10 Field scanning methods of particle size measurement 10.1 Introduction Field scanning methods are those in which the size distribution of an assembly of particles is inferred from the interaction between the assembly and a measurement probe. In the simplest systems, the powder (or slurry) is probed or classified in order to generate a single point on the distribution curve. For example, one might monitor the 100-mesh percentage oversize from a mill in order to control a continuous milling operation. If the percentage increases, the residence time in the mill is increased in order that the product size remains unchanged. It is commonly found that comminution shifts the whole distribution to a finer size distribution, to form a homologous family of curves, and plotting particle size against milling time on a log-log scale generates a straight line. Knowledge of two points on the distribution curve allows one to generate the whole distribution. An alternative method for plotting such distributions is the Gaudin-Schuman plot where the cumulative weight finer than a given size is plotted against that size, with each scale on a logarithmic basis. For the majority of milled material the relationship between the two variables is linear except at the coarse ends of the distributions. The distribution is characterized by two parameters; a distribution modulus, n (slope), and a size modulus, k. Again, n remains constant for consecutive grinding of the same material. Djamarani and Clark [1] state that many industrial processes are defined by a coarse ( Q and a fine fraction (F), for example, oversize and undersize. In their example they use sieve sizes of 1400 |um and 180 |um that they fit to a Rosin-Rammler distribution. They define a curve of C+F against C/F from which the Rosin-Rammler constants can be read. Field scanning instruments are ideally suited to on-line analysis. Rapid control of crystal size from a crystallizer; granule size from a granulator;

Field scanning methods

525

product size from a milling operation; particle size from a reactor etc. can yield enormous dividends in terms of less wastage (i.e. more material in specification) and superior product quality. One problem associated with implementing this technology is the need to build an interface between the process and the measuring instrument. This often requires a dilution step that may alter the size of the particles. In the case of crystallizer control, for example, it may be necessary to remove two streams from the crystallizer and filter one so that the mother liquor can be used as the diluent. Process streams often operate at high flowrates and these have to be split in order to obtain an acceptable flowrate in the measuring device. This reduction has to be carried out with care in order to minimize sampling errors. Ideally, the whole of the process stream should be examined. Inserting a probe directly into a process line is usually not feasible due to servicing and downtime problems. It is therefore preferable to use a side-stream that can be isolated from the process stream. A sophisticated on-line analyzer can cost around $100,000 and the interface can easily double this cost. However, a 1% increase in yield can pay back this investment inside a year, making on-line size analysis very attractive. At the present time retroactive fitting of size analyzers is often necessary and one is often faced with space limitations. Designing these units into new process lines greatly reduces cost and makes their introduction more attractive. 10.2 Single point analyzers 10.2.1 Static noise measurement This technique has been applied to the measurement of the average size of milled silica powder (size range 2 to 5 |Lim) suspended in air [2]. A continuous sample is drawn from the product stream into a sampling probe and diluted with an air injector that also provides the driving force. The sample stream is then passed through a 'uni-flow' cyclone that splits the sample into two streams; a low concentration 'fine' stream and a high concentration 'coarse' stream. As the relative mass flow rates of the two streams depend strongly on the size distribution of the feed (at a given flow rate), an average size may be found from a measure of the two concentrations. Most particles suspended in air carry an electric charge, particularly if they have passed through a highly turbulent process. A probe inserted into the stream will detect this charge as an AC voltage that is strongly

526 Powder sampling and particle size determination

dependent on concentration. The system was calibrated by feeding in samples of known mean sizes and recording the signals these generated for comparison with signals from unknown samples. 10.2.2 Ultrasonic attenuation The attenuation of ultrasound by a slurry depends upon the particle size distribution and concentration of the solid phase. In order to separate these two variables it is necessary to carry out analyses at two different wavelengths, one of which is strongly dependent on concentration and the other on particle size distribution. The attenuation is also dependent on the spacing of the transmitter and receiver and other physical parameters in a predictable manner [3,4]. The first commercial ultrasonic on-line particle size analyzer was developed in the 1970's and was based on the measurement of ultrasonic attenuation at two frequencies with an empirical model to predict particle size and concentration [5]. Instruments based on this patent are available as the Denver Autometrics PSM-100, 200, 300 and more recently 400. These are pre-calibrated for the selected mesh size (100, 200, 300 and 400) and the mesh read-out is proportional to the mass percentage less than this. These instruments can operate at extremely high concentrations, up to 60% by weight, and have found their widest application in mineral processing plants for improved grinding circuit control. A major problem in the early development of the Autometrics' system was that traces of air could lead to substantial attenuation losses. The air must be stabilized or removed to allow accurate measurement of particle size. Removing the air with a device that utilizes a combination of centrifugal force and reduced pressure solved the problem. The need to remove air increases the cost of the overall system significantly and makes it an expensive instrument when compared with other instrumentation often installed in grinding circuits. Nevertheless, it appears to be perfectly compatible with other approaches when its inherent reliability and longterm stability as an accurate size analyzer is taken into account. Several articles have been written describing applications of the PSM systems [6-9]. The limitations of the system 100 are: (a) the percentage solids should be less than 60% by weight (b) the particle size distribution should be within the range 20% to 80% less than 270 mesh and (c) the slurry particles should not be magnetized. The PSM systems 200 and 400 are later instruments designed to overcome these limitations.

Field scanning methods

52 7

10.2.3 P-ray attenuation Instruments have been described that employ p-ray attenuation [10-15]. The accuracy of these devices is limited by their sensitivity to changes in feed density [16]. In order to calibrate it is necessary to re-circulate slurry samples in a closed loop at a number of dilutions for each slurry system, sieve analyses being carried on representative sub-samples. The signals from a scintillation counter can be used to control mill feed rate in order to compensate for changes in feed ore, grindability and feed particle size. Accuracies of 2% to 3% have been reported on Cornish granite, nepheline systems and copper and iron pulps in the size range 20 to 105 ^im [17,18]. 10.2.4 X-ray attenuation and fluorescence This sensor is based on the comparison of the absorption of two x-ray beams, one of which is sensitive and the other insensitive to variations in particle size [19-21]. Each sensing head is specific to a particular system since the relationship between the two beams is dependent on the composition of the solids in the slurry stream. The technique is limited to x-ray opaque material. Von Alfthan [22] describes an on-stream x-ray fluorescence system that consists of two flow cells through which the slurry passes. In the classifying flow cell, the slurry flows in a straight path behind a window; it then strikes an obstacle that causes slurry mixing as it enters a turbulent flow cell. X-rays excite the slurry in both cells and the resulting fluorescent radiation is a measure of particle size. The system, sold as the Courier 300, measures both x-ray scattering and x-ray fluorescence and is intended primarily as a composition monitor. The measured data can be analyzed to give chemical composition, solids content and maximum particle size. 10.2.5 Counter-flow classifiers Two instruments have been developed for on-line measurement of flowing powders coarser than 100 |Lim in size [23-26]. In the first instrument a side stream of solid particles from a process line is fed into an air elutriator that separates it into an oversize and undersize stream. The particle flow rate into the elutriator is measured and the cut size for the elutriator adjusted so that the flow of oversize particles out equals 50% of the inlet flow. The elutriator cut size is then equal to the average size of the powder. In the second instrument the flow rate is varied and the signal ratio of the two

528 Powder sampling and particle size determination

flowmeters is inputted as the j;-axis of an x-y recorder. The x-axis is reduced to the cut size for the elutriator. A sweep time of 40-60 s at flow rates of 2.4-3 g s"^ gives a cumulative distribution in the size range 100700 ^m. 10.2.6 Hydrocyclones An ideal on-stream sizing device would sample the whole of the stream and not include any special instrumentation. The nearest approach is to use a classifying hydrocyclone as these are easily installed and often form part of an industrial plant. By measuring the flow rates and pulp densities, and assuming a size distribution law for the feed, a computer program can be written to give the modulus and index of the feed. Under normal operating conditions the present state of the theory of cyclone operation renders this impracticable [27] although it can be used under favorable conditions [28]. Lynch et. al. [29] proposed that the percentage less than some chosen mesh size in the cyclone overflow could be related directly to the d^^^Q parameter of the cyclone, provided that the size distribution of the feed to the cyclone does not change appreciably. In closed production circuits there may be marked changes in the size distribution of the cyclone feed and an empirical relationship has been developed [30]. The application of this technique requires very thorough analysis of the circuit and repeated checking of empirical equations. An alternative approach has been to accept the inherent difficulties of sampling and install smaller, more precise, classifiers alongside the production classifiers [31]. Tanaka has also investigated the use of hydrocyclones for on-line analysis [32]. 10.2.7 The Cyclosensor This is a batch size analyzer [33] (Figure 10.1). An extremely dilute sample of milled ore is introduced, at a constant flow rate, to a coarse separator in the form of a tangentially fed cylindrical screen. The coarse fraction is allowed to settle and the fine fraction is further separated with an efficient hydrocyclone into a fine and a very fine fraction. The very fine fraction is discarded and the fine fraction is allowed to settle. The ratio of the times taken to fill the coarse and fine fraction collection vessels to indicated levels can be related directly to the particle size distribution. The cyclosensor has a sensitivity whereby a change of ±1.8% passing 100

Field scanning methods

Very fine

Metal core

Cylindrical screen

Coarse solids

529

Efficient cyclone

Fine solids

Fig. 10.1 The Cyclosensor. mesh can yield a 7% change in the ratio of the settling times. The reproducibility is such that for the same feed rate of the same solids the ratio of times remains constant to better than 1% and an increase in feed rate of 30% has no effect on the ratio. A patent has been issued on an instrument operating in a similar way [34]. It consists of a particle suspension sampler, a settler and a weight or volume sensor. Particle size distribution is determined from sensor output and the time for the settling particles to pass the sensor. 10.2.8 Automatic sieving machines This automatic wet sieving machine determines a single point on the size distribution curve in a few minutes without the need to dry samples [1,16]. The sieving vessel is first filled with slurry and topped up with water to a precise level to allow accurate determination of the mass of solids added (wi) by application of Archimedes' principle. The fine fraction is next removed from the vessel through a discharge valve. Screening is hastened by propeller agitation and with ultrasonics to maintain the sieve mesh free

530 Powder sampling and particle size determination

of pegged material. The weight of the residue (^2) is determined by further application of Archimedes' principle, and the fraction coarser than the screen size is given directly by (W2AV1). It is interesting to note that the capacity of the rapid wet sieving device, expressed as screen charge mass per unit screen area, is more than an order of magnitude higher than that normally recommended for conventional dry test sieving [16]. A description has been given of a technique using a two-cell compartment divided by a screen [35]. The slurry density in the two compartments is determined using nuclear gauges to provide a single point on the distribution curve. A fully automatic sieving machine that can determine seven points on the size distribution curve has also been described [36]. In this technique a pulsating water column is used with the application of ultrasonics and the charges are dried and weighed automatically. 10.2.9 Gas flow permeametry Air, whose pressure varies sinusoidally with a specific amplitude and frequency, is forced through a moving bed of powder [37-40]. At a known height in the bed the attenuated and retarded air pressure is tapped by a pressure transducer, so that the amplitude and pressure drop are measured after being separated into the pulsating and steady flow components. The amplitude attenuation of the pulsating pressure is related to bed porosity and specific resistance. Using the Carman-Kozeny permeametry relationship the average size of particles can be evaluated. The bed is packed into a test cylinder and discharged by a vibratory feeder at the bottom after measurements have been taken. This enables a new bed to be packed and measured within minutes. Air permeability has also been used to determine the surface area of cement [41]. A porous piston compresses the sample of cement into a cell. Air is passed through a bottom porous plate, through the sample and porous piston, into the atmosphere. The inlet pressure is automatically adjusted and recorded to give a known air flowrate and the surface area is evaluated from the inlet pressure. The cell is emptied automatically becoming ready for the next test. Weiland [42] used a similar idea but based on the Blaine permeability method. An automatic weigher produced a packed bed of powder, of known voidage, in a standard cell. Air was drawn through the bed by the passage of water from one reservoir to another. After a certain volume of air had passed through the bed, measured by a certain volume of water flowing, the time required was converted to an electrical proportionality

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531

signal. The measurements were repeated every 4 min and the signals used to control the feeder to a grinding mill. 10.2.10 Correlation techniques Correlation techniques can be used with signals from the attenuation of radiation, such as light, but these are mainly used for low concentration systems. The signals from two sensors in close proximity, situated in a flowing stream of slurry, are cross-correlated to give an autocorrelation function. Stanley-Wood et. al [43,44] found that this function obtained from alternating current transducers, initially designed to measure mass flow rate, gave a measure of the particle size of a sand/water mixture. A measure of mean size could be achieved by allowing the normalized signal from a correlator to be divided in two and passed through either high or low pass filters. This results in an inequality, due to variations in frequencies from large and small particles; the ratio of this inequality can be used to determine mean size after calibration. The particle size was between 70 and 2000 \\xxv with a concentration between 10% and 30% by weight. k Reflected

Vay Incident i^y\

Fig. 10.2 Interaction of a ray of light with a spherical particle. 10.3 Light scattering and attenuation 10.3.1 Introduction When light strikes a particle, some of it is absorbed, some is refracted, some diffracted and some transmitted (Figure 10.2). The amount absorbed depends upon the optical properties of the particles and surroundings and

532 Powder sampling and particle size determination

is also a function of the cross-sectional area of the particles. The absorption, or turbidity, can be used to determine a mean particle size and, in conjunction with sedimentation, a size distribution. For very small particles however, the laws of geometric optics no longer hold and a correction has to be applied in the form of an extinction coefficient, K, which is defined as the effective particle cross-section divided by its geometric cross-section. This may be determined theoretically over the whole particle size refractive index domain using Mie theory or, over limited ranges, with modified theories. Other interactions between the particles and the incident radiation, such as state of polarization, light flux at a fixed angle to the direction of the incident beam and angular spectra can be used for particle size determination. Interaction between the incident and diffracted radiation gives rise to interference phenomena with characteristic maxima and minima in intensity [45]. In order to describe fully the scattering pattern it is necessary to assume that the particles are optically homogeneous and spherical and, in order to give independent, incoherent scattering, in a dilute random arrangement. 10.3.2 Turbidity measurements Turbidity has been widely used for determining the particle size distribution (PSD) of particles in suspension, since it is experimentally simple, can be used over a wide size range and does not disturb the system under investigation. It is also fast, reproducible and inexpensive. If a light beam falls on an assembly of macroscopic particles the attenuation is given by: /-/oexp(-aA2Z)

(10.1)

where / is the transmitted intensity when a light beam falls on a suspension of particles of projected area a and number concentration n and traverses it by a path of length L\ /Q is the transmitted intensity when no particles are present. Turbidity gives a measure of the attenuation of a beam of light passing through a suspension. More generally, equation (10.1) may be written: I = lQQxp{-KanL)

(10.2)

Field scanning methods 533 where the extinction coefficient, K, may be evaluated theoretically thus permitting the determination of particle size. If c^ is the volume concentration: (10.3)

^v=~^d^

where d^ is the mean volume diameter. The projected area (a= an) of an assembly in random orientation is: (10.4)

a = —nd} 4 ' where d^ is the mean surface diameter; Hence:

^

I = IQ exp

3KrO 2d,sv

(10.5)

J

where d,,, is the surface-volume mean diameter. Hence: / 1 \ / = /Q exp —Kc^S^L V

/ = /Q exp(-

(10.6)

4 TI)

(10.7)

where x is the turbidity. For a suspension of non-spherical, non-monosize non-adsorbing, isotropic particles, in the absence of multiple scattering: X --

2d„,

(10.8)

The surface volume mean diameter for a suspension of spherical particles is given by:

Y,d^f(d)M _ 0

Y^d^f(d)M 0

(10.9)

534 Powder sampling and particle size determination

Equation (10.8) can be written in the form: 00

T = ~\Kd^f{d)dd 4o

(10.10)

This is a Fredholm integral equation of the first kind. The regularized solution to this equation has been applied to the measurement both for the moments and the size distribution of a wide range of latices [46]. K has been given by van de Hulst [45] in terms of particle size/refractive index domain. Mie theory applies to the whole domain but in the boundary regions simpler equations have been derived. For dilute suspensions of particles smaller than 0.04 |Lim in diameter, the turbidity can be calculated from the equation:

r=

3271^ ( w - i f ^ - ^ /

(10.11)

c is the mass concentration, A^ is the Avogadro Number and/is very nearly equal to unity [45 p396]. Turbidity measurements have been carried out on non-uniform latices and it is suggested that this is one of the most useful of the light scattering techniques for average size determination [47]. PSD can be estimated from the turbidity at different wavelengths provided the other variables are known. Kourti et. ah [48] assumed a log-normal PSD and observed that the parameters of the estimated distribution were so highly correlated that an infinite number of distributions could explain the data. However, all the alternative solutions were found to have the same weight average (surface-volume mean) diameter. With turbidity ratio, the ratio of the turbidities at two wavelengths, one of which is chosen as basis, is used. This has been successfully applied with large particles [49], (0.650.1 |Lim). Nicomp Model 380/L is designed for on-line monitoring either by itself or in combination with the Particle Sizing System AccuSizer. These instruments are available from Particle Sizing Systems. Otsuka Photal is a dynamic light scattering spectrophotometer that provides sub-micron sizing in the 3 nm to 3 |Lim size range and also provides information on the shape of polymers. Wyatt QELS is a compact add-on instrument that can be connected to a Dawn® Eos or a miniDawn Tristar in order to determine particle sizes and their distributions. The combined system gives the ability to size very small particles (under 10 nm), as well as very large particles on-line after they have been separated by some kind of fractionation. The Wyatt QELS comes with the ability to measure the correlation function at 18 angular positions. In the microliter batch mode, the system collects data from small samples that have been injected into special blackened cuvettes. Unfractionated samples produce complex correlation functions whose

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departure from exponential decay arises from the presence of heterodisperse components in the suspension. In the flow mode, the instruments may be used to collect, simultaneously, the dynamic and classical light scattering data from which the molar mass and root mean square radii are calculated from each slice (See section on fractionation). For the mini-Dawn Tristar, dynamic light scattering signals are only collected from the 900 location, whereas for the Dawn Eros dynamic light scattering signals can be collected at any one of its 18 detector locations. 10.14.12 Discussion The basic theory and discussion of results are covered in papers by Thomas [308]. who uses a Brookhaven Instrument Fiber Optics QuasiElastic Light Scattering System (BI-FOQELS) with dynamic light scattering obtained using the BI-DLS and diluted samples. An autodilution unit has been described to analyze on-line particle growth during a polymerization process [309]. The results compared favorably with off-line dynamic light scattering and on-line turbidimetric data [310]. Several data analysis software packages are available and average sizes generated by these are not comparable [311-313] De Jaeger et.al. [314] carried out inter-laboratory tests using polystyrene lattices with particle sizes ranging from 30 nm to 2 \xm. They concluded that reliable particle sizes could be obtained for diameters less than 0.5 |Lim. In the range 0.5 to 1 |um this was only possible within a very narrow range of concentration. For the largest size investigated (about 2 jLim) the measurements were less reliable. In comparison tests, using standard latex particles, it was found that DLS gave data that is approximately 0.005 |im larger (0.064 |Lim) than electron microscopy and light turbidity methods, i.e. 0.059 ± 0.002 |Lim. In a comparison between the Coulter N4 and the Malvern Autosizer it was found that both instruments gave good results with monodisperse latices [315. For bimodal distributions, the two modes were not always detected and, if they were, the locations of the modes were incorrect [316]. Koehler and Provder [317] sized monodisperse PMMA latexes with a range of instruments: Disc centrifugal sedimentation (DCP), sedimentation field flow fractionation (SFFF), hydrodynamic chromatography (HDC), photon correlation spectroscopy (PCS), turbidimetry and transmission electron microscopy (TEM). TEM gave the smallest sizes, DCP and SFFF were in fair agreement in the center and PCS the highest sizes.

602 Powder sampling and particle size determination

In an evaluation of a range of instruments Lange [318] stated that turbidimetry appeared the most reliable approach to average size determination, whereas ultracentrifugation, DCP and TEM with image analysis were superior for determining size distributions and polydispersity. Lee et. al. [319] compared FFF, PCS and TEM for sizing acrylic latexes. They stated that FFF is a useful tool for accurately determining mean size and size distribution due to its simplicity and ease of operation. PCS provided reasonable data for small diameters and narrow distributions but suggested that multi-angle analysis was needed for larger particles and broader distributions. Multi-angle PCS was also preferred by Bryant et.al [320,321] for measuring multi-modal PSD's, and they showed that accuracy increased with increasing number of angles. Four instruments were evaluated using eight polystyrene latexes, ranging in size from 0.039 to 0.804 |Lim, from Duke Standards [322]. The instruments were: Matec CHDC-2000, Brookhaven BI-DCP, Coulter N4Plus (PCS) and Hitachi H-7000 FA (TEM). TEM gave average sizes close to nominal values, CHDF gave values slightly larger than nominal except for the lowest size where it gave a value of 0.046 |Lim, PCS and DCP gave reasonable values. The measurement time was unduly protracted with the DCP for the finest fraction, the generated size being 0.70 jiim for a run time of 2 hours reducing to 0.056 |am when this was extended to 6 hours. It was found that both PCS and CHDC gave much broader distributions than DCP and TEM. For polydisperse (bi- and tri-modal) CHDF and DCP provided the most accurate distributions whereas PCS failed to capture the whole distribution. Photon correlation spectroscopy measurements for growth rate, together with a quartz crystal microbalance for mass deposition, have been integrated into a single platform to permit simultaneous in-situ real time measurement at times and temperatures representative to those found in aviation fuel systems [323]. Kroner et. a/.[324] compared DLS with static light scattering for determining soot particle size in a premixed flame. They concluded that static is preferable to dynamic since the latter procedure requires detailed information about the flame. 10.14.13 Spectral turbidity Beckman DU 7500 spectrophotometer has been used to determine the size distribution of "monodisperse" latex in the size range 200 to 800 nm, to

Field scanning methods

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Study agglomeration during crystallization and attrition of potassium sulphate. A polychromatic light beam from a uv source passes through a silica fiber to a sensor immersed in the suspension. After crossing the measurement zone the transmitted light passes through a fiber to a holographic grating that splits the light into a spectrum that falls on to a 256 photodiode array. Using Mie theory the spectral turbidity yields the particle size distribution of the powder in suspension [325]. 10.14.14 Diffusion wave spectroscopy (DWS) DWS addresses dynamic light scattering in the multiple scattering concentration range. Pine et. al. [326] describe the theory for the technique and it has been applied to the determination of mean size and polydispersity [327,328]. The method has also been used for on-line measurement of concentrated suspensions [329]. 10.14.15 Photon migration In photon migration, an intensity-modulated light beam is launched into the sample and the photons diffuse through the sample and are detected [330]. The transmitted signal is attenuated and phase shifted relative to the incident beam. Measurement of the phase shift and attenuation as a function of modulation frequency yields scattering coefficient and particle size. Mie scattering theory is applied to generate particle size. The theory can be extended to higher concentration regimes. The particle size distribution is determined by determining the scattering coefficient at one wavelength over a range of known particle concentrations. 10.15 Turbo-Power Model TPO-400 in-line grain size analyzer Nisshin developed this instrument for the cement industry. At preset times it automatically samples a few kilograms of material and feeds it into a turbo classifier. The fines are fed into a micron line that determines the Blaine number for the powder. 10.16 Concentration monitors Monitek instruments measure the concentration of suspended solids in a liquid by shining a light through the stream and detecting the amount of light that is scattered by the suspended solids. The scattered light is seen as turbidity hence the name turbidimeters. Suspended solids scatter light

604 Powder sampling and particle size determination

in all directions so that there are many potential viewing angles; 90° sidescatter instruments are called nephelometers. Forward scatter instruments sample a more representative cross-section of a process stream and can monitor as wide range of particle sizes from 0.01 to 100 \\m. For accurate measurement Monitek uses a ratiod forward scatter intensity where the scattered intensity is divided by the direct beam signal. 10.17 Shape discrimination The morphology of particles is an important characteristic that can seriously affect powder handling and end-use properties. Off-line techniques are often not suitable for monitoring industrial processes since extracting the particles from the process can alter their shape, e.g. particles taken from a crystallizer may fracture or aggregate. To resolve the problem an in-line camera, capable of imaging crystals produced in a commercial crystallizer, was developed [331]. The instrument is based on a borescope and video camera that fits inside the housing of a laser backscatter probe, which installs in a standard ball valve. A strobe light is used to "freeze" crystal motion. Crystal features seen directly include shape, surface roughness, inclusions and transparency. The information content of the uv/vis spectrum of sub-micron and micron size particles yields information on the size, chemical composition and shape of the particles [332]. The angular dependence of the scattered intensity is given by the Rayliegh-Gans-Debye (RGD) theory. The form factors for various particle shapes were calculated as a function of the angle of observation ^and wavelength X of the incident light. Comparison of the scattering intensities for particles with different shapes showed that each differently shaped particle had a unique surface pattern thus suggesting the possibility of selecting combinations of X and ^to enable shape discrimination. 10.18 Miscellaneous 10.18.1 Back-scatter intensity A relationship has been derived between average particle size and concentration and the back-scatter intensity of a light beam entering a slurry of non-transparent particles [333]. Concentrations used were 0.3 to 2.5% and the average sizes were 40 to 1200 |im. The light source and detector were built into one tube that was mounted on the wall of a 1 liter

Field scanning methods 605

vessel that contained an agitated suspension of the particles under test. The derived relationship took the form: ib, -h.={hm-h.)exp(kcPd'^)

(10.45)

The suffixes refer to the back-scatter intensity from; b^ = total, b^ = container walls, b^ = maximum possible. For aluminum silicate, experiment yielded/? = 0.77, q = 1.67, k = 0.20. In a second paper [334] the technique was extended to on-line. A similar technique to the above, but using ultrasonics, has also been described [332,336]. 10.18.2 Spectroscopy photo-acoustic (PAS) and photo-thermal (PTS) The surface of a specimen may become heated through irradiation, the degree of heating depending on the material's absorption coefficient at the particular wavelength of radiation. A wavelength scan across a suitable part of the electromagnetic spectrum thus causes temperature changes that reflect the adsorption spectra at the point of illumination. In PAS the heating serves to increase the pressure inside a small chamber in which the sample is situated, being irradiated through a window. A recording of the pressure variations versus wavelength of illumination reflects the absorption spectrum of the material. In PTS one records the increase in thermal emission from the sample induced by irradiation. PAS techniques require samples to be placed in a spectrophone for analysis. PTS methods allow constant free on-stream inspection at a distance. Particle size may be inferred from the signal level. Since specific surface increases with decreasing size the signals also decrease. A discussion of these techniques has been presented by Kanstad and Nordal [337]. 10.18.3 Transient electric birefringence A dilute suspension of electrically and optically anisotropic colloidal particles becomes birefringent when subjected to an electric field. In random orientation the suspension is optically isotropic but when the grains align with a uniform electric field the suspension becomes anisotropic; in particular the effective refractive index of the ordered suspension parallel to the field direction differs from its refractive index

606 Powder sampling and particle size determination

perpendicular to the field. This double refraction, or birefringence, has been used for evaluating the size distribution of sols in solution. Experimentally, a colloidal system, in random orientation, is illuminated with polarized light. The system is subjected to an electric field that aligns the particles due to the interaction between the field and any permanent dipole or electrical polarizability of the particles. The birefringence grows as the particles align; when the field is removed the birefringence decays as the particles revert to random orientation. For a monodisperse suspension the decay rate can be described by a first order rate equation. For a polydisperse suspension the decay rate is a sum of exponentials. Measurement of the decay rate permits computation of particle size [338]. Haseler and Hinds used this procedure to determine the size distribution of anisometric silver halide crystals using an instrument that they developed called an electric field birefringece. They found that the technique was capable of good accuracy and high precision [339]. 10.18.4 Crossed lasers A description of a crossed laser beam technique for particle sizing and its application to shock tube experiments was presented by Waterson and Chou [340]. 10.18.5 Frequency domain photon migration A method for on-line monitoring of particle size distribution and volume fraction in real time using frequency domain photon migration measurements (FDPM) has been described. In FDPM the time dependence of the propagation of multiply scattered light provides measurement of particle size distribution and volume fraction. The technique has been applied to a polystyrene latex and a titanium dioxide slurry at volume concentrations in the range 0.3 to 1% [341]. FDPM consists of launching sinusoidally modulated light into a scattering medium at a single point source and detecting the modulated light at another point some distance away from the source. The photon density wave is attenuated and phase-shifted relative to the incident signal as it propagates through the scattering medium due to the scattering and adsorption properties of the sample. These properties can be measured by fitting the phase shift and modulation to the appropriate solution of the optical diffusion approximation, which describes the transport of light in random media. Particle size distribution and volume concentration can be

Field scanning methods

607

determined from multi-angle measurements of FDOM and determination of the isotropic scattering coefficient. The technique is fast and the equipment relatively inexpensive. Moreover, since photon migration measures the time it takes for light to travel through the sample rather than the intensity of the detected signal, it is self-calibrating. 10.18.6 Laser induced incandescence (Lll) Aerosol particles are heated close to their evaporation temperature by a high energy laser pulse and start to emit thermal radiation. As the particles cool, mainly by heat transfer to the carrier gas, their thermal emission intensity decreases with time. Due to their higher heat capacity large particle cool more slowly than small ones and the cooling time can be used as a measure of particle size. Early applications mainly concentrated on average parameters for soot particles in flames [342] and this was extended to determination of a detailed characterization of the size distribution and internal structure of aerosols at room temperature [343]. The results showed good agreement with TEM and DMA data. Particle sizes were in the nanometer range at number concentrations down to 103 cm'^. Other accessible parameters are the diameters of agglomerates, the volume fraction and the mean number of primary particles [344]. LII has been applied ti in-situ measurement of primary particle size on the manufacture of carbon blacks [345]. The system has also been applied to the measurement of nanosize particles on soot and vehicle exhausts. Measurements on carbon black particles gave data which correlated well with product properties. Tests with titanium dioxide and metal powders were encouraging. [346] 10.18.7 Spectral transmission and extinction Cemi used spectral transmission and extinction using UV, visible and near IR to measure slurry particle size distributions with undiluted continuous flow [347]. The method uses multiple linear detector array spectrometers. It also uses multiple sample cells of different optical depths optimized for a specific spectral range, multiple optical paths and multiple linear detector arrays.

608 Powder sampling and particle size determination

10.18.8 Turbiscan multiple light scattering measurements Turbiscan On-Line monitors and quantifies the effects of process variables in dispersed systems. It operates in the volume concentration range from 0 to 60% and the size range of 0.1 to 5,000 |am. The vertical scan macroscopic analyzer consists of a reading head that moves along a flat bottomed cylindrical cell to scan the entire sample length. The optical sensor consists of a pulsed near-infra-red light source and two synchronous detectors: The transmission detector monitors light transmitted through the suspension and the back-scattering detector receives the back-scattered light at 135°. The optical sensors acquire transmission and backscattering signals in from 0.1 to 10 seconds, every 40 |Lim along the sample tube for a maximum of 80 mm, and these signals are digitized and displayed by the software indicating real-time changes in transmission and backscattering intensities. These parameters are directly related to particle size and volume concentration. Turbiscan Lab measures concentrated suspensions at up to 95% by volume. The mean particle diameter can be calculated over the size range 0.05 to 1000 |im. Turbiscan Ma 2000 measures the destabilization of concentrated dispersions and determines the mechanisms driving it. The ma 2000 is used to improve formulations, document stability tests and shorten stability test time. Anisotropic particles have been measured using a variety of techniques and correlation between them was found to depend on particle morphology [348]. For cylindrical glass fibers photocentrifuge data gave good correlation with image analysis using the Turbiscan, whereas for platelets laser diffraction gave the best correlation. The correlation between Turbiscan for flake-like mica was found to be very good whereas the photocentrifuge gave better agreement with rod-like copper oxalate. In both cases some information from the image analysis data was required in order to make assumptions to simplify the deconvolution data of size and shape from the collected data. References 1 2 3 4

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