Minerals Ealgl~ering, Vol. 2, No. 2, pp. 193-205, 1989 0892-6875/89 $3.00 + 0.00 Printed in Great Britain © 1989 Pergamon Press plc

THE THEORY OF ELECTROSTATIC SEPARATIONS: A REVIEW PART II. PARTICLE CHARGING

E.G. KELLY % and D.J. Spottiswood §

% Dept of Chemical & Materials Engineering, University of Auckland, Auckland, New Zealand

Metallurgical Engineering Dept, Colorado School of Mines Golden, CO, U.S.A.

(Received 1 September 1988)

ABSTRACT

This paper, the second in a series on the theory of electrostatic separations, briefly reviews the methods and equipment available for the measurement of electric fields, electric charges, contact-charge accumulation, and conductivity. Particle charging by the three major processes relevant to commercial separators (corona, or ion bombardment, induction, and tribocharging) is then discussed.

I. INTRODUCTION

In any separator, the separation is brought about by suspending the particles in a medium and subjecting them to a separating force that acts on some particle property. In the case of electrostatic separations, the primary separating force is given by

F -- Q.E (I)

where F is the vectorial sum of all the forces, Q is the total charge, and E is the electric field intensity at a point P in space. While in reality secondary forces must also be considered, it follows that information about the two parameters E (electric field strength) and Q (electric charge) are central to an understanding of electrostatic separations. However, whether or not a particle has a charge as it enters an electric field will depend markedly on its conductivity, and thus knowledge of the relative conductivity of the particles is also important. The following is a brief review of the techniques available for electrostatic measurements. More detailed reviews have been given by Secker and Chubb [I], and Cross [2].

II. PROPERTY MEASUREMENTS

(I) Measurement of Electric Fields.

Electric fields at a surface or in a space can be measured by appropriate electrometers, of which there are two main types; capacitive probes [3,4] and field mills [5,6]. These instruments are based on the principle that when a grounded, electrically conductive, "sensing" surface is exposed to an electric field, an electric field is induced on it. The magnitude of the charge is proportional to the local field intensity and to the total area exposed to the field.

A number of commercial instruments are based on the electric field mill. In these, the electric field falling on the sensing surface is interrupted by a rotating shaped sector. The periodic voltage generated is amplified by an AC amplifier, the rectified output of which is displayed on a meter. The advantage of this system is that the sensitivity can be quite high, and the charge sign can be determined. The main disadvantage is that the physical size of the probe limits the resolution obtainable, and the response characteristics mean that it is best suited to static or relatively slowly varying fields. There are a number of versions of capacitive probes. While differing in their treatment of the signal collected, they all operate on similar principles

193

194 E.G. KELLY and D. J. SPOTTISWOOD

which involve determination of a number of capacitances and voltages in the system; primarily those across the grounded sample, the sample to probe air gap, and those of the instrument itself. Negative-feedback electrometers use negative feedback to greatly increase the input resistance of the measuring circuit amplifier. This virtually puts the probe at ground potential, and allows the accurate definition of the area that the probe actually sees. The system is also simple and compact, with no moving parts. Its principle disadvantage is that accidental charging of the probe may lead to false readings. Singh and Hearn have described an electrostatic probe that is capable of detecting the charge on individual particles as small as 50 microns. It can also detect bipolar charging of particles [7].

The positive-feedback electrometer has a vibrating device in the probe head between the sample and the sensing surface. The instrument can be made very sensitive with a fine spatial resolution.

In the presence of space charges such as corona, more sophisticated biased probes must be used [8,9], although under some conditions, the field mill principle can still be used, in which case it is used in a form known as the electrostatic flux meter [10,11].

(2) Measurement of Electric Charges.

While in principle the above capacitive probes can be used to measure electric charges at surfaces as well as electric fields, they are not suitable for the irregular geometry of real particles. In such a situation, perhaps the simpliest and the most accurate method for measuring electric charge is with a Faraday pail. Its operation is based on Gauss' Law, which states that

Q = $ (2)

where ~ is the electric flux (Coulomb).

Thus, when a charged particle is placed in the pail, the flux from the charge on the particle produces an equal charge on the outside of the pail that can be measured by an electrometer. The outside of the pail must be shielded to ensure that no stray charges are picked up, and methods of calibrating the pail have been described [12].

The "separation tower" has been suggested as a suitable method of measuring the charge-to-mass ratio of small particles [13]. The method involves tribocharging of the particles in a fluidized bed, from which they discharge into a tower where they fall freely between two electrodes. The particles are collected at the bottom in individually shielded Faraday trays, and their placement allows the charge-to-mass ratio to be determined. The major limitation of the method is that it measures tribocharging, and thus gives little information about the charging that will occur by other mechanisms.

(3) Measurement of Contact-Charge Accumulation.

In an effort to quantify tribocharging, a number of studies have measured contact-charge accumulation [14,15]. Many of these studies appear to give conflicting results, but this can be attributed to inadequate consideration of the differing experimental conditions (particularly their deviation from equilibrium), and the difficulty in determining the truly relevant properties of the material being studied. One of the more successful studies used a spherical metal contactor that could be touched, in a controlled and reproducable way, to an insulator specimen. Charging and backflow time constants were determined, and it was shown that contact-charge accumulation on insulators is due to slight electrical conductivity [16].

(4) Measurement of Conductivity.

Meaningful measurement of conductivity is very difficult because over and above the problems of dealing with an irregular particle, the significance of inherent and induced "contamination" clearly indicate that most reported data on particles will be very specific to the given experiments. Cohen's review on the conductivity of alumina is a good illustration of these problems [17]. Lawver and Wright [18] described a concentric cell for measuring the conductivity of a bulk of granular material. They considered this type of cell appropriate for the determination of conductivity relevant to high tension separation because particle/particle contact would be significant in

The theory of electrostatic separations 195

such a separator. Mugeraya and Prabhakar investigated the effect of applied voltage, compaction, moisture, and temperature on the conductivity of beach sand minerals [19].

Other workers have concentrated on measuring the conductivity across a single grain. In one instance, a number of mineral grains were rested between two parallel conducting rods [20], while the U.S. Bureau of Mines used one particle at a time [21].

Although there is now a better understanding of the effect of semiconductor characteristics in electrostatic separations, most phenomena have so far been studied by empirical methods. It is possible that more fundamental studies using the techniques developed for semiconductors [22] will be of benefit. Carta et al [23] have described how the work function, Fermi level VF, forbidden gap Vg, and charge carrier concentrations (n and p) can be determined.

III. MECHANISMS OF PARTICLE CHARGING

While there are a number of ways of charging particles [24], only three are serious contenders for charging particles in commercial electrostatic separations; corona or ion bombardment charging, induction charging, and tribocharging. These are illustrated in Figure I, and will be discussed in this section. Other mechanisms, such as photoelectric [25] and pyroelectric [26] charging have been shown to be to exploitable, but have had little commercial success.

(I) Corona Charging.

The highest particle charge levels in electrostatic separation are achieved by ion bombardment (corona charging), the basic concepts of which are illustrated in Figure la. Essentially, the method involves the charging of particles as they pass between two electrodes. Due to the high voltage used, the gas between the electrodes is ionized, and these ions charge the particles by bombardment.

(a) Coronas. Under normal conditions gases are non-conductors. However, if the potential between two electrodes is raised to a sufficient level, the ionization and conductivity of the gas increases greatly as a corona discharge occurs. Further increase of the voltage eventually leads to an uncontrollable current flow due to spark-over or arcing (the actual spectrum of processes is somewhat more complex [27]). Figure 2 shows the typical form of the corona voltage-current relationship.

Practical systems involve asymmetrical electric fields because the electrodes are of significantly different size and shape; for example, a wire and a cylinder (drum). In these cases the corona between the electrodes consists of two parts; a relatively narrow "glow" region at the small electrode (because it has the steepest field gradient), and a "dark" region over the remaining space to the large electrode.

The nature of the corona differs, depending on whether the wire electrode is negative or positive. A positive corona has a gentle glow-like color, is relatively steady and uniform near the wire electrode, and can be produced in any gaseous medium. A negative corona concentrates as tufts of glowing gas spaced at intervals along the wire, but is possible only with gases such as oxygen that provide electron attachment. Both positive and negative corona discharges each have their applications, although the negative corona is preferred because it has a higher spark-over voltage that allows a more intense corona to be produced in air.

The glow region is where gas ionization occurs, while the dark region contains neutral molecules plus a small fraction of anions and electrons moving, respectively, to the negative and positive electrodes. Typically, particles to be separated are charged in the dark region: the glow region is normally so narrow that its only function is to generate electrons. While higher charge densities on particles can be achieved in the glow region because of the higher field strength there, charging is erratic and thus less efficient [28].

In practice, it is desirable to maximize the corona current, without suffering spark breakdown. Calculation of the current-voltage characteristics is

196 E.G. KELLY and D.J. SPWTISW~~D

complicated for all but the simplest of geometries 1291, although techniques for more complex geometries have been described 130,311.

0 - Electrode l

a- ++++++ 0

0 o++++++

++ + + +++ +c + N QQ _ _ _ _ _ _

T

@@

+ + + + + +

_ _ _ _ - -

++ ++ + c+

8 _=- _ - --

+ + + + + +

0 a+++++ + + + + + _ -

7Y + + Chmging Charged

C - Conductor N-Non-conductor

F6 _+- 6 +c+ +++ - *- Iy+ -D _ _ - -

-=_ +-

+ + + + + +

+ 0 +c+ + + 0 C- _ - + + +v+ + +

F.

F. _ _ - - - 3ii-y 0 + + + +F. +

++++t+ + + 0 - - -F- - - .

Fig.1 Particle charging processes: (a) Corona charging. (b) & (c) Induction charging. (d) Particle/particle and (e) particle/surface tribocharging.

The theory of electrostatic separations 197

i i i i I I

Kilovolfs

Fig.2 Typical form of the corona voltage-current relationship.

Lama and Gallo [27] have presented an empirical equation for the maximum prespark corona current for a needle-to-plane corona:

Ima x = Vs(V s - Vt)S-2 (3)

where I is the maximum presparking current, V s is the sparking voltage, S is the ~dle to plane electrode spacing, and V t is the corona threshold voltage. Thus, increasing the electrode spacing and the voltage increases the allowable current. With wire-to-plane coronas, the maximum current increases with wire-to-plane distance, and is relatively independent of the wire diameter. Other empirical data has been reviewed by Fraas [32].

High concentrations of dust particles can, by themselves having a charge, lower the total space charge between electrodes. This lowers the field and thus the charging of the particles of interest [29]. The phenomena is more significant in electrostatic precipitators, but could be a problem with electrostatic separators if there is a high proportion of dust in the air, or in the particle stream.

Humidity is recognized as having a significant affect on the corona. The effect is difficult to study. Not only does the presence of water affect the ionization processes in opposing ways [33], the number and density of water droplets in the air is dependent on the quantity, size and nature of "dust" nucleation sites [34]. Abdel-Salam showed that for positive wire-to-plane coronas the effects of humidity could be calculated under certain conditions. With thin wire electrodes, the corona inception voltage decreases with increasing humidity, while at high voltages, the corona current decreases as the relative humidity increases [33].

(b) Particle Charging. The charge acquired by a particle depends on its size, its dielectric constant, the field intensity, and the concentration of ions in the gaseous medium. Charging in a corona is usually considered to be due to two main processes: ion bombardment (or field) charging and diffusion charging, the latter becoming insignificant with particles greater than I micron in diameter [35].

Ion bombardment results from bombardment of the particles by ions moving under the influence of the applied electric field. If a spherical particle with a uniformly distributed free surface charge Q is placed in a uniform electric field E in a gas, the free and induced charge on the particle distort the original°field, and impart to it a radial component. If an ion is attracted to the particle and approaches from an angle 8 for which the radial force is negative, it will be captured (Figure 3) and will add to the charge on the particle. These additional charges change the field around the particle (Figure 3b), eventually stopping charging altogether. The maximum free charge Qmax on the surface of the spherical particle is [29,36,37]:

Qmax = ~eoKed2Eo (4)

198 E.G. KELLY and D. J. SPOTrXSWOOD

where

K e = 2[ er,p er~p +- 21 ] + I (5)

and e is the dielectric constant of the particl~2 For a non-conducting particel~, K tends to unity, e for air is 8.85 x 10- F/m, and E for air is about 3 x ~0 -b V/m, with t~e result that the maximum charg~ d~nsi~ o (Qmax/area) possible on a non-conducting particle is about 2.66 x 10 -v C/m .

:::::::::::::::::::::::::::::::::::::::::::::::::::: ::::::::::::::::::::::::::::::::::::::::::::::::: :~ :, :,:

~iiiii~iii~!~i~i~i~iiiiiiii ~ililiiiiiiiiiiiii:iiiiii

® ® Fig.3 The electric field near an uncharged (a) and a partly charged (b) particle, showing how the region of charge capture (unshaded) decreases

as the particle charges.

The particle charge as a function of time t is usually expressed by

Q = Qmax (6) t + T

where T is the particle-charging time constant, given by:

4 e o T = (7)

ciqi6

where c~ is the ion con.~ntration (m-3), qi is the ion charge (Coulomb), and 6 is the+ion mobility (m- /V.sec).

Malave-Lopez and Peleg [38] have suggested that electrostatic charging and decay can be better analysed by using a linear relationship

t = K I + K2t (8)

Qt - QO

where Qe is the charge density at time t, QO is the initial charge, KI, K 2 are constants. Typically, the charging time is of the order of a few milliseconds [36], although it may not immediately be distributed uniformly over the surface [39].

Barthelemy and Mora [40,41] carried this analysis further and presented Eq. 4 in the form

Qmax = ~eoKsde2Eo (9)

The theory of electrostatic separations 199

where d e is the diameter of an electrical equivalent ellipsoid, and K the charging shape factor (a function of ellipticity z/x and the diele@tric constant e of the particle). Some values of K are: r,p s

Shape Charging shape factor K for: s

= Non-conductor, K = 5 z/x Conductor, Ks = s

5 36.2 25.15 I 3.01 2.15 0 0.666 0.532

which shows that the effect of shape and conductivity are significant. For example, conductors will attain higher maximum charges than non-conductors, elongated particles (z/x = 5) greater charges than spherical particles, and spherical particles greater charges than flakes (z/x = 0). Similar conclusions on the effect of shape were obtained by Vereshchagin et al. as a result of their theoretical analysis of the forces on a semi-elliptical particle [42].

Real particles may have sufficiently sharp surface points that they can build up enough charge to generate a corona that causes a loss of charge. Not only will this prevent that particle from attaining its maximum charge; it can also bombard other particles with opposing charges, so lowering their charge. The effect will lower the efficiency and is equivalent to charging by bi-ionizing electrodes [43].

Barthelemy and Mora [40] also considered the case of the charging of particles on a grounded surface. Under these conditions, the conductor leaks charge to ground, while the non-conductor's charge builds up. In practice, equilibrium charges % will be established, with the conductor having a small charge (because incomplete leakage), and the non-conductor having a less than maximum charge (because some leakage occurs), according to the relationship:

0max0e = 1. { I K 1 1. fn(E'/2K1 -1}1/2 (10)

where fn(E) is a function of the electric field, and K 1 is a leakage constant for the particle.

The order of magnitude of fn(E)/K I is 10 -14 (equivalent total resistance of the particle), that is, it tends t~ zero for a non-conductor, and to infinity for a conductor. Because the charging time is rapid, the attainment of a steady state charge is therefore as depicted in Figure 4.

(2) Induction Charging.

Induction charging is that process whereby initially uncharged particles in an electric field assume the field polarity. If a conducting particle then contacts a conducting surface, it conducts charge of one polarity to the surface, leaving the particle with a net charge of the opposite polarity. Once charged the particle then tends to be repelled from the surface because it now has the same charge polarity as the surface (if the surface is grounded, the other electrode at least has an opposite charge and attracts the particle). Non-conducting particles, having no net charge, are neither attracted nor repelled by the field (Figure lb).

Induction charging may also occur between conducting particles in an electric field by the manner illustrated in Figure Ic.

The charging characteristics will be described by an equation of the form of [40]

Q = CpV[1-exp(-t/~pCp)] (11)

200 E . G . KELLY and D. J. SPOTTISWOOD

where C is the capacitance of the particle, V is the voltage differential, and ~ ~he particle's equivalent total resistance.

P

Q

¢ 0

I

( ~ Conductor

Maximum

Steady State

( ~ Non-Conductor

Maximum

f Steady State

Time Time

Fig.4 Steady state charge on (a) a conductor, and (b) a non-conductor [After Barthelemy and Mora (40)].

(3) Tribocharging.

Tribo- or frictional charging is that process whereby a charge exists on a material after the parting of a solid/solid contact (a similar phenomena also occurs with solid/fluid contacts). The process is illustrated in Figures Id & le, and the two solids can be any combination of conductor, semiconductor, or non-conductor (dielectric). The magnitude of the final charge will actually be the result of two processes; the charge transfer that occurs during the contact, and the charge backflow that occurs as the materials are parted.

Although the phenomena of tribocharging was first recorded over 2500 years ago, the process, particularly with regard to non-conductors, is still not fully understood, and there is still debate about the actual mechanisms involved.

Much of the confusion in the literature can be attributed to the experimental conditions of different researchers not being equivalent. Problems immediately arise concerning the concept of "contact". Firstly, on the micro scale, there is the difficulty of knowing the true surface contact; even the best prepared surfaces can have relatively little true contact. Then, on the macro scale; some experiments have involved contact only, some sliding, some deformation of one component, and others a combination of these.

Difficulties also arise from problems due to specimen contamination. However, perhaps the most significant fact is that when the charging involves a non-conductor, the process is necessarily one of nonequilibrium.

Harper [15] in his comprehensive review made it clear that the mechanisms depend on the given combination of materials, and that metals and semiconductors behaved quite differently to non-conductors (of which there are two different types, those that charge freely, and those that are reluctant to charge).

In reviewing the literature, it is found that three general classes of charge-transfer mechanisms have been proposed; electron or ion transfer determined by bulk properties, electron or ion transfer determined by surface properties, and transfer related to mechanical dislodgement.

(a) Contact Electrification of Metals (Conductors). When two metals are brought into contact, charge is transferred between them until their Fermi levels equalize. The charge Q retained is given by

The theory of electrostatic separations 201

Q = Co.V ° (12)

where V is the contact potential difference, and C o is the contact capacitaffce. C is readily measured and is related to the surface topography; it is essentially equal to the capacitance of two perfectly smooth bodies at a separation equal to the mean asperity height [44]. Although earlier work [45] claimed that Q decreased as the bodies were parted (due to electron backflow by tunnelling), the more recent work indicates that this does not occur, and that Q is entirely due to the equalization of the Fermi levels on contact.

(b) Contact Charging Between Conductor and Non-conductor. It has for some time been recognized that the charge transferred between a conductor and a non-conductor tends to correlate with the work function difference between the two materials [46-49]. Such a correlation implies that electrons are transferred between conductor and non-conductor until thermodynamic equilibrium is established. Doubt about this mechanism has arisen because it has often been assumed that for thermodynamic equilibrium to be established, the charge must be distributed through the bulk of the material; something that is clearly not possible given the low mobilities of charges in non-conductor s.

It is now recognized that the charging of non-conductors occurs at the surface, and that there are sufficient sites to account for the charges found in practice. Charge transfer occurs fairly rapidly [50] (of the order of a few microseconds) by electrons tunnelling between the conductor and localized surface states in the non-conductor in the vicinity of the contact. The surface states act as "traps", providing or absorbing electrons [51-55]. Back tunneling (i.e., loss of charge as the bodies separate) is insignificant unless the surface is very highly charged [54].

Much of the confusion in the experimental results on contact charging is clarified by the work of Homewood and Rose-Innes [16] on charge accumulation from repeated contacting. They showed that between each contact, as a result of a small electrical conductivity in the non-conductor, charge redistribution away from the point of contact occurs, thus allowing further charging to occur on recontact. Hence, while local equilibrium may be established on contact, the total charge on a particle depends on the contacting rate, the distribution of the contacts over the surface, the nature of the contact (single "point", rolling, or sliding), and the conductivity of the material.

It is possible that some charge transfer in frictional contacting occurs by material transfer [56], but it is not considered a major mechanism [57].

(c) Contact Electrification Between Non-conductors. Duke and Fabish have described a model for predicting the results of insulator/insulator contact charging which they attribute to the filling of intrinsic localized "bulk" molecular-ion states in the outermost few micrometers of the (polymeric) materials involved [58]. Shinbrot proposed an alternative mechanism that involved the reversal of double-layer dipoles. Implications of this theory include an increase in charging with surface deformation, and thresholds for contact potential and surface roughness below which contact charging ought not occur [59].

(4) Charging Rate.

Based on the discussion above it can be seen that the charging rate of any particle can be described by an equation that considers the two processes that occur; the addition of new charge, and the loss of existing charge. Both processes can be described by similar exponential expressions, but with differing time constants. For example [9] :

dQ

dN = Qc[I - exp(-tb/Tb)] - Q[I - exp(-tc/Tc)] (13)

where Qc is the charge in the region of contact during contact,t h is the time between contacts, t c is the time of contact, Th is the time constant for the initial decay of charge, Tc is the time ~onstant for backflow to the contactor, and N is the number of contacts. Solution of Eq. 13 leads to an equation of the form:

202 E, G, KELLY and D. J. SPornswooD

Q(N) = K I - K2exp(-NK 3) (14)

where KI, K 2 and K 3 are constants and N is the number of subsequent contacts.

(5) Coehn's Rule.

Coehn's rule is an attempt to predict the charges on two materials after they have been in contact. Qualitatively, it states that "when two materials are contacted and separated, the material with the higher dielectric constant becomes positively charged". The rule has been quantitatively formulated as [60]

Q/A = 15 x I0-6(er,i - er, 2) (15)

where Q/A is the surface charge density (C/m2), and er, I and er, 2 are the dielectric constants of the two materials.

Given the complexity of tribocharging and its dependence on trace components, it is unrealistic to expect that such a rule will be very reliable, and this has been found to be the case. However, as a better understanding of tribocharging is developed, it is possible that some general relationship may be found for predicting tribocharges. Duke and Fabish [58] claim that their quantitative model of contact electrification is a step in this direction.

IV. CONCLUDING REMARKS

The concluding paper in this series will consider the practical aspects of electrostatic separations, and will, in particular, contrast theoretical and empirical information.

NOMENCLATURE

C = particle capacitance (F), (C/V) P

C = contact capacitance (F), (C/V) o

c i = ion concentration (m -3)

d = differential

d e = diameter of an electrical equivalent ellipsoid (m)

E = electric field intensity (V/m)

E = uniform electric field intensity (V/m) o

e = relative permittivity (dielectric constant), Eq. 2 r

= dielectric constant of particle. er,p

F = force (N)

fn(E) = a function of the electric field

Ima x = maximum presparking current in a corona (A)

K = constant

K e = given by Eq. 5.

K = charging shape factor s

N = number

Q = total charge (C)

Qe = equilibrium charge (C)

Qmax = maximum free charge on the surface of a particle (C)

The theory of' electrostatic separations 203

Qo " charge in the region of contact during contact (C)

Qt " charge density at time t (C)

QO = initial charge (C)

qi = ion charge (C)

S = needle to plane electrode spacing (m)

t = time is)

t b = time between contacts is)

t c = time of contact (s)

V = voltage (V)

V = contact potential difference iV) o

V s = corona sparking voltage iV)

V t = corona threshold voltage (V)

B 8 = angles

6 = ion or charge carrier mobility (m2/V.s).

T = particle-charglng time constant (s)

T b = time constant for the initial decay of charge (s)

T c = time constant for backflow to the contactor is)

= electric flux (C).

= particle's equivalent total resistance P

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204 E . G . KELLY and D. J. SPOTTISWOOD

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ME 2/2--D

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