PROPERTIES OF POWDERS. PART IX. T H E SCATTERING O F LIGHT BY GRADED

PARTICLES I N SUSPENSION.

BY THOMAS MARTIN LOWRY AND MALCOLM CHARLES MARSH.

Received 2 7 th September, I 9 2 7 .

I. Introduction.

Previous work, both practical and theoretical, on the scattering of light has been concerned with particles whose diameter was of the order of the wave-length of the light. The theoretical aspects of this problem were considered by Lord Ray1eigh.l On the practical side, Keen and Porter2 and Raman3 have studied the colour produced when minute particles of sulphur are precipitated from thiosulphates by the action of acids, whilst Wells and Renwick have recently studied the turbidity produced by precipitates of the type used in photographic emulsions. Work has also been done by Raman and others on the scattering of light by vapours, liquids and solutions. The work described in the present paper is of a different order, since it deals exclusively with particles produced by mechanical grinding, and graded by elutriation in a slow current of water. These particles, which have a diameter of about 10 to IOOH (0.0 I to 0-1 mm.) are therefore intermediate in size between the very small particles of an ultramicroscopic colloidal suspension (d = 0-25 to 0’006p) and the relatively large particles ()Ioo~) which are left behind when the (‘ grit ” is separated from a coarsely ground powder by elutriatiori in water. The purpose of the experiments was to find out the extent to which the opacity of a pigment may be increased by reducing the average size of the particles, and the range selected was intended to represent the ultimate products of fine-grading on a large scale, assisted perhaps by some process of grading which would return the coarser particles to the mill to be reground. The main result of the experiments is to indicate that a maximum opacity must exist for a given surface-concentration of the powder, but that this maximum lies well beyond the limits of fineness that can be attained by the methods of grinding now in general use. There is, therefore, a wide margin available for increasing the covering power of a given weight of material ; but further investigation is required to show how far the increased covering-power may be counterbalanced by an increase in the quantity of the medium used to convert the dry powder into a paint.

Collected Paprrs, 5, 547.

Phot. Journ, 1927, 67, 185. Slbid., 1921, 100, 102.

PYOC. ROY. SOC., 1914, 89,.370. 4 Chemical Reviews, 1927, 3, 331.

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196 SCATTERING OF LIGHT BY PARTICLES IN SUSPENSION

2. Grading of Particles. The material selected for the first experiments was a very good sample of

ground barytes. When examined under the microscope, the particles were seen to consist of transparent cleavage-fragments of the original crystals. The powder was graded in elutriators of the type described in Part V. of the present series of papers (" A new elutriator for rapid use ").6 For water-velocities of I to I 2 -5 mm. per second a 3 cm. tube was used, while for speeds less than I mm. per second a large (24 litre) cylindrical separating funnel was used to give a tube-diameter of about 12 cm. The rate of flow was regulated by using a number of different jets for the overflow; it was kept steady by maintaining

a constant head of water, and the velocity was determined by measuring the total flow ot water per minute. The maxi- mum velocity of flow was 12'5 mm and the minimum 0.05 mm. per second; between these limits 12 inter- mediate velocities were used to grade the sample into 13 frac- tions. Tap water was used, and no attempt was made to correct for small variations of temperature (A I' C.), since these have already been shown6 to be un- important.

I t has been stated that the velocity of the water in an elutriator is a maximum on the centre line of the tube, and falls off uniformly to zero on approaching the walls; thus it has been calculated that the maximum velocity in the central line of the

FIG. I.

lower narrow tube of Crook's elutriator is twice as great as the average velocity deduced from the overflow of the jet.7 In both of the elutriators used in our own experiments, however, it was noticed that when the water-current was turned on, after the water in the elutriator had been stationary overnight, the turbid liquid was bounded by a horizontal plane (Fig. I ) which persisted throughout the length of the tube from the point where swirling ceased. This observation proved conclusively that the

Trans. Faraday SOL, 1922, 18, 32. 7 Baker, Geol. Mag., 1920, 57, 321 ; compare Boswell, Trans. Faraday SOC., 1922,

18, 36.

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T. M. LOWRY AND M. C. MARSH I 9 7

velocity of the water was constant over the cross-section of the tube. I t is suggested that this result may be due to the presence of the solid in the conical portion of the elutriator ; but it was found to be independent both of the mass of solid present and of the velocity of the water.

3. Measurement of Particles, I n order to determine the average size of the particles in the various

fractions, the "diameter " of IOO particles of each grade was measured by means of a microscope with a calibrated eye-piece scale. As far as could be judged, the particles of each fraction were of approximately uniform bulk, but owing to their irregular shape there was a considerable variation in the readings of the '' diameter." When, however, the readings were grouped in 4 sets of 25, the difference between the largest and smallest average was always less than 5 per cent. The square of the average "diameter " of 1 3 fractions of barytes is set out in Table I.

TABLE ~.-ELUTRIATION OF BARYTES.

Limits of Water- velocity.

(Mm. Per Sec.).

0.050 to 0.075 '075 to 'I00 'I0 to '20 -20 to -30 -50 to -75 '75 to 1-00

1'0 to 2'0 2'0 to 3'0 3'0 to 4'0 4'0 to 5'0 5.0 to 7-5 7'5 to 10'0 10-0 to 12.5

Water-veloci ty (Mean).

(Mm. Per Sec.).

0.0625 0.0875 0.150 0.250 0'625 0.875

1'50 2-50 3-50 4-50 6.25 8'75 11-25

Mean " Diameter " of

Particles. (10-4 Cms.)

7'09 9-07 14.2 16.8 24'7 28-3

41'5 5 7'4 66.5 74'5 90.2 108.6 126'7

Square of Diameter.

10 - 8 Sq. Cms.

50'3 823

202

276 610 8 I0

1722 3295 4422 5550 8136

11,790 16,050

Lowry and McHatton6 found that the mean diameter of particles of barytes was related to the water velocity in the elutriator according to the formula :

log d = 2-67 + Kv where d is the mean diameter

v is the water velocity K is a constant depending on diameter of the tube and

temperature of the water.

This formula could be used to express the data of Table I., over the range within which it was first applied, namely from 4 to 8 mm. per second ; but it broke down completely for smaller velocities. Fig. 2 (a) and (b), in which the water-velocities in the large and small elutriator respectively are plotted against the square of the mean diameter, indicates that there is a rough proportionality between these quantities, as required by Stokes' Law, since the points all fall fairly near to lines through the origin. A closer agreement can be obtained in the case of the small elutriator by ignoring the origin,

I 3

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198 SCATTERING OF LIGHT BY PARTICLES IN SUSPENSION

and drawing the line through a point rather below the axis of zero diameter, i e . , by supposing that Stokes’ Law applies when a constant increment is

a. Large Elutriator. b. Small Elutriator.

Water Velocity (mm. per sec.). FIG. 2.-Elutriation of Batytes.

SECTOR PHOTOMETER

LOW POWER MICROSCOPE

* I : : SCR€LN , I

- 1 BlPRl5M 7 ’ ,- ‘ I

’ +I

1,

I . , *

, I

I

I

I ,

F I X E D SECTOR 4 I

SUSPENSION 1 OF BAQVTES

FIG. 3.

added to the square of the dia- meter, or by supposing that the irregular particles behave like spheres whose diameter is slightly larger than their own mean diameter. The data for the large elutriator lie on a curve which approximates to a straight line passing through the origin although the curve cuts the axis of diameter squared in a negative value as in the case of the large elutriator. The slope of the straight line is 1380 for the small elutriator and 980 for the large one. We therefore conclude that :-

(I) With a tube 3 cm. in diameter and velocities from I

mm. to 12.5 mm. per second, Stokes’ Law is obeyed within the limits of accuracy of the experi- ment, assuming the particles to behave as spheres of slightly larger diameter than the mean width of the particles.

(2) With a tube 12 cm. in diameter, and velocities below I

mm. per second, Stokes’ Law is only approximately obeyed.

(3) The diameter of the tube has an effect on the constant in Stokes’ formula.

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T. M. LOWRY AND M. C. MARSH I99

Optical Density

Log +.

4. Measurement of Fraction of Light Scattered. A Hilger sector-photometer was used to compare the intensity of two

beams of light. The light passing through the (‘ fixed ” sector was reduced in intensity by passing through a suspension of barytes in a suitable liquid ; a similar cell containing the liquid was placed in series with the ‘( variable ” sector in order to compensate for the loss of light in the clear medium. The instrument was arranged (Fig. 3) with the sectors in a horizontal plane, so that the light passed vertically through the suspension ; and it was run at a high speed, in order to eliminate flicker, and so to make it possible to take visual observations.

Some difficulty was experienced in obtaining a uniform surface-concen- tration of the powder in the cell. At first, attempts were made to prepare a suspension in the form of a jelly ; but later it was found better to suspend the powder in medi- cinal paraffin, to a known “ concentra- tion ” in milligrams per c.c, and to pour the well- stirred suspension 0 3 into a cell of known depth. In this way a very uniform sur- face - concentration in milligrams per square centimetre 0.2 was obtained; and experience showed that settlement of the solid in the cell did not cause any appreciable altera- O’ ’ tion in the intensity of the transmitted light.

I n order to de- termine the law of absorption for vari- ~ X K Y * - ZO 40 60 80 100 I20 ous surface-concen- trations, experi- ments were made in which the fraction of light transmitted was measured for four different surface concentrations of one particular grade of powder. The results are shown in Table 11.

FIG. 4.-Covering-pwer of Ground Barytes.

Ratio.

TABLE II.-SURFACE-CONCENTRATION AND OPTICAL DENSITY OF GROUND BARYTES.

0‘22 0.5 I 0.64 1-04

Surface-Concentration (Grams per Sq. Cm.).

0.07 I 0.070 0.070 0’069

I -I------- 3.10 7-28 9-12

Ij.10

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zoo SCATTERING OF LIGHT BY PARTICLES IN SUSPENSION

When plotted against one another these numbers gave a straight line passing through the origin, showing that the optical density is directly pro- portional to the surface-concentration. This fact greatly simplified the succeeding work, since, instead of using the same surface-concentration for all grades of powder, the absorption for a standard surface-concentration could be deduced from observations at any convenient concentration ; in particular, the surface-concentration could be adjusted so that the optical-density of the layer was of a suitable order of magnitude for accurate measurement.

The optical densities of 13 different grades of ground barytes are set out in Table III., and are plotted in Fig. 4, for a surface-concentration of I mg. per sq. cm. ; the proportion of light (I, - I)/I scattered by a layer of powder of this surface-concentration is also shown for each sample.

TABLE III.-OPTICAL DENSITY OF GROUND BAKYTRS.

Refractive index of medium = 1.484 (by Refractometer). Refractive index of particles = 1.636 (Landolt and Bornstein).

Grade of Particles (Water Velocity).

Mm. per Sec.

'05 to 0.075 '075 tO 'I0 'I0 to '20 '20 to -30 '40 to '50 30 to -75 '75 to 1'0 1'0 to 2'0 2-0 to 3.0 4'0 to 5.0 5'0 to 7'5 7'5 to 10'0 10.0 to 12.5

Mean Diameter of

Particles.

P.

7-1 9'1 14.2 16'8 21'2

24'7 28 '3 41'5 5 7'4 74'5 90.2 108'6 127.6

Surface. Concentration of Particles.

Mgm. per Sq. Cm.

3-28 4-30 4'46 7'96 9.26 10'0 I 6.2 I 1.8 16.9 21.6 32'4 3 1.8 41'7

Optical Density

0.68 0.72 0 54 0'90 0.71 0.69 0.91 0'49 0.5 8 0.64 0.81 0 -65 0'73

Ratio of Iptical Density

to Surface Concentration.

0.207 0.167

0.113 0.077 0.069 0.056 0.041 0-03 4 0'030 0'025 0.0214 0.0175

0'121

Fraction of Light Scattered

I0 - I Io'

Reduced to I Mgm. per

Sq. Cm.

0'38 I 0.321 0'243 0.229 0.163 0.147

0'09 I 0.076 0.064 0'056 0.048 0'040

0'122

5. Covering-power of Pigments, The curve showing the relation between light stopped and size of

particles is roughly hyperbolic in form, so that most of the points are not far removed from two intersecting straight lines of very different gradient. The optical density of the powder is therefore increased only slowly by further grinding so long as the average diameter of the particles exceeds sop or When, however, the diameter is reduced below 30p or & mm., corresponding with a water-velocity of about I mm. per second in the elutriator, the optical density of the powder increases very rapidly as the diameter of the particles is decreased. Indeed the optical density of these fine particles is so great that it might be of real service, when valuing commercial samples, to estimate them separately by elutriation at I mm. per second, in addition to estimating the "grit " by elutriation at 7 or 4 mm. per second.

Since barium sulphate forms transparent crystals, and would probably

mm.

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T. M. LOWRY AND M. C. MARSH 20 I

be just as transparent as (say) magnesium sulphate if it could be obtained in solution, it is clear that the high covering-power of the fine particles must disappear again on further sub-division, and must therefore reach a maximum at some intermediate stage, perhaps in the range of colloidal solutions. This maximum is not reached, however, in the range of sizes that can be reached either by careful grinding, or by elutriation. Since, however, the scattering of light is a function of the refractive indices of the particles and of the medium, the present pioneer series of observations ought obviously to be followed up by measurements with particles of other substances which can be used either as pigments or as fillers, and in media such as are used to convert these substances into paints.

6. Summary.

(a) A sample of ground barytes was separated into 1 3 fractions by elutriation at water-velocities of 0.5 to 12-5 mm. per second.

(b) The diameters of the particles were measured and used to test the validity of Stokes’ Law, as applied to crystalline particles of barytes.

(c) The various fractions were suspended in medicinal paraffin and the light-transmission was measured. The optical density is proportional to the surface-concentration of the powder, but increases slowly as the diameter is reduced to sop and much more rapidly when the diameter is reduced below 30p.

(d) The probable existence of a maximum degree of opacity on further subdivision is indicated.

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