Particle size determination by beta-ray absorption

121

Powder Technology. 9 (1974) X21-124

0 Elsevier Sequoia S A., Lausanne -Printed

in The Netherlands

Particle Size Determination by Beta-Ray Absorption G. CUR210 Ist~tuto dr Impiantr Nucleari dell’Uniuersita.Prsa (Italy) (Received

September

20,1973,

accepted

September

28,1973)

Summary A cumulatme method for partrcle size determination has been developed The mass deposrted from a homogeneous suspension IS determined by a beta-absorptton thickness measurement techmque. Expertmental tests on some different samples of so11 are reported; the results are successfully compared with those obtained usmg the conventional methods of the Andreasen pipette and sedrmentatzon balance.

INTRODUCTION

The measurement of the rate of particle sedimentation in liquid or gaseous media is the basis of most of the methods of particle size determination. Many devices have been developed to measure the rate of sedimentation without disturbing its natural development. Methods employing radioactive substances have been extensively studied and adopted [l-6] ; general reviews of the “nuclear methods” are presented in refs. 7 and 8. The use of a p-source in particle size determination is described by Connor et al. [ 53 ; in their apparatus the mass of the particle which is deposited on the bottom of the sedimentation tube is measured by a back-scattering thickness measurement technique_ In his general review, Ramdohr [S] mdicates a further development of the method by which the mass of the deposited particles is measured by P-absorption. This method is here adopted in order to test the possibility of creating a device for routine measuring of particle size of soil sam-

pies. It employs a Sr’” P-source, placed near the bottom of the sedimentation cylinder. The source is set so as to permit its S-radiation (their maxrmum range in water is 12 mm) to pass through the lowest portion of the sedlmentation cylinder and its thm base. A fldetector, located under the cylmder base and close to it, counts the fl-particles which are able to pass through the cylinder base. The sedimentation brmgs a notable increase m density on the bottom of the sedlmentation cylinder, i.e. m the same portron of space which the fi-partrcles drrected toward the counter pass through_ The increase m density causes an increase m the stopping power of the medium and consequently a decrease in counting rate. So rt is possible to obtam the quantity of deposited material from the pcounting rate by a previous calibration of the apparatus_ Therefore, by contmuous measuring of counting rate, cumulatrve settling curves can be drawn from whrch size distnbutlon 1s calculated [9] _

EXPERIMENTAL TION The

apparatus

APPARATUS

(Fig.

1)

AND

consists

CALIBRA-

of

a sedl-

of 20 mm i-d.; a slot along the whole cn-cumference was made m Its wall near the base, and several drops of a SrsO mtrate solution were put mto it and allowed to dry. The activity of the source is about 5 PCi. Epoxy resin was used m order to hold the source to the wall and to attach a perspex shielding ring around it. The terminal part of the sedimentation cylinder was made of aluminium alloy, so it was mentation

cylinder

122

,

I,,

I

0 GEIGER-YULLER --

COUNTER

1

PARTlCLlEO SIZE

-

Fig. 1. ExperImental

apparatus.

Fig. 3

possible to obtain easily small thicknesses 0.1 mm) for the base of the cylinder and for the wall at the height of the p-source. The P-detector below the base of the cyhnder is a thm window Geiger-Muller counter; an automatic counting system counts the pulses from the detector and records them with a prmter. The calibration of the apparatus was done by measuring the counting rate of the G.M. as a function of the quantities of various types of soil completely deposited on the base of the sedimentation cylinder filled with distilled water to a height of 10 cm; to the water was added sodium oxalate (0.8 g/I) to avoid flocculation. In Fig. 2 some calibration points and the average calibration curve are reported; the counting rate with pure water was about 100 cps.

Cumulative

EXPERIMENTAL

size distribution

100

(P’

of -a clay sample.

TESTS

(-

‘Ooc 50

1

\I

I\

.0

04

I

I

I

I

06

12

WEIGHT

Fig. 2. Calibration

curve.

OF

I

16 DEPOSIT

Several sedimentations were done with different types of soil samples previously passed through a 75 pm sieve. From the counting rate versus time curves were obtained the cumulative settling curves by means of the calibration curve, and then size distributions were calculated by the expression derived by Oden [lo] : W = P -

t (dP/dt)

where P is the fraction deposited in time f and W is the fraction of material greater in size than the Stokes’ diameter corresponding to the settling time f: t = [IS V

hllI@(P

- P’kl

where g = viscosity of sedimentation medium (g/cm set), h = sedimentation height (cm), d = Stokes’ diameter (cm), p = density of set-

I

I

20

24 (0)

PARTICLE

Fig. 4. Cumulative sample_

lb

SIZE

size distribution

100

9’

of

a silty

clay

123

3

SAMPLE 01 1

I

, PARTICLE

10

SIZE

II. 100

(r-

Fig. 5. Cumulative size distribution of sample.

)

a silty

clay

tling particle (g/cmj), p’ = dens&y of sedlmentation medium ( g/cm3), g = 980 cm/sec2 _ The values of t(d_P/dt) (or of dP/d log f) were obtamed by numerical or graphical differentiation of the cumulative settling curve. Figures 3--7 show cumulative size distribution for five different sol1 samples; the concentration of particles in the aqueous suspension was included between 2 and 15 g/l. The cumulative size distributions obtained for the Same type of soil sample with the Andreasen pipette and with the Sartorius balance are also shown in the figures.

CONCLUSIONS As can be seen, the curves of Figs. 3-7 show good agreement, and the experimental points obtained by the “nuclear method” are scattered from the points obtained by the “traditional methods” to the same degree m

-i--l

H

fl

1

PARTICLE

SIZE

100

(PI

Fig_ 7. Cumulattve SLZ~distributmn of a calcium carbide powder. which these points scatter from one another, and the order of magnitude of the scattering is the same observed m other comparisons of conventional methods [ 11]_ The method for size analysis of soils adopted here has several important advantages: Settling can be followed remotely; it 1s undlsturbed by the presence of sampling devices and response is instantaneous and free of inertial effects. The method can be applied to opaque systems. Measurements are possible in a wide range of particle concentration. P-absorption depends directly on deposited mass, and because of the slight dependence on the atomic number of the stopping material, a single cahbratlon is enough for common samples of soil. The radiation hazard IS negligible in comparison with the radioactivation method (for which neutron irradiation is also necessary), with the -y-ray absorption method (which employs y-sources of hundreds of mC1 [4] and with the P-back-scattering method (which employs P-sources of 1 mCi 153 _ Performance is very simple, costs are a_cceptable and the whole apparatus can be easlly rendered portable.

ACKNOWLEDGEhlENTS “.

1

PARTiCL’:

SIZE

IdO 9’

Fig. 6. Cumuld.tive size distribution 01 a silt sample.

Many thanks are due to Prof. Ing. L. Carotl of the Istituto di Costruzioni Stradali e Trasporti dell’universita di Pisa for many helpful

124

discussions and to Dr. G-P. Barzon of CAMEN, S. Piero a Grado, Pisa (present address Nwzleare Somala, Box 300, Mogadiscio, Somalia) for the measurements performed with the Sartorius balance.

REFERENCES 1 B M. Abraham, H.E. Flotow and R D Carlson, Anal Chem ,29 (1957) 1058 2 P Connor, W.H. Hardwick and B J. Laundy, J Appl Chem., 8 (1958) 716. 3 AM Gaudm and M C. Fuerstenau, Eng. Muting J., 159 (1958) 9, 110.

4 C-P. Ross, Anal. Chem., 31 (1959) 337. 5 P. Connor, W-H. Hardwick and B.J. Laundy, J. Appl. Chem., 9 (1959) 525 b H. Ramdohr and W. Kuhn, Kemtechmk. 6 (1964) 416. 7 E. Broda and T. SchZjnfeld, The Technical Applications of Radtoactivity, Vol. 1, Pergamon Press, Oxford, 1966. 8 H. Ramdohr, Kemtechnik, 4 (1962) 318 9 T. Allen, Particle Size Measurement, Chapman and Hall, London, 1968. 10 S. Oden, Proc. Roy. Sot. Edinburgh, 36 (1916) 219. 11 G. Barresi, Riv. Strada, 38 (1969) 4