Particle size measurement using non-invasive dielectric sensors

85

Powder Technology, 73 (1992) 85-90

using non-invasive dielectric sensors

Particle size measurement J. R. Simons*

and R. A. Williams

Department of Chemical Engineering, University

Manchester Institute of Science

in revised form June 22, 1992)

Abstract A new non-invasive technique incorporating the use of capacitance transducers has been developed which can be employed in measuring the size distribution of dilute sedimenting suspensions. This paper describes the measuring principle and compares two sets of particle size analyses, those of a sieved fraction and a polydisperse population of silica spheres, with those obtained by conventional sizing methods, based on the Andreasen sedimentation principle and on an electrical sensing zone technique using an Elzone instrument. Comparison of the capacitance technique is also made with the X-Ray Sedigraph method.

Introduction

Knowledge of the particle size distribution is the most basic requirement when dealing with particulate substances and consequently a great amount of effort has been devoted to the development of sensitive, reliable sizing methods, especially to those which involve the minimum amount of interference to the dispersion under investigation. This has resulted in the use of increasingly sophisticated and costly instrumentation. Often the sensing principle is based either on laser light diffraction, ultrasound, the use of high energy radiation, or the detection of the passage of individual particles using the Coulter electrical sensing method. An alternative approach, in which rugged, non-invasive solid-state sensors are employed to monitor small changes in solid volume fraction with time (from which the particle size distribution can be abstracted) is described in this paper. The method works independently of the optical opacity of the dispersion, is safe, rapid and readily automated. In addition, the necessary instrumentation can be constructed at relatively low cost. Measurement

principle

The use of capacitance measurement in solid/liquid systems is based on the principle that the change in the population of solids between a pair of capacitance *Present gineering,

address: University

(UK)

0032-5910/92/$5.00

Department of Surrey,

of Chemical Guildford,

and Process Surrey

GU2

En5XH,

sensing electrodes will vary the effective dielectric constant, or permittivity, E,, of the suspension and, therefore, the measured capacitance can be used to give an indication of the concentration of the solid phase present at time t. Although the use of capacitance techniques for measuring phase concentration is not unknown, the instrumentation employed in the present work utilises new technology which enables any stray capacitance and baseline drift inherent within the electric circuits to be substantially reduced, thereby allowing very small changes in solids concentration to be measured. A complete capacitance transducer system consists of two parts; the capacitance sensing electrodes and the accompanying sensor electronics (in general, a capacitance-to-voltage converter). Quite unlike conventional radiation-based devices, the instrumentation is, in principle, very simple, inexpensive and relatively easy to construct. The analyser depicted in Fig. 1 consists of an array of eight pairs of capacitance electrodes mounted vertically down the side of a sedimentation column, of length 260 mm and i.d. 25 mm. The electrodes are embedded in acrylic and are flush-mounted to the inside wall of the settling chamber (i.e. non-invasive) to ensure minimal material hang-up during settling and, hence, disruption of the suspension flow. They are also intrusive, in the sense that they are in contact with the suspension, although capacitance measurements can be made in a non-intrusive manner but at the expense of a reduced sensitivity. In normal operation the entire column is screened (or guarded) to prevent atmospheric electromagnetic interference.

0

1992 - Elsevier

Sequoia. All rights reserved

present, but also on the bulk conductivity; indeed, the complex, or effective, permittivity of a particulate suspension can be expressed in two parts by [4]:

Fig. 1. Schematic diagram of the sedimentation analyser. A, connecting pin to transducer; B, capacitance electrode; C, settling chamber (25 mmX260 mm).

Cf Rf -+

A

@ 77

Fig. 2. A typical three-terminal immune measurement scheme.

capacitance

sensor with stray-

Each electrode pair consists of a source electrode, S, connected to a driving voltage supply (often an integral part of the capacitance sensing electronics) and the detecting electrode, D, connected to the input of the system electronics, which is usually the ‘virtualearth’ end of an operational amplifier (Fig. 2). The output voltage, V,, is therefore directly proportional to the input voltage, Vi,. This type of electronics configuration is known as a ‘stray-immune’ scheme, since the stray capacitances between the electrodes and the system screen (CsI and C,,) impose little effect on the measurement of the electrode capacitance, C, (C,, is in parallel with the voltage source and C,, is ‘shortcircuited’ by the virtual-earth effect). Such a circuit is incorporated into the capacitance transducers used in the instrument described here. These transducers operate on the charge transfer principle [l], although alternative transducers are available [2]. Measurement is therefore effected by transmitting a very short charge (15 V) pulse from a source electrode and monitoring the charge recovered by the opposite detecting electrode. This procedure can be repeated sequentially for each electrode pair down the column, controlled by an interfaced P.C.-based data acquisition system [3]. The capacitance measurements obtained are dependent not only on the relative permittivities of the seperate phases

where e,, and E, are the effective low and high frequency permittivities respectively, 7 is the dielectric relaxation time, ev is the absolute permittivity of a vacuum (= 8.854~ lo-l2 Fm-l), al is the bulk conductivity (Sm-l) and w is the angular frequency of the electrical excitation frequency (o= 24. The terms in the first bracket (the Debye equation) represent the dielectric relaxation (or dispersion) process due to the polarisation of the suspension, whilst the second bracket represents the contribution from, for example, the ionic conduction of the suspension. Note that in this work, E’ has virtually no dependence on the operating frequency of the chargiug cycle, 1 MHz, since this is well below the region of dispersion of the suspending medium, centred around 17 GHz. A much simpler expression for the effective permittivity is [S]: c, = (I- 4&P + +&:

(2)

where LY=(p- l)l(p+ 1) and es and e, are the permittivities of the solid and liquid respectively. p may be considered as a shape factor, e.g. p= 2, (Y=l/3 for spheres. However, this equation is not valid for suspensions of colloidal particles in electrolyte solutions at low excitation frequencies, since it has been found [6] that very high values of ee result in such cases, much larger than the largest permittivity of the constituent components. This is probably due to the polarisation of the electrical double layers surrounding the particles. The effect can be reduced by operating at higher frequencies (Myers and Saville [7] found high permittivities existed only below 20 kHz for their system of latex particles, d,=O.191 pm, in lop4 mol dmp3 HCl). Since the capacitance transducers used in this work normally operate at 1 MHz, the effective permittivity of the suspension under investigation is assumed to follow the rules governed by, for example, eqn. (2). For a suspension of low-loss dielectric particles in a conducting fluid, the true capacitance of the suspension, C,, is related to G,, the fluid conductance by

Ul: C, = C, - O.&G,

(3)

where C, is the measured capacitance and T= is the charge pulse duration (in this case, SO ns), i.e. system conductance results in charge loss. By having a short pulse duration the effect of G, can be minimised, but

87

for accurate determination of capacitance for most dispersions measurement of conductance is required. Indeed, for a given sensitivity of transducer, there is an allowable range of system conductance above which capacitance measurement would be impossible due to saturation of the transducer [8]. Hence, the measuring technique described here may not always be suitable for sensing the presence of solids in high conductivity aqueous electrolytes, but is ideal for monitoring the dispersed phase size distribution in low conductivity solid/aqueous liquid systems, liquid/liquid emulsions and solid/organic liquid systems. Use of the capacitance measurement technique in monitoring the behaviour of complex solid/liquid dispersions has been documented elsewhere and has been shown to have no effect on the process being measured [2]. In this paper, the principle of using the same technique to obtain particle size measurements is demonstrated. The measurements are performed at low solids concentration so that sizing information can be abstracted from Stokes’ law at near-infinite dilution. Results are reported for two different types of particle population and are compared with those from two other sizing methods. The first is another sedimentation-based technique employing and Andreasen pipette, whilst the second involves an electrical sensing zone method.

Experimental Material preparation and charactetiation

Soda lime glass ballotini (Potters Ballotini, Barnsley) was selected as a source of spherical particles, scanning electron microscopy (Fig. 3) confirming that the particle population was essentially spherical in nature but occasionally contained some platey material. The apparent density of the particles (measured by liquid pycnometry) was found to be 2 448 kg mp3. Before use the particles were washed in dilute hydrochloric acid, to remove iron contaminates, and then rinsed thoroughly with high purity, resin-cleaned water. The microelectrophoretic properties of the particles were then determined in several concentrations of KC1 electrolytes [9]. The electrolyte used in this work was lo-’ mol dmW3 KC1 at pH 8.7, in which the particles exhibited a zeta potential of -78 mV (i.e. a high negative charge), indicating a stable, non-flocculating suspension. Two types of particle size population were prepared by sieving and sub-sampling standard graded batches of ballotini, in order to yield a sieve fraction of 20-32 pm and a log-normal size distribution (log mean particle size, i= 1.64, standard deviation, ap = 0.51) with a weight mean size x,=5.15 pm. These will be referred to as Samples 1 and 2, respectively.

Fig. 3. Scanning electron micrograph of the glass spheres in the sizing measurements (scale bar indicates 40 pm).

used

The sedimentation experiments were performed at a room stabilised temperature of 21+ 0.7 “C and calculations were based on liquid density and viscosity values of 1000 kg rnp3 and 1.0X lop3 Nsmp2, respectively. The dielechic sensor sizing method The particle size population to be measured was introduced to the sedimentation cell (Fig. 1) in the form of 0.123 dm3 of slurry at a solid weight fraction of 0.04, equivalent to a solid volume fraction of 0.0165. This value was shown in pre-test trials to yield reproducible measured concentration profiles. Changes in the initial solid volume fraction could be monitored at any of the eight sensing positions - in this case sensor number 3 was used, corresponding to a zone 64-88 mm below the top interface. The data collection and interpretation system was automated using a P.C. [2]. The size distribution was then back-calculated using the conventional incremental analysis method employed in Andreasen and Sedigraph-type devices, as described by Allen [lo]. This method is based on the change in mass (with time) of the sample (or sensing volume, as in this case) under investigation being related to the Stokesian velocity of the settling particles. The Andreasen pipette sizing method

For comparison, size analyses were also performed in a standard Andreasen pipette assembly (0.6 dm3

88

capacity), with the sampling tip of the pipette located 200 mm below the top of the suspension. A solids volume fraction of +s =O.Ol was used in all tests. The height of the suspension dropped 4 mm on each occasion when a 0.01 dm3 sample was removed for drying and weighing at the pre-determined time intervals. For a detailed description of the sizing technique, see Allen

4

1.2

WI-

2 s

0.9

2.7 i

2.4 2.1 E 2 e

1.8

0.6

The electrical sensing zone analyser An Elzone particle size analyser

(model 80 XY, Particle Data Ltd., Cheltenham) was used as the third sizing device. This instrument operates on the principle of the Coulter electrical sensing method, but with enhanced ‘resolution’ by providing size distribution data in 128 channels, the particle diameter ratio between the first and last channel being 25:l. However, the instrument is capable of measuring particles in the range of 0.3 to several hundred microns by the use of different orifice diameters. For the work presented here, the analyser was calibrated for 48 ,um and 240 pm diameter orifice tubes, using the standard dispersions of 5 pm and 38 pm latex particles supplied by the manufacturer. Coarser sizes were measured using the larger orifice, with fine size fractions analysed using the small orifice, the suspending electrolyte being ISOTON II (Coulter Electronics). The data were then re-calculated by combining information derived from the appropriate channels in order to match the size intervals obtained using the other two comparative methods. The tiny solid samples required for this sizing technique (to make up very dilute suspensions of < 0.05 wt.%) were prepared by grab sampling (using a spatula) from small sub-samples of the original particle population. Since this method is prone to errors associated with sampling, each population was subjected to four independent size analyses. The averaged results are presented in weight size distributions.

Results Sizing using the dielectric sensors (OS) The non-invasive sedimentation sensors yield a con-

tinuous output signal of the solids concentration over a given sensing zone. For the sensing arrangements described above, the change in concentration with time is depicted in Figs. 4 and 5 for Samples 1 and 2, respectively. Two general features are immediately apparent. First, the time taken for the finer and more polydisperse suspension (Fig. 5, Sample 2) to sediment is approximately forty times greater than for the nearmonodisperse size fraction. This is obviously due to the hindering effect of differential particle settling [ll] and to differential settling itself. Secondly, the signal

0.3 p' 1.5 0~ 0 60

180 300 Time (s)

420

Fig. 4. Data from sensor 3 showing the change in solid volume fraction with time for Sample 1.

2 1.8I 1.6

;

0.6 0.4

i

0.2 0.8LL OO 30

60 Time

90 120 150 (s)xlOz

Fig. 5. Data from sensor 3 showing the change in solid volume fraction with time for Sample 2.

appears to be much noisier for Fig. 5 than for Fig. 4, especially at very low solid volume fractions (4%< O.OOS), even taking into account the larger vertical scale used in the former. This could be due to several factors. The sensitivity of the baseline drift to temperature and power supply fluctuations, as well as changes in the fluid conductivity with time [2], may create instabilities within the capacitance transducers. This effect will be more apparent on a longer time scale. More relevant, perhaps, is the effect of differential settling in dilute polydisperse suspensions, which would result in (nonuniform) fluctuations in the number of particles within a sensing volume with time (and hence an apparently noisy signal), as fine particles are swept up by the fluid displaced by the coarser ones [12, 131. From the concentration profiles, the weight of particles passing within a known time period can be calculated and hence, using the same method as that for Andreasen pipette analysis, the percentage undersize of the largest particle present in the sample can be inferred.

89

Comparison with the electrical sensing zone and Andreasen pipette methods

Sizing results using the electrical sensing zone (ESZ) and Andreasen Pipette (AI’) methods, considering the same size intervals, are given in Figs. 6 and 7. In general, there is good agreement with the three methods, except that the ESZ did not appear to sense the same proportion of fines material below 25 pm in the case of the closely sized sample (Fig. 6). On the basis of other sizing studies [14] this may be a general characteristic of the ESZ method, possibly caused by coincidence errors (e.g. two fine particles being counted as one coarse particle). Errors in grab sampling could also lead to coarser size representation.

Fig. 6. Comparison of size measurement in terms of size vs. cumulative percent Sample 1.

methods, expressed finer than size, for

100 90

80 I 70 : 60 E 50 ; 40

Conclusions

2 30 m 2 20 2 10 0

Fig. 7. Comparison of size measurement in terms of size vs. cumulative percent Sample 2.

methods, expressed finer than size, for

TABLE 1. Comparison of percentile cumulative wt.% values of the three sizing methods, DS, AP, ESZ Sizing method

DS AP ESZ

For the polydisperse sample (Sample 2), the results from the three methods are comparable, although the DS method consistently predicts a slightly coarser size distribution. This is possibly due to cluster formation amongst the finer particles, leading to settling velocities greater than the corresponding Stokes’ velocities of the individual component particles. Kaye and Boardman [15] have noted that this phenomenon is a common source of error in size analysis techniques which involve the use of Stokes’ law in interpreting sedimentation results, since it leads to coarser size distributions being predicted. They suggested that for accurate analyses using settling suspensions the solid volume fraction should not exceed 0.0005, which would only be feasible in, say, a photo-sedimentation technique or in a dielectric sensor with minimal baseline drift. In principle, detection of very small changes of volume fraction is quite feasible using high-sensitivity dielectric sensors [16]. The sensing system used in this work was constructed primarily for general purpose measurements in the volume fraction range 0.01-1.00. In polydisperse distributions hydrodynamic clusters are more stable in the region of the mean particle size. Hence, in the size analysis of Sample 1, it is possible that the DS technique indicates more coarse particle content due to the formation of clusters of particles approximately 30 pm in diameter. The phenomenon is not so noticeable with the AP, since this technique involves the use of a lower initial solid volume fraction (1.0% v/v as opposed to 1.65% v/v in the DS) and the clustering effect has been shown [15] to reach a maximum at 2-370 v/v. The particle size distributions are summarised in Table 1 and the agreement is quite satisfactory.

Sample

Sample 2

1

10%

50%

90%

10%

50%

90%

18.1 18.9 22.2

27.5 27.0 27.7

41.0 35.6 38.5

3.2 3.0 3.0

6.6 6.5 6.4

11.6 11.9 11.9

An incremental sizing method using novel, non-invasive dielectric sedimentation sensors has been shown to offer an attractive and convenient alternative to existing techniques for sizing solid/liquid dispersions. The results obtained for two types of particle size population correlate well with those yielded by the established techniques of the Andreasen pipette and the electrical sensing zone analyser. Direct comparison of the methodology of the capacitance measurement technique can be made with that of, for example, the X-ray Sedigraph [lo]. Both operate on the same principle that particles in a dilute suspension (typically < 1% v/v) will settle at their Stokesian velocities and, therefore, by measuring the change in solids concentration with time at a particular height in a settling chamber, back-calculation will yield the particle size distribution. Whilst the use of X-rays

90

depends on the difference in the absorption coefficients of the phases present and the capacitance technique on the difference in permittivities, in theory both methods could be used in liquid/liquid as well as solid/liquid systems. The main advantages of the capacitance measuring technique over the X-ray sizing methods, however, are its safe operation (i.e. no radiation hazards) and its relatively simple and inexpensive construction. Although limited to low conductivity media, such an instrument could provide rapid size analyses for a wide range of two-phase dispersions.

Acknowledgements

permittivity at low frequency effective permittivity permittivity of bulk liquid phase permittivity of solid phase absolute permittivity of a vacuum permittivity at high frequency standard deviation dielectric relaxation time pulse duration solid volume fraction angular frequency of electrical excitation signal

References

This work was supported by the Science and Engineering Research Council via the Specially Promoted Programme in Particle Technology.

S. M. Huang, R. G. Green, A. Plaskowski and M. S. Beck, IEEE Trans. Instrum. Meas., 37 (1988) 368. S. J. R. Simons, Ph.D. Thesis, University of Manchester

List of symbols 4

C, Csl, C,, C, 4

! x j S vi, K % z

measured system capacitance stray capacitances between electrodes screen true system capacitance particle diameter detecting electrode excitation frequency of the transducers system conductance imaginary number in eqn. (1) source electrode input voltage output voltage weight mean size log mean particle diameter

Greek letters

;

index in eqn. (2) shape factor in eqn. (2)

and

5 6 7

Institute of Science and Technology, 1991. S. J. R. Simons, R. A. Williams and C. G. Xie, Advances in Measurement and Control of Colloidal Processes, ButterworthHeinemann, London, 1991, p. 107. J. B. Hasted,Aqueous Dielectics, Chapman and Hall, London, 1973. B. Bianco and M. Parodi, J. Electrostat., 15 (1984) 183. W. B. Russel, D. A. Saville and W. R. Schowalter, Colloidal Dispersions, Cambridge University Press, Cambridge, 1989. D. F. Myers and D. A. Saville, J. Colioid Interface Sci., 131 (1989)

448.

8 C. G. Xie, R. A. Williams, S. J. R. Simons, M. S. Beck and R. Bragg, Meas. Sci. TechnoZ., I (1990) 1216. 9 B. M. W. P. K. Amarasinghe, Ph.D. Thesis, University of Manchester Institute of Science and Technology, 1990. 10 T. Allen, Particle Size Measurement, 4th edn., Chapman and Hall, London, 1990. 11 R. A. Williams, B. M. W. P. K. Amarasinghe, S. J. R. Simons and C. G. Xie, Powder Technol., 65 (1991) 411. 12 R. H. Davis and K. H. Birdsell, AZChE .J., 34 (1988) 123. 13 R. H. Davis and M. A. Hassen, J. Fluid Mech., I96 (1988) 107.

14 A. Michael, Advances in Measurement and Control of Colloidal Processes, Butterworth-Heinemann, London, 1991, p. 369. 15 B. H. Kaye and R. P. Boardman, Interactions Between Fluids and Particles, Inst. Chem. Eng., London, 1962, p. 17. 16 R. A. Williams, T. M. Shi and S. J. R. Simons, to be submitted to Coil. Surf., 1992.