Field Scanning Methods of particle size measurement
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Field Scanning Methods of particle size measurement

DisciplinaProcessamento de Minerais I211 materiais2.062 seguidores
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out to monitor the wet grinding of submicron color 
pigment using diluted, extracted samples. Further work was proposed to 
investigate the effect of particle shape. 
A redesign of the FBR-sensor was performed to reduce the 
measurement volume and increase the upper volume concentration level to 
1%. The improvements also permitted a low number concentration to be 
monitored (<10^ particles cm&quot; )^ so that the instrument could be used in a 
stream-scanning mode and as an in-line counter to monitor particles in 
10.3.7 Optical back-scattering 
The mixing process of pesticide dispersion in a spray tank mounted on a 
tractor was monitored using optical back-scattering probes mounted in the 
tank [89]. A granulated powder was fully dispersed in 20 s whereas a 
powder product took 4 min. 
10.3.8 Transmission fluctuation spectroscopy 
A transmission signal measured on a flowing suspension of particles shows 
significant fluctuations which contain complete information on particle 
size and concentration. Details have been published in three parts [90-92]. 
In parts one and two the basic properties were studied for a beam of 
uniform intensity. The theory was extended in part three to a Gaussian 
beam with experimental tests to follow. 
10. 4 Light scattering theory 
10.4.1 The Rayleigh region (d« X) 
In the Rayleigh region the intensity of the scattered radiation in a direction 
making 6 with an incident beam of unit intensity is given by [45]: 
2^Y(l + cos^ )^ 
^^ I ^ ^ ( 1 0 . 1 4 ) 
\^m J Ir&quot; 
where a is the particle polarizability, r is the distance from the particle to 
the point of observation and X^ is the wavelength of the incident radiation 
in the medium surrounding the particle. 
540 Powder sampling and particle size determination 
The intensity is the sum of two terms: 
L, = \cc\ 2n 
\ 4 
and h=M 
cos^ <9 
which refer respectively to the intensities of the vertically and horizontally 
polarized components. For spheres: 
2 3(m-\)V (10.15) 
Equation (10.15) has been applied to very small particles but is more 
relevant to the size determination of molecules. For m-\->Q 
a = ( » , ^ - l ) ^ . 2 ( \u2122 - , ) ^ (10.16) 
where m is the refractive index of the particle relative to that of the 
surrounding medium and Fis the volume of the particle. 
10.4.2 The Rayleigh-Gans region (D < A) 
The Rayleigh-Gans equation for the angular dependence of the intensity of 
the scattered light is given for spherical particles of low refractive index by 
the equation [45]: 
j0=h \u2014{smu - ucosu) (l + cos^^) (10.17) 
Again, the two terms in the fmal brackets refer respectively to the 
intensities of the vertically and horizontally polarized components, /Q is the 
intensity of the incident beam, D is particle diameter and: 
2TID . e 
u = sm \u2014 
A^ 1 2 
and k = 2n_ (10.18) 
Equation (10.17) reduces to equation (10.14) when the middle term is 
equal to one. The scattering pattern is however modified by this term, thus 
Field scann ing m ethods 541 
enabling a size determination to be carried out in the Rayleigh-Gans 
region. Differentiating equation (10.17) with respect to u and putting 
d/^dw = 0, for minimum intensity gives: 
sin u-ucos u = 0 (10.19) 
and, for maximum intensity: 
3wcos u - u^sin u -3sin u =0 (10.20) 
The first minimum is at w = 4.4934 radians corresponding to: 
- ^ s i n 4 = i : ^ = 0.715 (10.21) 
X^ 2 2n 
Similarly the first maximum occurs at: 
\u2014 s i n ^ = 0.916 (10.22) 
A graphical solution for all maxima and minima has been determined by 
Pierce and Maron [93] who, together with Elder [94,95] extended 
equations (10.21) and (10.22) beyond the Rayleigh-Gans region, 
{m-l^' 0) to 1.00 < w < 1.55, deriving the following formulae: 
\u2014 s i n ^ = 1.062 - 0.347m (10.23) 
\u2014sin ^ = 1.379 - 0.463m (10.24) 
These equations give the positions of the first intensity minimum and 
maximum respectively. 
The range of validity of these equations has been investigated by 
Kerker [96]. The angular positions determined experimentally were 
found to depend on concentration hence it is necessary to take reading at 
several concentrations and extrapolate to zero concentration. This 
concentration dependency has also been noticed with depolarization and 
dissymetry methods becoming negligible only when particle separation 
exceeds 200 radii [97]. 
542 Powder sampling and particle size determination 
10.4.3 High order Tyndall spectra (HOTS) 
When a dilute suspension of sufficiently large, mono-disperse, spherical 
particles is irradiated with white light, vivid colors appear at various angles 
to the incident beam. The angular positions of the spectra depend on m 
and A hence they may be used to determine particle size in colloidal 
Since the red and green bands predominate it is usual to observe the 
ratios of the intensities of the vertical component of the red and green light 
in the scattered radiation as a function of 9. When these ratios, R = 
r^ed^ C^Teen ^^^ plotted against d, curves showing maxima and minima 
appear, the maxima being the red order, the minima the green. Smaller 
particles yield only one order but the number of orders increases with 
increasing particle size. 
HOTS have been studied extensively in monodisperse sulfur solutions 
by La Mer [98-101], by Kenyon [102], in aerosols by Sinclair and La 
Mer [103], in polystyrene latices by La Mer and Plessner [105] and in 
butadiene latices by Maron and Elder [106]. The following equations 
derived by Maron and Elder for the angular positions of the first red and 
green order, 0^^ and 0^^ are particular examples of equation (10.22). 
^ 1 = 0.2300 (10.25) 
-0.3120 (10.26) 
Pierce and Maron [107] show that the angular positions of the red orders 
are identical with the angles at which minima occur in the intensity of the 
scattered light when the incident light has a wavelength of y .^ Similarly, 
the angular positions of the green orders coincide with the angles at which 
minima occur with incident light of wavelength A/. Consequently, for the 
same effective incident wavelengths, minimum intensity and HOTS 
represent equivalent measurements. For equations (10.25) and (10.26), 
solving with equation (10.23) with m= 1.17 gives: 
1.062 - 0.347(1.17) = 0.2300/^ 
.*. /^= 0.3506 jLim (0.4673 jum in vaccuo) 
Field scanning methods 543 
1.062-0.347(1.17) = 0.3120/A; 
.'. A'^=0. 4756 |am (0.6340 jum in vaccuo) 
This method is qualitative unless A^ and /^ are known. 
The above equations yield weight average diameters. With increasing 
m the evaluation of D becomes more difficult due to reduction in the 
intensity of the maximum and broadening of the peak. The method has 
been used for the size range 0.26 to 1.01 |Lim [108]. 
10.4.4 Light diffraction 
The far-field diffraction pattern of an assembly of particles yields 
information concerning their size distribution. For particles dispersed on a 
transparent slide the geometrically scattered part of the incident beam may 
be eliminated by coating the slide with aluminum and then removing the 
particles. The particle size distribution of the particles can then be 
determined from the resulting far-field diffraction pattern [109-112]. This 
effect was utilized in the Talbot diffraction size frequency analyzer (DISA) 
[113] that used a series of interchangeable filters to determine the number 
size distribution of the resulting apertures. Talbot later described a filter 
that transmitted amounts of light proportional to particle volume [114]. He 
also incorporated the principle in a slurry sizer, the Talbot Spacial Period 
Spectrometer [115,116]. 
Gucker et. al. [117] developed equations from the Lorentz-Mie theory 
relating the size of the Airy points to particle size. Davidson and Haller 
[118] applied these equations to 0.07 to 0.50 \\m latices deposited on 
microscope slides and obtained poor agreement that they attributed to 
strong particle-slide interaction.