Mixing

Columns are commonly sized with a dispersion method which uses the Peclet number, a dimension-less criterion, to characterize mixing. It is assumed that an axial dispersion model adequately reflects flow structure in the collection zone. It is also possible to use a tanks-in-series flow model. The Peclet number reflects the ratio between the downward path of particle and the average length of its stochastic drift due to mixing (diffusion). It is equal to UL/D, where U is the mean velocity of the phase of interest (for particles it is the sum of downward liquid velocity and a hindered settling velocity), L is the characteristic length scale for the apparatus (collection zone height of the column), and D is the turbulent dispersion (diffusion) coefficient. The latter can be determined by a tracer technique or by using one of several approximation formulae. D ranges from 0, for perfectly mixed systems, to infinity, for plug flow. The following variables have an effect on the Peclet number: bubble size and number of bubbles (which are dependent on gas rate and surface tension), slurry rate, particle settling velocity, collection zone height and diameter. At a constant collection zone volume, a taller column is better from a flow structure perspective as less mixing is induced. Peclet number can be estimated using one of the experimental relationships, or from particle residence time distribution (RTD) similar to that in chemical reactors or separation equipment. RTD can be directly measured using a tracer method. Dispersion of the RTD can be used to calculate turbulent diffusion D and other column flow structure criteria.

The absence of an agitator limits the formation of large scale flow loops unless the column is operated in a high air rate, churn-turbulent flow or the feed distribution of either air or slurry is not even. Low mixing intensity and lack of circulation contours cause particle residence times to be highly dependent on the particle settling velocity. Reduced mixing leads to lowering of local upward flow intensities which minimizes particle entrainment to the froth. Thus, at a constant collection zone volume (slurry retention time), its increased height leads to lower mixing intensity and improved (due to this) metallurgical results up to the point when restrictions in carrying capacity limits concentrate (float product) yield. Also, higher superficial slurry velocity reduces negative influence of mixing and slime entrainment intensity.

Careful design and positioning of any baffles (horizontal or vertical), the feed system, and any internal piping that may be needed minimize local turbulence. The feed pipe must be located high enough in the column to maximize the collection zone length but also low enough to limit turbulence at the slurry-froth interface.

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Solar Panel Basics

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