**8.3. Electrostatic separation**

Almost all minerals show some degree of conductivity. The electronic separation process uses the difference in electrical conductivity or surface charge of the mineral species of interest. The electrostatic separation process is generally confined to recovering valuable heavy minerals from beach-sand deposits. However, the growing interest in plastic and meta recycling has opened up new applications in secondary materials recovery [15].

When particles come under the influence of electrical field, depending on their conductivity, they accumulate charge that depends directly on the maximum achievable charge density on the particle surface. These charged particles can be separated by differential attraction or repulsion. Therefore, the first important step in electrostatic separation is to impose an electrostatic charge onto particles. Three main types of charging mechanism are the contact electrification or triboelectrification, the conductive induction and the ion bombardment (**Fig. 5**). Once the particles are charged, the separation can be achieved by the equipment with various electrode configurations [13],[15].

**Fig. 5.** Representative methods of electrostatic separation: contact charge (a), ion attachment (b) and induced charge (c) [13].

In the combination with attrition, desliming and gravity separation, the electrostatic separa‐ tion technique is successful in the beneficiation of phosphate ores by removing silica and/or carbonates, mostly on laboratory scale. However, low capacity of electrostatic separators limits their use in large-scale production. This technique is used to concentrate the phosphate ores of different types [1].

Effective beneficiation can be achieved by various processes depending on the liberation size of phosphate and gangue minerals and other ore specifications. Different processes like screening, scrubbing, heavy media separation, washing, roasting, calcinations, leaching and flotation may be used. For example, crushing and screening are used to remove coarse hard siliceous material, and attrition scrubbing and desliming are used to remove clayey fine fractions. If silica is the main gangue material, flotation is the conventional mineral process‐ ing technique used. Igneous-type ores are also amenable to flotation, which is the best

Almost all minerals show some degree of conductivity. The electronic separation process uses the difference in electrical conductivity or surface charge of the mineral species of interest. The electrostatic separation process is generally confined to recovering valuable heavy minerals from beach-sand deposits. However, the growing interest in plastic and meta recycling has

When particles come under the influence of electrical field, depending on their conductivity, they accumulate charge that depends directly on the maximum achievable charge density on the particle surface. These charged particles can be separated by differential attraction or repulsion. Therefore, the first important step in electrostatic separation is to impose an electrostatic charge onto particles. Three main types of charging mechanism are the contact electrification or triboelectrification, the conductive induction and the ion bombardment (**Fig. 5**). Once the particles are charged, the separation can be achieved by the equipment with

**Fig. 5.** Representative methods of electrostatic separation: contact charge (a), ion attachment (b) and induced charge (c)

approach for the processing of this type of phosphate ore [16].

390 Apatites and their Synthetic Analogues - Synthesis, Structure, Properties and Applications

opened up new applications in secondary materials recovery [15].

**8.3. Electrostatic separation**

various electrode configurations [13],[15].

[13].

**Fig. 6.** Particle charging mechanism: the particle charged positively has lower work function and the particle charged negatively has higher work function (a) [1] and the illustration of the separator chamber (b) [17].

The triboelectrification is a type of electrostatic separation in which two nonconductive mineral species acquire opposite charges by contact with each other. The particle charging process is the critical step for the triboelectrostatic separation since the separation efficiency is a function of the difference in charge polarity and the magnitude of different particles.3 Oppositely charged particles can be separated under the influence of electric fields. This process uses the difference in the electronic surface structure of the particles involved. A good example is the strong negative surface charge the silica acquires when it touches carbonates and phos‐ phates. The surface phenomenon that comes into play is the work function, which may be defined as the energy required to remove electrons from any surface (**Fig. 6**(**a**)). The work function is defined as the minimum energy that must be supplied to extract an electron from a solid. The particle that is charged positively after particle-particle charging has lower work function than the particle that is charged negatively [15],[17].

The particle residence time, i.e. the time for the particle traveling through the separation chamber (**Fig. 6**(**b**)), is controlled by the particle vertical motion. However, the horizontal particle motion (*y*) is controlled by electric field deflection. The relation governing the horizontal displacement (*x*) of moving particle is [17]:

$$\frac{\mathbf{d}^2 \overline{\mathbf{x}}}{\mathbf{d}t^2} = \overline{\mathbf{E}} \frac{\mathbf{q}}{\mathbf{m}} \tag{1}$$

<sup>3</sup> The charge density achieved with conventional pneumatic chargers (including tubing charger, cyclone, honeycomb, static mixer, etc.) and belt charger is about 5 – 8·10−6 C/m2 . Since the theoretical limit for the charge is 2.63·10−5 C/m2 , clearly, there is a huge potential in improving the charging efficiency [17].

where *m* is the mass of particle, *x* is the horizontal displacement vector, *t* is the time, *E* is the electric field intensity and *q* is the charge of particle. The charge-to-mass ratio *q*/*m* is referred to as the particle specific charge. If the resistance of air with the viscosity *η* is also considered, the horizontal motion of moving spherical particle of radius *r* is given by the equation:

$$\frac{d^2\overline{\mathbf{x}}}{dt^2} + 6\pi \left. \frac{\eta}{m} r \frac{d\overline{\mathbf{x}}}{dt} \right| = \overline{E} \, \frac{q}{m} \tag{2}$$

From **Eq. 2**, the speed of the particle as a function of time can be derived:

$$\frac{d\overline{\mathbf{x}}}{dt} = \overline{E}\frac{q}{6\pi\eta r} \left[ 1 - \exp\left( -\frac{t}{m \;/\ \, 6\pi\eta r} \right) \right] \tag{3}$$

where *<sup>t</sup>* > > <sup>m</sup> <sup>6</sup>*πη*r or *t* → ∞. The terminal horizontal speed of particle is:

$$
\left(\frac{d\overline{x}}{dt}\right)\_{\text{horizontal}} = \overline{E}\,\frac{q}{6\pi\eta r}\tag{4}
$$

Under these conditions, the terminal horizontal speed is independent of the mass. However, since the time *t* is in the range of milliseconds, the mass does play an important role in determining the horizontal motion of the particle as well as the resultant trajectory that affects the separation performance [17].

The particle motion in the vertical direction is influenced by the gravitational force and gas drag force. The governing equation is [17]:

$$\frac{d^2\mathbf{y}}{dt^2} = 6\pi r \frac{\eta}{m} \frac{d\mathbf{y}}{dt} + \mathbf{g} \tag{5}$$

where *η* is the dynamic viscosity of gas and *g* is the gravitational acceleration. For the initial conditions of *t* = 0, *y*(0) = 0 and d*y*(0)/d*t* = *V*0, **Eq. 5** can be solved as follows:

$$\mathbf{y}\left(\mathbf{t}\right) = \frac{\left(\mathbf{g} + \mathbf{V}\_0 \mathbf{E}\right)\exp\left(\mathbf{B}\mathbf{t}\right) - \mathbf{B}\mathbf{g}\mathbf{t} - \mathbf{g} - \mathbf{V}\_0 \mathbf{B}}{\mathbf{B}^2} \tag{6}$$

where *B* = 6*πηt*/*m*. The particle trajectories can be obtained from **Eqs. 4** and **6**.

The tube-type separator has the pre-charging zone and the separation zone as the integral parts of the machine (**Fig. 7**(**a**)). The pre-charging zone, or the triboelectrification process, exploits the difference in the electronic appearance of the particles involved. The particles become

charged by the particle-particle contact, particle-wall contact or both. The particle-particle contact between different particles results in the transfer of electrons (charges) from the surface of one particle to the surface of the other one. After this transfer, one of the particles is positively charged and the other one possesses the negative charge. The separation zone consists of two vertical walls of rotating tubes, which oppose each other and which are electrified by oppo‐ site potential. As the charged particles enter the separation zone, they become attracted by oppositely charged electrodes. The separated products are collected at the base of separator. This separator removes very effectively silica from other nonconductive minerals, such as calcium carbonate, phosphate and talc [15].

where *m* is the mass of particle, *x* is the horizontal displacement vector, *t* is the time, *E* is the electric field intensity and *q* is the charge of particle. The charge-to-mass ratio *q*/*m* is referred to as the particle specific charge. If the resistance of air with the viscosity *η* is also considered, the horizontal motion of moving spherical particle of radius *r* is given by the equation:

(2)

<sup>2</sup> <sup>6</sup> *d x dx q r E dt m dt m* h + = p

1 exp <sup>6</sup> / 6 *dx q <sup>t</sup> <sup>E</sup> dt r m r*

<sup>6</sup>*πη*r or *t* → ∞. The terminal horizontal speed of particle is:

æ ö <sup>=</sup> ç ÷

*horizontal* 6 *dx <sup>q</sup> <sup>E</sup>*

Under these conditions, the terminal horizontal speed is independent of the mass. However, since the time *t* is in the range of milliseconds, the mass does play an important role in determining the horizontal motion of the particle as well as the resultant trajectory that affects

The particle motion in the vertical direction is influenced by the gravitational force and gas

where *η* is the dynamic viscosity of gas and *g* is the gravitational acceleration. For the initial

The tube-type separator has the pre-charging zone and the separation zone as the integral parts of the machine (**Fig. 7**(**a**)). The pre-charging zone, or the triboelectrification process, exploits the difference in the electronic appearance of the particles involved. The particles become

<sup>2</sup> <sup>6</sup> *d y dy r g dt m dt* h = + p

( ) ( ) () 0 0 2 g V E exp Bt Bgt g V B y t <sup>B</sup>

ph*r* ph

é ù æ ö = -- ê ú ç ÷ ë û è ø (3)

è ø (4)

(5)

<sup>+</sup> - -- <sup>=</sup> (6)

2

392 Apatites and their Synthetic Analogues - Synthesis, Structure, Properties and Applications

From **Eq. 2**, the speed of the particle as a function of time can be derived:

ph

*dt*

2

conditions of *t* = 0, *y*(0) = 0 and d*y*(0)/d*t* = *V*0, **Eq. 5** can be solved as follows:

where *B* = 6*πηt*/*m*. The particle trajectories can be obtained from **Eqs. 4** and **6**.

where *<sup>t</sup>* > > <sup>m</sup>

the separation performance [17].

drag force. The governing equation is [17]:

**Fig. 7.** Operating principle of electrostatic separator: (a) V-stat separator, (b) plate-type separator and (c) roll-type sepa‐ rator [15].

In the horizontal belt-type separator, fast-moving belts travel in opposite directions adjacent to suitably placed plate electrodes of the opposite polarity. The material is fed into a narrow gap between two parallel electrodes. The particles are swept upward by a moving open-mesh belt and conveyed in opposite directions, thus facilitating the particles' charging by contact with other particles. The electric field attracts the particles up or down depending on their charge. The moving belts transport the particles adjacent to each electrode towards opposite ends of the separator [15].
