Mass hydrocyclones

Theoretical representation of the behaviour of a hydrocyclone requires adequate analysis of three distinct physical phenomenon taking place in these devices, viz. the understanding of fluid flow, its interactions with the dispersed solid phase and the quantification of shear induced attrition of crystals. Simplified analytical solutions to conservation of mass and momentum equations derived from the Navier-Stokes equation can be used to quantify fluid flow in the hydrocyclone. For dilute slurries, once bulk flow has been quantified in terms of spatial components of velocity, crystal motion can then be traced by balancing forces on the crystals themselves to map out their trajectories. The trajectories for different sizes can then be used to develop a separation efficiency curve, which quantifies performance of the vessel (Bloor and Ingham, 1987). In principle, population balances can be included for crystal attrition in the above description for developing a thorough mathematical model. 

Definitions. The performance of a hydrocyclone is generally characterised by means of a grade efficiency or Tromp-curve which is the fractional mass recovery expressed as a function of particle size. 

In the grinding operation of Fig. 13.3, a ball mill is in closed circuit with a hydrocyclone classifier. The mass flow rates of the classifier feed, oversize, and undersize are denoted by the symbols A, O,... 

During the last few years, interest has increased in reactors in which high mass transfer is realized by means of liquid jet or injection devices providing gas or liquid entrainment jet reactors (N3, B30), hydrocyclones (Bll), venturis (S16, J2), and other high-velocity gas-liquid contactors. 

Gravity and centrifugal sedimentation can be combined for the same sample in order to directly determine Stokes diameter for a wide range of particle sizes. In such a way conversion are avoided and a mass distributions, applicable to processes where gravimetric efficiencies are relevant, can be properly derived. Ortega-Rivas and Svarovsky (1994) determined particle sizes distributions of fines powders using a combined Andreasen Pipette-pipette centrifuge method. They derive relations useful to model hydrocyclone separations, which were later employed to describe apple juice clarification. 

If hydrocyclones are to be used to produce thick underflows, the total mass recovery of the feed solids has to be sacrificed because throttling the underflow orifice inevitably leads to some loss of the solids to the overflow. A hydrocyclone as a single unit cannot therefore be used for both clarification and thickening at the same time. Typically the underflow concentrations that can be achieved with hydrocyclones are up to 50% by volume or more. In this they compare favourably with gravity thickeners and hydrocyclone systems are often used to replace the much larger and more expensive gravity thickeners. 

Figure 3.18 shows the particle size distribution, by mass, of the solids used in the tests (chalk), as obtained with the Ladal Pipette Centrifuge and the Andreasen Pipette Method. As can be seen from the log-probability plot, the distribution is very nearly log-normal and thus suitable for testing the performance of the hydrocyclone. Furthermore, the medium size of the chalk (3.9 microns) is within the range of cut sizes expected from the hydrocyclone (2 to 4 microns) which is a requirement for effective separator testing. 

In the case of really small cyclones (e.g. 10 mm diameter units), these are sometimes cast into disks and such disks are stacked into columns. Such systems resemble other chemical engineering columns for mass transfer or cartridge systems for filtration. One problem common to all compact multiple hydrocyclone systems is with the operator s inability to see any blockages. He or she must then diagnose any such difficulties from other operating performance such as an increase in pressure drop. Having detected a blockage problem, the only remedy available is to replace the unit or the whole column and clean it off-line. 

The rest of this chapter, however, is concerned with continuous counter-current washing. The separators used may be sedimenting centrifuges, gravity thickeners or filters but the preferred choice is often hydrocyclones. The inherent advantages of hydrocyclones are compactness, small hold-up of liquid, high shear forces and turbulence in the flow, the latter two of which improve mass transfer and dispersion. 

Figure 15.18 gives a summary of one experiment from this study that demonstrates well the capability of the arrangement in this application. The required near-complete separation of solids in the 44 mm hydrocyclones used was not a problem and therefore no additional separator on system overflow was needed in this case. Furthermore, all three stages could be set to have the same split ratios Rf of 26% (underflow to feed). The washing efficiency was about 97% but intermediate sumps had to be provided for mass transfer from within the porous solids to take place. 

One of the most complicated systems for mass balance calculations is a multistage countercurrent washing system. Figure 16.27 shows an example of a nine-stage system, with an additional separator on the system overflow as is used to minimize product losses in washing of wheat starch. The most suitable separator in this specific application is a 10 mm hydrocyclone operated at a... 

The modification of hydrodynamic aspects is exploited in the falling-film cell [12], where the electrolyte flows as a thin fllm in the channel between an inclined plane plate and a sheet of expanded metal which work as electrodes. Other proposal is to include turbulence promoters in the interelectrode gap in conventional parallel plate electrochemical reactors [13-16], or the use of expanded metal electrodes immersed in a fluidized bed of small glass beads, called Qiemelec cell [17]. Likewise, the Metelec cell [18] incorporates a cylindrical foil cathode concentric arranged around an inner anode, with a helical turbulent electrolyte flow between the electrodes. The electrochemical hydrocyclone cell [19] makes use of the good mass-transfer conditions due to the helical downward accelerated flow in a modified conventional hydrocyclone. 

Because an overall mass balance must apply, the total efficiency Ej can be determined by measuring any two of the three streams (feed, underflow, and overflow) for total solid amount, assuming no accumulation of solids in the hydrocyclone. 

Consider a single-entry separator used either for separating solid particles from a fluid or separating solid particles having sizes above a particular value from those having sizes below the particular value. Let u/Jy. be the total mass flow rate of solids in the feed fluid whose total volumetric flow rate is Qf. In such a separator, there are only two product streams, the overflow (/ = 1) and the underflow (/ = 2). The total mass flow rate of solids in the overflow and the underflow are, respectively, and u/Jj- The overflow is identified with essentially the carrier fluid and the finer particles, whereas the underflow is assumed to have most of the coarser particles and small amounts of carrier fluid. Figure 2.4.1 illustrates this for a hydrocyclone (Talbot, 1980). Sizes of various natural and industrial particles are shown in Figure 2.4.2. 

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