Experimental techniques for monitoring sedimentation in optically opaque suspensions

Colloids and Surfaces, Elsevier

Science

43 (1990)

Publishers

1-32

B.V., Amsterdam

-

Printed

in The Netherlands

Experimental Techniques for Monitoring Sedimentation in Optically Opaque Suspensions R.A. WILLIAMS, Department Technology, (Received

C.G. XIE,

R. BRAGG

of Chemical Engineering, P.O. Box 88, Manchester, 18 November

and W.P.K.

AMARASINGHE

University of Manchester Institute M60 1QD (United Kingdom)

1988; accepted

7 February

of Science

and

1989)

ABSTRACT A review of established

and developing

techniques

for monitoring

solid flux, and in some cases

particle size, is presented for sedimenting multi-phase systems that are opaque and therefore unsuited to interrogation using conventional optical methods. The techniques are classified according to the physical principle employed for the measurement, relative cost of the equipment, precision, versatility, ease of operation, state of development and their ability to function in noninvasive or invasive modes. Requirements and limitations of these techniques are discussed with respect to their application dal suspensions. Practical

examples

to colloidal dispersions,

of phase-flux

(ii) capacitance, (iii) inductance pling of a sedimentation process.

determinations

emulsions

and to mixed colloidal/non-colloi-

are given for devices involving

and (iv) direct measurement

by physical

(i) ultrasonics,

interruption

and sam-

1. INTRODUCTION

Experimental measurements of the sedimentation or creaming behaviour of emulsions, colloidal dispersions or mixtures of colloidal and non-colloidal particulates become increasingly difficult as the volume fraction of the ‘solid phase (s ) is increased and as the particle/droplet size is decreased. In the case of a particulate suspension, direct observation of particle flux under the influence of an external force field is possible for low volume fraction suspensions, provided that the particles are large enough to be seen using optical microscopy. Measurements may be made on colloidal dispersions if the particle size and velocity are compatible with the requirements for laser-light diffraction or photon-correlation techniques, again at very low volume fraction. A number of instruments are available to measure the velocity, solid concentration and mass flow rates of liquid/gas [ 1 ] , liquid/liquid [ 21 and solid/liquid [ 31 systems. Unfortunately, the application of such well-established methods to many dispersions of technological interest is thwarted if either the liquid phase(s)

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or suspension is opaque; and this is a common occurrence. Long established sizing methods such as the sedimentation balance, Andreasen pipette, and centrifugation work well for specific applications at low volume fraction (independent of the opacity of the electrolyte) where ‘rapid’ measurements are not crucial, but have limitations for more complex dispersions. Although some optically-based techniques, such as the scanning laser-microscope for in-situ particle sizing [ 41, may be used at high volume fraction, measurements are made in the vicinity of the walls of the containing vessel, and are therefore generally unsuited to the measurement of macroscopic sedimentation properties. Consequently interrogation of the behaviour of systems such as those involving the formulation of products to minimise sediment formation with time (pigments, paint, emulsions/foods, personal products), or maximising the sedimentation rate (thickening, solid/liquid, and solid/solid separations), or monitoring the effect of polydispersity on sediment formation and cohesivity (ceramics), or the design of hydraulic conveying systems (coal, clay slurries ) relies wholly upon inferential, or ex-situ techniques. There is a considerable incentive to develop techniques that are capable of performing in-situ measurements of average solid concentration, particle velocity, and particle size in such hostile conditions. Model-independent techniques are particularly attractive, for example the ability to obtain data without recourse to a model which itself requires detailed knowledge of the system under investigation (particle size distribution, properties of the suspending electrolyte etc.). Some methods can be applied only to small active volumes over long time scales, whereas others require large measurement volumes over short time scales, and therefore the accuracy and precision of techniques vary widely. The lack of suitable instrumentation has been partly responsible for the relatively slow development of a comprehensive understanding of sedimentation phenomena in complex polydisperse suspensions, and in the verification of some theoretical and simulation based sedimentation models [ 51. The purpose of this paper is to present a classification of some of the direct and inferential methods that have, or are being, developed to measure the flux of multiphase systems and to report experimental measurements using selected techniques. 2. DEFINITION

OF EXPERIMENTALLY

MEASURABLE

PARAMETERS

Quantitative descriptions of the dynamics of the sedimentation of particulates in a fluid medium may be approached either by considering the relative motion of the solid (via expressions for particle velocity [ 61) or the movement of the liquid through a particle network (via filtration type equations [ 71) with respect to a datum position. Whichever approach the experimentalist chooses to adopt (the former being the more common) the parameters of most interest

$eax.ge;ent

,Sensor

Fig. 1. Schematic a liquid.

device

diagram defining a measurement

system for a particulate phase sedimenting

in

are the velocities of the particulates and the spatial distribution of the particulates in the space and time dimension, as reviewed elsewhere [ 81. In terms of common practical situations, Fig. 1 shows a typical sedimentation process in which n particulate phases are settling under gravity in a fluid contained in a vessel of known geometry. The solid phases may exhibit polydispersity in size, density, shape etc. and may carry a surface charge determined by the properties of their respective electrical double layers. If the vessel is closed, the net flux of the fluid will be in the upward direction, and the net movement of solid will be downwards, although some solid phases may move upwards with the fluid, depending on their relative size and density. At any time the total volume fraction is given by the sum of the volume fractions of the liquid & and solids @si components, $L+i

hi=l

(1)

i=l

Considering a one-dimensional system and a viscous incompressible fluid, the process can be described by mass and momentum equations for the fluid and solid, viz., for the liquid phase

(2)

4

for the solid phases

-Di(uL-USi)+

C

k=l

Cik(Ufjk-USi)-Ri=O

(3)

The most important terms in Eqns (l-3) are the drag coefficient Di, the compressive stress between the particles (expressed here in terms of the stress modulus G(@L) [9] ), the electrical retardation force R, resulting from sedimentation of the ith particle with zeta potential [, and a particle-particle interaction coefficient, C, which corrects for frictional effects resulting from particle collisions. Other terms in these equations represent the system pressure P and velocity U of a phase or solid species. Solution of these equations to obtain the parameters of technological interest such as the variation of pressure, velocity and volume fraction presents a difficult computational exercise, particularly for polydispersed systems at high solid fraction (which involve large particle numbers and dominance by the less well-defined interaction terms). Therefore, direct measurement of some of these variables is required and this usually involves monitoring some property averaged over a sensing volume (Fig. 1) at an instant of time, or over a known period of time. Although it would be highly desirable to be able to measure Usi (h,t) and ~si (h,t), it will be shown later that, for opaque suspensions, present instrumentation is generally limited to estimating the net flux and net solid volume fraction. In practice, two types of information may be obtained. (i ) From direct measurements of solid volume fraction & (h,t) at a point h (or in volume V) at time t (4) and net solid flux Fs (having units m3 m-’ s-’ or kg mm2 s-l) at that point over a time interval, or between two or more measurement points (or volumes) 1

Fs(h,t+ht)

=z

t=t+cTt

n

5 5 Usi#sidt t 0 1 I

5

For most types of instrumentation, acquisition of this information is via a model or calibration. If sufficient sensors are available to monitor Gs (h) continuously over the entire length z of the sedimentation column (i.e. z/d/z sensors), then F( h,t) can be obtained by integrating signals from all sensors. (ii) By inferrence from @s(h, t) and Fs (h,t) data, and with judicious assumptions, it may be possible to derive second-order information on the particle velocities Usi and a polydispersity factor. For example, in the case of a single structurally- and morphologically-homogeneous solid phase the size distribution pi = f (di) may be deduced. Circumstances may permit cross-correlation of signals derived from two or more sensors, from which additional flow data may be deduced. Examples of these techniques will be given later. Measurements will be complicated further if the flow of the phases is not uniform across the measurement volume, as might be caused by secondary circulation effects in a batch operation, or wall effects. For some instrumentation this presents no real measurement problem for type (i) applications, but such effects render interpretation of these measurements extremely difficult in order to deduce micro-scale (type ii) information. This problem can only be surmounted by use of higher sensitive imaging techniques, which are under active development [lo]. 3. CLASSIFICATION

OF MEASUREMENT

TECHNIQUES

The experimental techniques that are available to monitor the change in the composition of an opaque dispersion in space and time will be classified according to one of five principles underlying the measurement. The classification is summarised in Table 1, together with an appraisal of the practicalities of each method. A number of factors have been included, some of which are determined by the measurement principle itself (e.g. if the system involves operation in an invasive or non-invasive mode, or a contacting or non-contacting mode) whilst others reflect the limitations imposed by the development of suitable sensors and associated instrumentation (e.g. the cost and flexibility of ultrasonic transducers for particle sizing). In some cases the use of subtle non-invasive tracer techniques can greatly enhance the measurement technique and some methods are based solely on the use of tracers. The table is intended to be a useful guide, which is unlikely to be exhaustive, but aims at citing key references where more detailed descriptions of the techniques applied to sedimentation systems may be found. The common feature of these systems is that they seek to detect changes in the average volume fraction (Eqn (4) ), and some can be used to measure flux directly (Eqn (5 ) ) . As noted previously, the use of multiple arrays of sensors can provide powerful tools for analysis of sedimentat,ion processes, if geometric and economic constraints permit.

suo!srads!p Bmluauupas

anbado u! sluaura.msl?aur az!s pm xnu ‘UO~~E.I~U~XIO~ asqd

~03sanb!uyal

Ieluau+adxa

30 uoym9~ss~q3

The principles of each of the five types of measurement considered:

will now be

3.1 External radiation In these methods the measurement involves direction of a beam of radiation across the sedimenting zone, and monitoring the modulation of the beam due to phase perturbations in the suspension. Hence a source and a detector are required. The sources used most commonly are neutrons, y-rays, X-rays, ultrasonics and microwaves. The net attenuation of the incident light IO, due to scattering and absorption, depends upon the absorption coefficients cyiof the constituent phases and may be used to deduce the volume fraction of a given phase. For a suspension containing two phases A and B, the received signal I is given by I=IOexp[-~CYAD$A+c@#n]

(6)

where D is the path length (Fig. 1) . Consequently if cri\/as and D are known then @Aand &, can be determined, otherwise a relatively simple calibration procedure must be undertaken where the received signals at GA= 1 and & = 1 are used to generate a calibration line. @s = (ln I-ln

l~~~=,j)/(ln IctiB=lj -1n IcGAelj )

(7)

The principal advantage of such measurements is that they are largely independent of the physical properties of the suspension (temperature, pressures, viscosity, electrolyte composition). However their application may be limited to processes with slow sedimentation kinetics, since high accuracies can only be achieved over relatively long periods for y- and X-ray methods although some rapid scanning systems do exist. Furthermore a single intensity of incident radiation is not suitable for the entire range of solid concentrations and different sources may be required. Safety problems are encountered for the high energy sources, which tend to make methods based on ultrasonics and microwaves rather more attractive. Since the measurements are averaged over space and time there is an obvious advantage in using multiple beam systems, either at the same vertical position h, or cross-correlating signals from vertically-spaced sensors. Neutrons The use of neutron radiation is increasingly popular in examining colloidal processes, particularly small angle neutron scattering (SANS ) for the measurement of particle size and radial distribution function of concentrated dispersions, as reviewed elsewhere [ 111. For example, for a dispersion of identical spheres of diameter d, the intensity of the scattered signal I(Q) is used to obtain a structure factor S(Q),

8

I(Q) =K(pk -~t)~p(Q)s(Q)

Vi&

(8)

and Q= (4n/A)sin(8/2)

(9)

where A is the wavelength of the incident neutrons, p$, pi are the scattering length density of the solid and liquid. Apart from providing structural information, the void fraction can be measured (q& = Ns V,/ V) although only a few investigations appear to have been undertaken [ 121. Yuen et al. [ 131 reported void fraction measurements using a variety of ‘portable’ neutron sources ( 241Am/Be, 252Cfand 241Am/Li, corresponding to average energies of 5.1, 2.8 and 0.4 MeV, respectively), but the method imposes geometrical constraints and demands very careful calibration, The use of a pulsed neutron activation (PNA) technique was adopted by Banerjee and Lehey [ 143, and this offers the possibility of measuring $(h,t) and F( h,t). In Table 1 this falls under classification as a method based on external radiation, but in essence it is natural tracer technique involving emitted radiation as a result of external excitation. Pulses of radiation are used to activate oxygen atoms present in the suspension, thereby producing the radioisotope 16N ( 71/2 = 7.12 s) which is detected by scintillation detectors positioned below the neutron source. At present experimental methods based on neutrons are a novel research tool and are not available in the form of commercial instrumentation. X- and y-radiation

The most frequent use of external radiation involves X-rays and y-rays, which are employed in concentration and massflow meters [ 151, and the determination of flow patterns and solid distribution in reactors [ 161. For several decades absorption has been used for experimental measurements of solid concentration profiles in sedimentation columns. Typically a single source and single detector are used to scan the column (e.g. Kearsey and Gill [ 171 used yradiation, Gaudin and Fuerstenau [ 181 used X-radiation) and @(h,t) is derived from Eqn (7). Such methods are suited to dispersions that settle very slowly, in order to allow long counting times for each sequential measurement down the column, thus improving the accuracy of the measurement. Some commercially produced instruments are available, as reviewed by Allen [ 191. Multiple sensor systems must be used for suspensions that settle rapidly, although this can prove to be expensive and therefore it may be preferable to seek an alternative method of measurement. Multiple scattering techniques hold some promise for the future, for example, utilising Compton-scattered yphotons and an external radiation source which may permit imaging of the phases, provided they are of sufficient size to be resolved [20]. At present scattering techniques are generally limited to single sensor arrangements in

9

the analysis of the sediment thickness, such as used by Conner et al. [ 211 as a particle sizing device by measuring P-scattering from the base of a sedimentation tube irradiated with a “Sr-Y source. Ultrasonics Ultrasonic transducers can provide a non-invasive and on-line measurement of @(h,t) and/or Pi(h,t). There are three principal techniques used for these purposes, and since this type of measurement is an important tool for studying sedimentation processes, each method will be described in detail below. (i) Measurement of mean-square value of the amplitude modulated signal. A narrow and parallel ultrasound beam can be projected across a measuring volume, and interact with the flowing sample inside it. The inhomogeneities present in the sample scatter the ultrasound beam. The depth of modulation is a function of suspended solids concentration, flow velocity and particle size, and in general the following relationship holds [ 221, R,= KU;d”@”

(10)

where U, is the mean flow velocity, K,a,b and c are constants and R, is the mean-square value of the received amplitude-modulated signal. Therefore, in a constant velocity solid/liquid dispersion, if the particle size distribution remains constant, then the received signal will be dependent only upon suspended solids concentration. If velocity varies, then the concentration measurement can be achieved by compensating for this change using the cross correlation technique, as described by Beck and Plaskowski [lo] + In Balachandran and Beck’s [ 221 experimental arrangement, ultrasonic transmitting and receiving transducers were flush-mounted. A measuring circuit of phase-locked loop configuration was used for controlling the transmitting oscillator, such that a constant acoustic path length is maintained between the transducers. (ii) Beam velocity measurement. In measuring creaming profiles in oil-in-water emulsions, Hibberd et al. [ 231 found that if the velocity of ultrasound through the continuous and dispersed phases is different, and if the droplet size is much smaller than the wavelength of ultrasound, the velocity of ultrasound v through the emulsion depends only on the concentration of the dispersed phase, i.e. (Urick [24] ) (&Z/V)‘=

[I--$d(l-Pd//k)l

[1-$dd~--/&~:/~d~:)l

(11)

where Pd and pc are the densities of the dispersed and continuous phases respectively. @d may be determined by measuring the time for a pulse of ultrasound to cross the sample, and this is described as an illustrative example of the ultrasound measurement technique in section 4. Bonnet and Tavlarides

10

[ 25 ] and Wedlock [ 261 have employed a similar method to measure $J(h,t) for colloidal solid/liquid dispersions. (iii) Scattered intensity measurement. In solid/liquid dispersions particles, whose density and velocity of sound are much higher than those of the medium in which they reside, can be considered as acoustically hard (rigid and inelastic). If suspended particles are sufficiently separated such that no multiple scattering occurs, then the scatter can be regarded as incoherent and thus a function of the number of particles inside the scattering volume. Based upon this theory, ultrasonic transducers have been investigated for measuring particle concentrations (Young et al. [27], Lenn [28] ). To overcome the sensitivity of concentration measurement of particle size and the problem of nonlinearity [ 271, Lenn [ 281 has developed a measurement technique using multiangle ultrasonic scattering. In his experiments, he found that the intensity of the backscattered sound (measured at 170” scattering angle) is a function of sedimenting particle concentration and size, but the ratio of 10’ scatter to 170’ scatter is a function of size only. The operating frequency was also carefully selected so that the instrument can give greatly reduced sensitivity to particles below a chosen cut-off size, Although ultrasonic measurements hold considerable promise for application in the analysis of sedimentation processes, all three methods described above may not work well as the volume fraction of the solid phase approaches unity, and a single transducer may not be suitable for universal use, independent of the properties of the individual phases to be examined. In the case of the method (i) the monotonically increasing relationship between, for example%and$ (Eqn (lo)), will no longer exist, since the mean-square value of the amplitude-modulated signal tends to saturate. When using the beam velocity measurement technique (method (ii) ), high concentration suspensions may make the ultrasonic beam very difficult to propagate through the sample, though ultrasonic signals of very high energy can be tried at the expense of increased complexity of the instruments and therefore the cost. Measurement techniques based on the scattering principle (method (iii) ) apparently will fail to operate, since the assumptions of incoherent scattering (no multiple scattering) will be violated as solid volume fraction increases. Therefore, alternative measurement techniques should be adopted, such as the conductance and capacitance measurement techniques. Microwaves

Microwaves find applications for use in the form of Doppler velocity meters in single and two-phase systems. To our knowledge their potential for measurements in multi-phase systems has not been investigated in any great detail, probably due to the poor spatial resolution that can be achieved, and biasing from reflections. However, the use of a bistatic device, in which a separate

11

oscillator and receiver are employed, can yield information on the average bulk velocity from the average frequency of the Doppler signal (Stuchly et al. [ 291). Alder et al. [ 301 give a review of the principles governing microwave measurements and their application. However, it is clear that microwave attenuation techniques can be applied to measurement of water content in liquid mixtures and some measurements have been reported by Clegg [31] for water/oil mixtures. In summary, the continuing development of semiconductor transducers favours the application of ultrasonic methods for determining @(h,t) and F( h,t) for many applications. At present the cost of ultrasonic transducers is high, but the ability to function in a non-invasive and non-contacting mode is attractive, and avoids the stringent safety precaution required when dealing with nucleonic methods. If structural information of very small particles is required, then there is little alternative to the higher energy neutron radiation. 3.2 Emitted radiation Radioactive tracers Radiation emitted from a tracer particle that has been planted, or occurs naturally in the suspension, forms the basis of several detection techniques, mostly permitting the measurement of F(h,t) only. Tracer species that are introduced to the suspension can be used to indicate the net sedimentation velocity, an example being pulsed neutron activation (described in the section on external radiation methods). For systems where one or more phases produce radiation (either naturally or after labelling ) in a homogeneous manner, this property can be used for phase-flux measurements, and occasionally information on the concentration of phases may be derived [ 321. The use of radioactive tracer/labelling methods is well known in determining residence time distributions in process reactors, and in a similar manner injection of tracer particles can be used to monitor sedimentation velocities, assuming that the particles are of similar composition, size and density to the solid phases present in the suspension. The number of tracers required depends on the effective void fraction of the phases and the nature of the sedimentation process, but the method remains somewhat cumbersome. Nuclear magnetic resonance A more elegant solution for the flux determinations is to utilise the multiplicity of atomic tracers available in the form of polarisable nuclei, by positioning permanent magnets around the sedimentation vessel, which results in reorientation of those nuclei that possess a significant dipole moment. If a demagnetising coil is placed either side of the magnet position and operated intermittently, then bands of orientated and non-orientated nuclei can be generated (in a controlled manner ) , and the relative upward and downward fluxes

12

can be determined at detectors placed either side of the demagnetising coils. This nuclear magnetic resonance (NMR) principle has been used for flow measurements of two-phase solid/liquid and liquid/liquid systems [ 331. Magnetic tracers Permanent magnetic tracers that can be detected by measuring the modulation of an existing magnetic field or the change in inductance of an electrical wire wound around the periphery of a sedimentation vessel may also be utilised. This technique has been used with considerable success in monitoring the behaviour of opaque suspensions of naturally ferromagnetic particles [ 341, and a commercial instrument is available for industrial use [ 351. Examples of practical measurements using this method are given later. With the exception of the special case of processing ferromagnetic materials, methods based on emitted radiation are usually difficult to implement and the least attractive of the five methods for @( h,t) and F( h,t) measurements. 3.3 Electrical properties In recent years significant exciting advances in instrumental techniques based on electrical measurements have been made. Measurements based on monitoring changes in electrical potential, dielectric constant, and electrical resistance involve abstraction of electronic data and subsequent processing, often via a microcomputer. Therefore measurements can be performed rapidly, accurately and repeatedly using sensing transducers that are relatively inexpensive, compared with emitted radiation methods. A number of sedimentation processes have been examined using these methods, for opaque and nonopaque dispersions. Electrochemical methods Electrochemical methods represent the least common class of measurement within this category. Here three techniques are of interest, namely, sedimentation potential (or Dorn effect) methods, microelectrochemical methods, and electrochemical noise. (i) Sedimentation potential. The electrical potential generated when solids or liquid droplets, carrying a surface charge, move with respect to the host electrolyte can be used to derive phase flux information. This phenomenon arises from the non-uniform distribution of charge, due to partial detachment of the outer part of the electrical double layers surrounding the moving droplet or particle. For the simplest case, of a low volume fraction of rigid non-conducting spheres carrying a charge Qi, in a suspension with bulk conductivity LO,the potential gradient ,?? (V m-l) between two vertically-spaced reversible electrodes a distance Ah apart, is given by:

13

e= (dh/~,)

~ Nsi UsiQi i=l

(12)

A typical value for ,??is between 10 and 20 V m-l. The velocity of a liquid phase, such as an emulsion droplet, can be estimated in the same way [ 361, but correction factors will be required, depending upon the size of the mobile phase relative to the thickness of the double layer and the conductivity of the droplet [ 371. Elton and Peace [ 381 extended the use of Eqn (12) to analyse the particle size distribution of a polydisperse suspension, however, this has not been exploited in any detail as a viable experimental method. In principle techniques based on the Dorn effect may be used at very high volume fractions, subject to a model for the further correction factors required to account for multiple-particle interaction. Marlow et al. [ 391 report the successful application of such a model when using the potential generated on applying an external oscillatory compression sound wave to back-calculate a value for the ‘acoustophoretic mobility’ of particles in an opaque polydisperse suspension. In general, methods based on sedimentation potential are best suited to monosized low volume fraction suspensions, and to electrolytes in which a significant double layer is developed (i.e. at low ionic strengths). (ii) Microelectrochemical methods. Microelectrochemical methods [ 40,411 have found specific application in quantifying turbulent transport effects in sedimentation processes where external mixing, or micro-inhomogeneities are present. For example, Nonaka and Uchio [ 421 used this approach to determine the effect of polydispersity and external shear under conditions to mimic the operation of an industrial thickener with a sedimentation rake. This was achieved by extending Eqns (2 ) and (3 ) to consider the transport of material due to gravity and fluctuations due to turbulent diffusion. The mean and fluctuating components of the flow velocity were measured by monitoring the diffusion current [ 431 for the reaction Fe (CN )i- + e = Fe (CN)i- between a silver foil electrode (anode ) and a moveable platinum wire electrode (cathode), using conventional electrochemical equipment. It was claimed that this approach offered a useful means of establishing $ (h,t ) and that the model based on the decay theory of turbulent diffusion provided a good fit to experimental data. Such methods are of course limited to aqueous electrolytes, with moderate ionic strengths ( - 0.1 mol dm-3) and assumes that the redox couple does not influence the sedimentation process by causing modifications to the surface chemistry of the solid particles. (iii) Electrochemical noise. Electrochemical noise is the analysis of seemingly random fluctuations detected by one, or more, electrodes placed in the sedimenting suspension. The use of so-called “noise measurements” has been ap-

14

plied quite widely for velocity, voidage and phase-size measurements, when the fluctuations of an externally applied signal (often, the impedance ) are monitored with time. For example, Davis [44] claims a size resolution down to 20 pm in a gas-liquid mixture, using 6 pm diameter probes. Indeed, the microelectrochemical method described earlier, employs, in part, measurements of random noise. However, in its simplest form the concept of electrochemical noise involves the interpretation of noise arising from isolated or passive electrodes without any (or very little) external signal, and therefore instruments that rely on modulation of an external input (capacitance, conductance etc. ) are rather different and will be described later. There have been surprisingly few studies of the effects of passive-noise, such as that measured using a very high impedance voltmeter, although its existence and potentialities have been noted for gas-liquid [ 451 and solid-liquid systems [ 461. Although the mechanisms underlying the change in electrochemical potential when a solid particle (of known solid-state properties) impinges on a micro- or macro-electrode are not understood, in some cases there appears to be a functional relationship between the volume fraction of solid and the measured potential signal for given hydrodynamic conditions [47]. In extreme cases, individual particle-electrode collisions may be observed at high Reynolds number [48,49 ] but this type of investigation has not been extended to sedimenting systems, because of the nature of the measurement it requires contact with the dispersion, and may be highly intrusive unless the sensing electrodes are restricted to the periphery of the sedimenting vessel. Capacitance

Capacitance measurement techniques have been widely used in multiphase flow systems. They are suitable for measuring fluids consisting of two components of very different permittivities, such as gas/solids flow [ 50-52 1, wateroil mixtures [ 531, gas/liquid flows [ 531 and solids/water slurries [ 54 1. Capacitance sensors have the advantage of being non-invasive and may even be noncontacting, inexpensive, simple to construct and fast in measurement, and thus provide continuous on-line measurement for many industrial processes. A number of capacitance transducers have been developed so far, and this area has been reviewed recently by Huang et al. [ 551. In common with other electrically-based measurements the properties of the phases may, in some cases, prohibit use of such methods but in general, unlike optical transducers, the capacitance sensing technique can measure particulate suspensions of high volumetric concentration. Evenmore, this method has been investigated for not only obtaining local concentration distribution but also identifying flow regimes over the cross-section of a two-phase pipeline [ 561, and shows great promise. Surprisingly, capacitance transducers are less widely used for measuring concentration profiles in sedimenting dispersions than their conductance

15

counterpart (discussed elsewhere ). Since most particulate suspensions exhibit complex electrical permittivities t, (where E,= t’ -je” ) it is often necessary to measure both the conductivity and capacitance in order to obtain the actual value of @i(h,t ) . In section 4.2, a detailed example of a measurement of this kind is illustrated. In general, for the fluid system of low-loss dielectric particles dispersed in a conducting liquid, the following relationships exist:

cx=fl(EL,ES,@S)

(13)

G,=f,(a,,@s)

(14)

where C, and G, are the capacitance and conductance of the suspension, respectively, eLand oL are the permittivity and conductivity of the liquid phases, respectively, and es is the permittivity of the homogeneous solid phase. In the case of spherical particles, the effective (i.e. measured) permittivity of the suspension E, is related to the volume fraction Gs by the equation: E,

(h,t) = [ (1-~s)EL1'3+~SES1'3]3

(15)

Therefore, if either C, or G, can be measured independently, then the particle concentration can be easily inferred. But most capacitance measurement techniques, to a different extent, will be influenced by the system conductance. Therefore if the capacitance is to be determined accurately, a conductance measurement is required.

Conductance Conductance (resistance) measurement techniques have long been used to study the behaviour of fluidised systems [ 57,581. The conductance electrodes have to be invasive and contacting, but the simple electrode structure and the electronic measuring circuit (usually consisting of a function generator, a ballast resistor and a current measuring device) make this technique quite attractive. This system works on a principle analogous to that of the capacitance measurement technique described previously, but measures the conductance of the suspension (Eqn ( 14) ) instead of capacitance. Based on this principle, Nasr-el-din et al. [ 591 recently developed an intrusive electrode of special configuration to measure local concentrations in slurry systems. Wakeman and Vince [ 601 used an array of pin electrodes fitted axially along an experimental cylinder to investigate the kinetics of gravity drainage from porous media, and Wakeman and Holdich [ 611, using a similar electrode configuration, studied the solids concentration profile during sedimentation.

3.4 Physical properties

Physical measurements require the measurement of a macroscopic property of a suspension over a given volume with respect to time. In opaque systems the suspension density PM, mass, and the hydrostatic pressure represent the only accessible parameters. For special cases where a solid phase(s) is dispersed in a transparent or translucent liquid or gas phase(s) it may be possible to employ other methods that combine centrifugation with optical observations of the sediment volume. Sedimentation

balance

At low volume fraction and for particles larger than about 0.1 ,um, g(t) and pi may be determined by weighing the sediment as it accumulates at the base of the sedimentation column. At least four versions of these sedimentation balances are available [62] which have evolved in attempts to negate experimental artifacts associated with the changing buoyancy of the weighing pan, density convection currents and (in some designs) the intrusive nature of the balance pan. The method is not entirely satisfactory owing to the intricacies of the experimental procedure, and its application has been limited to very low solid concentrations as a size analysis technique. Hydrometers

and density tracers

Methods based on the measurement of density and hydrostatic pressure are generally less restrictive, in terms of the suitability of particle size and solid volume fraction. The use of density tracer particles and hydrometers provide an alternative to the more elegant techniques afforded by use of external radiation. Although less expensive and simple to operate, the use of single-stem or multiple-stem hydrometers in a small diameter sedimentation vessel is obviously highly invasive. Fully submergible density tracers or divers were used by Berg [63], and the position of the divers having a range of densities was determined by pulling the divers to the wall of the vessel. Other variations of the technique have since been implemented, such as roof-divers [ 641 and spinning divers, in conjunction with external detection devices to locate their position. The intrusive nature of divers and hydrometers can be minimised by reducing their size, and accuracy may be improved by utilising emitted radiation to enable their detection. In larger process-scale applications density tracers have proved to be invaluable in diagnosing operating conditions in classification equipment [65] by counting colour-coded tracer particles in the product streams. However, for small-scale laboratory use, the method remains unattractive, particularly for colloidal dispersions where much large invasive bodies perturb the sedimentation process to an unacceptable extent.

17

Pressure measurements Measurement of hydrostatic pressure using a fluid manometer or pressure transducer provides a useful tool for routine analysis. Until quite recently the method was confined to coarse particulate suspensions, in order to avoid blockage of the narrow bore capillaries connecting the sedimentation chamber to the differential manometer [ 661 or to a transducer [ 67-691. In the former case, problems with leakage of the manometer liquid into the sedimentation vessel tended to limit widespread application [ 701. However, more recently sensitive flush-mounted pressure transducers have become available which are suitable for use in direct contact with many liquids and colloidal dispersions, or via a membrane and fluid coupling (at the expense of some loss of sensitivity). For a single transducer mounted on a sedimentation column of diameter D at height h, the average solid volume fraction above the sensing position for a suspension with head z, can be followed with time, since

~~(z-h,t)=[(P(h,t)/g.(Z-h))-PLl/[Ps-PLl

(16)

The use of multiple arrays of pressure transducers interfaced to a microcomputer allows F( h,t) and by inference $(h,t) to be obtained. In addition, the use of transducers mounted above and below a membrane supporting the sediment allows the stresses associated with particle-particle/particle-wall interactions to be elucidated, as described by Edwald [ 711 and Raffle and King [ 68,691. The method is less well suited to dispersions that tend to gel, since all measurements of apparent hydrostatic pressure will be meaningless. The high cost of suitable transducers is an obvious practical limitation, but the significant advantage is that it is based on direct measurements of mass, and is modelindependent (unlike most of the electrical sensing methods). Oscillation method In general, centrifugal methods per se can only be used if the supernatant is transparent, but have been the subject of many papers and patented devices. Their advantage is that they offer rapid testing whilst also providing quantitative information about compressional effects. For example, Lockyear and White [ 721 developed a laboratory centrifuge test to simulate gravity thickeners. Similar methodology can be applied for completely opaque suspensions, but only changes in the centre of gravity can be exploited. At least two types of automated device can be used. (i) Mechanical oscillation. For low density suspensions, such as those encountered in biological systems, there is only a small difference in density between the component phases and a mechanical oscillation densitometer can be employed to achieve resolutions reported to be as low as lo-’ g din3 [ 731. Schneditz and Kenner [ 741 measured the sedimentation rate of red blood cells dis-

18

persed in isotonic sodium citrate using an in-situ oscillator technique, by monitoring PM(t) in the upper tip of an inclined U-tube. (ii) Natural pendulum oscillation. The second type of instrument utilises the change in the natural oscillation frequency of a counter-balanced pendulum (which houses a sedimentation tube) with the position of the centre of gravity [75]. The measurements are readily automated, and have been used to measure sedimentation characteristics of coal/liquid [ 76-791, dense medium processes [ 801, and aqueous clay suspensions [ 801. The method works quite well, but is severely limited in that it measures only one averaged property (a change in the centre of gravity) which is not easily related to @(h,t) and F( h,t). Rheological measurements In principle, it is possible to employ rheological techniques to monitor indirectly the change in /$ and & with time. For example, Vindevoghel [81] followed the change in viscosity with time under conditions of low applied constant shear stress as an in-situ measurement of the sedimentation rate of polydisperse glass beads (l-60 pm) in a glycerol/water suspension contained between concentric cylinders. Such techniques are not generally applicable to all dispersions but may be a useful guide to the behaviour of monosized systems. 3.5 Direct methods There is a significant advantage in using a direct method for analysing sedimentation processes, where measurements are made ex-situ on samples of the suspension mixture rather than relying on inference via a model. Therefore, it is often possible to determine @(h,t), F(h,t) and /l,(h,t), and information relating to the packing structure of the sediment. The major difficulty of many of these methods is that they are highly invasive, laborious, and depend upon the acquisition of consistently representative samples. Sampling Some of the earliest and simplest methods for analysing the sedimentation behaviour of opaque suspensions employed pipettes [ 82,831 or perforated tubes [84] to remove samples from a sedimentation column at certain heights and times. A number of methods based on analysing the sediment washed out from the base of sedimentation columns have also been proposed [85,86], but generally these have been applied to particle size analysis at low solid concentration, rather than to elucidation of sedimentation characteristics of suspensions. A variety of other techniques have been used to achieve isokinetic sampling, which ensures that the means and rate at which a sample is withdrawn are compatible with the velocity of the particular phase(s) being sampled, and therefore yield a representative sample of that phase. Isokinetic sampling of

19

gravitational sedimentation processes is not easy to achieve, particularly for solid/liquid suspensions containing a wide distribution of particle sizes, although some experimentally-based designs for static isokinetic sampling probes have been proposed [ 15,871. The sample volume must be carefully selected to allow statistically significant analysis, but without removing such a large amount of material to alter the process being examined. Sometimes static probes prove to be too invasive, in which case devices that take grab-samples may be adopted, since a short-term disturbance to the system may be less disruptive to the process. Di Felice et al. [88] give a good example of a grab-sampling device, which removes a 7 cm3 cylindrical volume from a solid/liquid column, from which ~si data were obtained. F5-index Routine tests of suspension stability in an industrial environment often involve a semi-quantitative assessment, such as the F&index test, which is used to rank the settling rate of magnetite/water suspensions used in coal/shale separation processes. The test yields a single number calculated from the ratio of the mass of solids drained off from an upper- and base-section of a sedimentation column, of fixed dimensions, after a standard settling time of 5 minutes [ 89 1. Such methods are of little use for diagnostic analysis. Freeze-etch microscopy In cases where direct sampling of a sedimentation process is not feasible (due to the inability to take unbiased samples, or when the disruption caused by the presence of the sampling probe affects the process itself) methods that prevent or physically interrupt sedimentation are often employed. Invariably such a procedure is time-consuming and requires many repetitive measurements in order to obtain a complete understanding of the sedimentation process. However the reliability and quality of the resultant data produced are perhaps the best that may be obtained by any method. For colloidal dispersions sedimentation phenomena may be followed by rapid freezing of the suspension after a given settling time, and microscopic examination of sliced sections. A similar procedure can be used by crash-freezing the small samples taken from a sedimentation process, followed by fracturing, etching by sublimation at reduced temperature and pressure, and then a platinum foil replica of the surface can be formed for examination in a transmission electron microscope (TEM) [ 90,911. An alternative procedure is by freeze drying, followed by examination by scanning electron microscopy (SEM). Hence, detailed information on particle size, coordination number, and volume fraction may be obtained [92]. For dispersions in which the host electrolyte is non-volatile oxygen plasma etching is possible [93] and an image of the surface can be taken directly using SEM or via a replication technique and viewed by TEM. Sedimentation experiments on suspensions containing larger parti-

20

cles or mixed colloidal/non-colloidal systems are usually done with large volumes of suspension and in larger vessels (to reduce wall effects); and rapid insitu freezing is often not feasible and other methods must be used. Physical interruption Most sedimentation processes are amenable to analysis by means of physically preventing the movement of phases by insertion, or removal of sections of the vessel containing the mixture [ 94,951. This is a terminal test, since, for example, the insertion of plates to isolate zones of the sedimentation column affects the subsequent behaviour of the unconstricted zones in an irreversible and catastrophic manner. Material contained with each isolated section may be removed for analysis to determine @(h,t), P,(h,t) and F( h,t) [96] as illustrated in the example presented in section 4.4. The vertical resolution (Ah) can be improved by increasing the number of dividing plates, but with a corresponding increase in the complexity of construction of the column. The main limitations of this approach lie in the design of a suitable leak-free valve mechanism, to minimise the dead volume within the valve, and in the careful operation of the slides (manual or automatic) to avoid disruption of the suspension in the vicinity of the valve. 4. ILLUSTRATIVE

EXAMPLES

OF PHASE CONCENTRATION

AND FLUX

DETERMINATIONS

In this section examples of four important techniques will be used to demonstrate the measurement of phase concentration and phase flux in sedimentation and creaming systems. Details of other experimental examples resulting to sedimentation systems are given in the respective references cited in Table 1. 4.1 Ultrasonic transducers for the beam velocity measurement An illustration of the beam velocity measurement technique for determining creaming profiles in oil/water emulsions is provided by the results of Hibberd et al. [ 231. Their measurements sought to determine the volume fraction of a dispersed emulsion &, using a pulse ultrasound of frequency 6.2 MHz. The time for the pulse to travel between two crystal probes (Mateval 601/5 mm type) across the cell containing the emulsion was measured using a timer. The probes were moved vertically up the cell, and the transit-time of the pulse was measured at different heights. This information was stored in a microcomputer, and then processed to yield & (h, t) . Figure 2a shows some typical results obtained for a calibration of the measured velocity versus volume fraction &, for a commercial salad-dressing-type

(a1

1600

$

1550

\ > 1500

0

0.5

1

%

1

0 0

50

100 h /

150 mm

Fig. 2. Use of ultrasound beam velocity: (a) ultrasound velocity versus volume fraction of dispersed oil phase (circles indicate experimental points, line is given from theoretical prediction using Eqn (11) ) for a salad-dressing-type emulsion, and (b) concentration profiles as a function of time for an emulsion containing 0.175 wt.% xanthan gum. (After Hibberd et al. [B] ).

emulsion, compared with a theoretical prediction based on Eqn ( 11). Concentration profiles & (h,t) were also obtained (Fig. 2b) for an emulsion containing 0.175 wt.% xanthan gum (p=999.33 kg me3, u=l483.4 m s-l). From these results it is evident that this type of ultrasonic technique provides an effective method for studying the creaming mechanism of liquid/liquid systems. 4.2 Capacitance

measurements

The following example considers a capacitance transducer based on the charge/discharge principle, in the measurement of the concentration of glass beads in distilled water (as widely used in industrial wet peening processes). The principle of the charge/discharge transducer has been described in detail elsewhere [54], and here only the measurement electrode configuration and results are illustrated.

22

An invasive electrode was used in the experiments of Huang et al. [ 541 (Fig. 3a), where the DC blocking capacitor (1 ,uF) was connected between the electrode and the charge transfer device (transducer) to prevent the DC component of the charging voltage pulses from being applied to the electrodes, and thus to avoid polarisation of the electrodes. The capacitance electrode configuration can also be made completely non-invasive and non-contacting but at the expense of reduced capacitance sensitivity. The system was calibrated for low solid concentrations ( qbs= 0.01,0.02,0.04, 0.06) with a charging pulse of z= 200 ns duration and a switching frequency of f= 2.5 MHz. Th e uppermost curve in Fig. 3b shows the measured capacitance (normalised by the estimated fluid capacitance at &=O, C,) versus #s. The liquid conductance was also measured using a conductance transducer. The measured conductance G, (normalised by the estimated liquid conductance at @s= 0, G,) is shown in Fig. 3b.

(b)

%I’C” @---o j1.4

2.5

2

1.5 -

-0.8 1.oe--Q__ II,Y,Q

0

_? 0.03

Cx/‘, 0.06

Fig. 3. (a) Invasive capacitance electrode system for measuring volume fraction of glass beads (loo-150 pm diameter) in distilled water at 2O”C, and (b) examples of measurements of normalised measured capacitance (CJC,), normalised measured conductance (C,/G,,,) given by Eqn (17),forz=200ns (AfterHuangetal. [54]).

23

It has been found that the actual fluid capacitance C, is related to the measured fluid capacitance and conductance G, via the following relationship [ 541 C, = C, - 0.5 zG,

(17)

According to this equation the effect of conductance can therefore be decoupled, and C, (normalised by C,) is plotted in Fig. 3b (the lowest curve), which shows the correct relationship between the inferred fluid capacitance and the solid volume fraction, i.e. the value of C, decreases monotonically with the increased solid concentration. The theoretical relationship is shown in Fig. 4, extending to very much higher solid concentrations. It can also be seen from Eqn (17) that the conductance effects on system capacitance can be reduced by shortening the duration of the charging pulse (z), which is equivalent to increasing the frequency in the sinusoidal measuring systems. The present authors are developing this approach to determine @s (h,t) and Fs(h,t) by means of an array of capacitance and pressure transducers mounted along a sedimentation column (Fig. 5a), where the capacitance transducer can either be one based on the charge/discharge principle (described above ) or based on the transformer-ratio-arm bridge technique (Fig. 5b) and a phase-sensitive detection (PSD ) principle developed by Xie et al. [ 511. In the latter case since the phase of capacitance and conductance component of a complex impedance is in quadrature, this PSD arrangement makes

Fig. 4. Dependence of effective permittivity E, on volume fraction of solid phase ity of solid phase es in water at 20 ’ C, as given by Eqn ( 15 ) .

permittiv-

(bl

1OkHz

Fig. 5. (a) Sedimentation and data acquisition system using an array of pressure and capacitance transducers, and (b) details of transformer-ratio-arm bridge transducer enabling simultaneous measurement of capacitance and conductance.

it possible for the instrument to measure them simultaneously, therefore the true relationship between C, and G,, if it exists, can be easily decoupled. Using such an experimental system (Fig. 5a), the solid flux Fs is related to the capacitance measurement via: Fs=-K,p,AhtdCj(t)/dt

(18)

j=l

or *

F s=-KP,

s

a/at{ K’(W}dh

(19)

h=O

where Kc is the correlation coefficient between capacitance and volume fraction of solids, Ah is the height of a capacitance segment in a column of height z (z = k-Ah). Hence, capacitance techniques, although in an early stage of de-

25

velopment, appear to offer a powerful and low-cost method for the analysis of sedimentation processes. 4.3 Inductance This method is based on the change in the inductance of a coil placed around a sedimentation column, as ferromagnetic phase(s) sediment under gravity in a diamagnetic liquid. The signal (mH) obtained from an impedance bridge is converted into a mV signal [ 971 and used to estimate the volume fraction and the average flux over a desired period. The principal application of this method has been for aqueous polydisperse suspensions of high density particulates (such as magnetite ( Fe304)P s = 5200 kg mm3, and ferrosilicon (Fe,Si) , p6 = 7000 kg me3) which sediment rapidly even at very high solid concentration. The initial rate of sedimentation as the solid/liquid interface passes through the coil sensing zone has been the subject of most investigations [ 341. Data from such measurements have been abstracted from several sources [ 34,97-1001 in the following examples. Figure 6 shows the measured change in volume fraction of solids with time, using a sensor coil placed near the top of a sedimentation tube. The average volume fraction in the sensing volume is derived from the measured suspension density pm: $(h+O.5&t)

= (An -&)/(Ps

-PIA

(20)

By integrating the signal a value for the average solid flux can be obtained,

Time / s Fig. 6. Charge in volume fraction of ferrosilicon particles (l-120 ,um) in tap water measured using an inductance coil mounted on the upper section of a sedimentation column. Broken line indicates 68 and 32% region, between which average setting rate is computed. (Data from Roberts and Cragg WI).

26

or an arbitrary rate of change of density can be defined (for example, this is shown as the period between 68 and 32% of the total change in density in Fig. 6). Figure 7 gives results obtained from inductance to measure the solid flux (here, expressed in terms of a settling rate based on the average change in density @,/dt ). The results show the effect of the size distribution and volume fraction/suspension density for ‘clean’ ferrosilicon suspensions containing particles between 1 and 120 pm (Fig. 7a), and a set of measurements on three diamondiferous dense media separation plants (A,B and C) each contaminated with different amounts of kimberlitic colloidal slimes (Fig. 7b). The technique provides a relatively simple and reliable measurement of suspension stability for the specialised application to ferromagnetic suspensions, and is best suited to systems with rapid sedimentation kinetics. Increasing the number of sensor coils would enhance the capability of such instrumentation.

20

30

40

50

60

70

Settling rate /g dm-3s-'

(b)

C

A

Settlingrate 1 g dme3s-' Fig. 7. Use of inductance

technique

to monitor

change in settling rate of (a) clean polydisperse

ferrosilicon suspension as a function of suspension density p, (kg rnm3) and the wt.% of particles below 45 pm diameter (broken lines indicate interpolated data), and (b) polydisperse ferrosilicon suspension taken from 3 diamondiferous dense media separation plants A,B and C, contaminated with 6 wt.%, 2 wt.% and 1.5 wt.% colloidal kimberlitic clays respectively. (Data from (97-1001).

27

4.4 Physical interruption A considerable amount of information on the particle size distribution, concentration and flux can be obtained from methods that irreversibly terminate the sedimentation process by physical interruption. Figure 8 shows the apparatus devised by Amarasinghe [ 961 to monitor sedimentation response of complex polydisperse suspensions of glass spheres (l80 pm diameter), as a function of @s, pi and zeta potential. Thin sliding plates are used to divide the column into five sections, using double-‘0’ rings on either side of the slide to effect a seal. Once isolated, the material contained in each section can be removed for analysis, in the currently reported work this involved measurement of C&and pi using an Elzone particle size analyser. Flux

Section

1 2 3 4

Valve -

mechanism

closed position

open position

Fig. 8. Sedimentation column fitted with a sliding valve mechanism column. (After Amarasinghe [ 961).

to isolate sections within the

28

measurements were also made by performing many replicate tests, but allowing sedimentation to proceed for different time intervals, therefore enabling calculation of the average flux across a section. Figure Sa,b,c shows the type of information obtained from a series of experiments to determine the sedimentation behaviour of a polydisperse suspension (normally distributed d= 36 pm, cr= 14 ,um, ps= 2700 kg md3, pL= 1000 kg (a1

(b)

I

0

I

I

I

o-

1

0.1 0.2 0.3 0.4 0.5

0

+

0

0

20

12 IO&F

g(h,t)

40 d / pm

Initial

3

4

(h ’ t) / m3mezs-' 5

dlstrlbution

60

Fig. 9. Experimental measurements using a physical interruption method to investigate the sedimentation behaviour of polydisperse suspensions of glass beads (cr= 14 pm, d = 35 pm, ps = 2700 kg mm”) in lo-” mol KC1 dm-3 at 20°C (pL= 1000 kg me3). (a) average volume fraction of solids OSin a single section (Fig. 8) versus height, with time, (b) average solid flux across a section over a specified settling time, (c) size distribution profile after a period of 25 s sedimentation, and (d) effect of the width (J of a normally-distributed size function on the sedimentation profile after 55 s settling time. (Data from [5,96] ).

29

rnm3) in lop3 mol dmm3KCl, f or an initial volume fraction @s= 0.2. Such data are well-suited to detailed studies of the effect of particle size distribution on the $-h-t profile, for example Fig. 9d, and the evolution of sediment structure with time [1011. This type of measurement is suited to most types of colloidal or mixed non-colloidal/colloidal suspensions, provided the method used to interrupt the process does not unduly bias the results. 5. CONCLUSIONS

A variety of experimental techniques are available to enable interrogation of sedimentation/creaming behaviour of opaque dispersions, although no general or simple method is suited for universal application to make these difficult measurements. The method suited to a given application depends on whether the purpose of the measurement is laboratory research, or an on-line tool in an industrial production environment, and the financial resources available. It seems likely that future developments will focus on the use of electronic/ solid state transducers (ultrasonic, capacitance, etc. ) to elucidate complex sedimentation mechanisms, particularly at high solid concentration where previously suitable instrumentation has been prohibitively expensive, or hazardous to operate. ACKNOWLEDGEMENTS

The authors are grateful to Professor M.S. Beck, Department of Instrumentation and Analytical Science, U.M.I.S.T. for useful discussions in preparing this review, and for facilities used in conjunction with a grant from the Specially Promoted Programme in Particle Technology, funded by the Science and Engineering Research Council.

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