floatable

Fig. 28. Model fit of floatable tracer concentration (Yianatos et al., 2010c).

Fig. 27. Normalized mineral tracer concentration (Yianatos et al., 2010c).

2

2

4

Normalized C(t), s-1

6

8

x 10-3

4

Normalized C(t), s-1

6

8

x 10-3

The use of radioisotopes has proven to be a powerful tool to study the hydrodynamic behaviour of large flotation machines. Mean residence time in pulp and froth zones were evaluated from RTD measurements for liquid, solids and gas radioactive tracers. Relevant parameters such as mixing regime, mixing time, flow distribution in parallel flotation banks, gangue and gas entrainment, particles segregation, have been evaluated using non-invasive sensors for radiation detection without disturbing the flotation operation. This information is fundamental for improving flotation machines operation, control and optimization.
