L E O N A R D H . C O H A N A ND N O R M A N H A C K E R M A N , C o llo id C o r p o r a t i o n , R a l t i m o r e , M d .
T
H E problem of testing emulsifying equipment is essentially one of determining the particle size distribution in a given emulsion. The im portant methods used for this pur
pose may be divided into three general classes.
1. There are those methods utilizing the relation between the velocity of a particle through a medium, the force applied, and the radius of the particle. The simplest such relation, Stokes’ lawr (4, IS, 88, 89, Jfi, 46, 62, 63, 64), states th a t
/ = Gmr]dx/dt (1)
where / is the frictional force between a spherical particle and the surrounding medium, r is the radius of the particle, 77 is the viscosity of the medium, and dx/dt is the velocity of the particle through the medium. M ethods used for determin
in g / depend on sedimentation (2, 5, 8, 13, 15, 16, 29, 30, 33, 35, 36, 441 48, 54, 56, 66-69, 71, 74, 76, 79), Brownian motion (0, 14, 15, 36, 66, 70), or diffusion (6, 10, 15, 21, 24, 36, 66).
Unfortunately, sedimentation methods require considerable time, particularly if the par tides are 1 ju or smaller. Centrifug
ing hastens the process b u t requires expensive equipment.
Measurement of particle size from the Brownian motion of individual particles is based on the Einstein equation (20, 22, 42, 58, 59)
r~7— 2 R T l' rr F
^ ~ N K ’ ~ dx/dt ( ) where ( A x ) 2 is the mean of the square of the distance which the particle moves in a time, t. R is the gas constant, T is the absolute temperature, and N is Avogadro’s number. If Stokes’ lawr holds, K = Girrr].
Instead of observing the motion of individual particles, as above, the net effect of such motion—namely, the am ount of diffusion—m ay be determined. This method for obtaining the velocity of motion and, hence, the particle size depends on Fick’s (23, 37, 43, 47) diffusion equation
— — p ' k H (? )
di dx'- w
where c is the concentration, t the time, and x the distance perpendicular to isoconcentration planes. D = R T where again K = Gtttt] if Stokes’ law' is obeyed.
By combining the diffusion and sedimentation equations, the volume per particle and also the molecular w'eight m ay be obtained w ithout assuming spherical shape (6, 11, 87).
2. The size and shape of individual particles may be de
termined w ith a microscope. W ith an ultramicroscope, only the average size can be determined (7,12,15,17, 28, 31,36, 66, 73, 75). Here again expensive equipment is necessary.
3. Finally, Rayleigh’s law' (25,27,43-58) m ay be used to obtain a measure of the particle size distribution. Rayleigh’s law' states
/ , = ~ D Sj \ l + c o s2 (4)
I , and la are the intensities of the scattered and incident beam, respectively, ¡3 is the angle between the scattered and incident beam, n is the number of nonconducting spherical particles per cubic centimeter, V is the volume of each par
ticle, and X is the w'ave length of the incident beam. D ' = kiii’ and D — kin, w'here ju' and y. are the refractive indices of the particle and medium, respectively, and k , k h and k 2 are
constants. Fi g u r e 1 . Pr o j e c t i o n La m p a n d Tu r b i d i m e t e r
In turbidim etry the intensity of light transm itted through the solution is measured, w'hile in nephelometry or tyndallom- etry the intensity of scattered light is measured directly (1, 3, 26, 27, 28, 32, 36, 41, 45, 49, 55, 57, 60, 61, 65, 67, 68, 69, 72, 75-78, 80).
Particle size m ay also be measured by the following m eth
ods, most of wiiich give only average size: osmotic pressure (determines number of particles); adsorption (determines total surface); ultrafiltration; rate of solution (determines total surface); dialysis; x-rays (width of x-ray line in diffrac
tion pictures); electro-viscous effect—for example, using Smoluchow'ski’s modification of the Einstein-Hatschek or K unitz equation— [Kuhn (36) and Roller (56) discuss some of these methods briefly]; and Langmuir trough (19) (average cross section).
The method described below’ for the measurement of effec
tiveness of emulsifying equipment w'as developed with a view to simplicity of apparatus and rapidity and ease of measure
ment. Briefly, the procedure consists in measuring the turbidity of a standard emulsion for various times of treat
m ent; hence, it belongs in the third class mentioned above.
Although it is not possible to measure the particle size distri
bution function, the relative performance of two pieces of emulsifying equipment or the performance of the same equip
ment a t different times or under different conditions m ay be easily determined. The low' cost of the necessary apparatus, combined with the speed and accuracy w ith which the results are obtained, should make this method valuable to manufac
turers and users of emulsifying equipment.
T u r b id im e t e r a n d S ta n d a r d E m u ls io n The turbidimeter was a converted Bausch & Lomb colorimeter.
Light from a Bauscli & Lomb projection lamp was reflected through the solution by the mirror below the cups.
210
For convenience the projection lamp and turbidimeter were fixed on a dead-black board and a mirror was fastened to the board to allow the operator to read the scale without moving his head from the eyepiece (Figure 1). To keep the intensity of illumination constant, a stop (a, Figure 1) was placed under the mirrorto assure a constant angle of reflection. Marks (6, Figure 1) on the mirror enabled the operator to make certain that the lamp was focused at the same point.
Tne turbidity of the emulsion was measured relative to a stand
ard placed in the left-hand cup, the unknown sample being in the right-hand cup.
APRIL 15,1940
The temperature at which the emulsions were prepared was kept a t 35° =* 3° C.
The procedure consisted in diluting the newly prepared sample to 0.5 per cent—i. e., 1 to 10. The dilute emulsion was placed in the right-hand cup and the scale value at which the turbidity equaled th at of the glass standard was noted. The average of four readings was taken. The average deviation from the mean in the central portion of the scale was approximately 0.03 division.
Frequently samples were obtained which were so transparent on dilution th at their turbidities compared to the standard were oS the scale. Rather than use several standards, the relative turbidities of the undiluted 5 per cent emulsion and the emulsion diluted to 1, 2, or 3 per cent were measured. The turbidity of the 0.5 per cent material was then found by extrapolation.
As shown in Figure 2, the turbidimeter reading, R, plotted against 1/C, where C is the concentration of the emulsion, gives essentially a straight line, so th a t the extrapolation can be readily made. R is proportional to the light transmission and is therefore inversely proportional to the turbidity.
R e s u lt s
M ost of the data herein were obtained from emulsions pre
pared by a new type of emulsifying equipment which is being developed a t this laboratory. The materials were placed in this machine unmixed and samples of the emulsion were re
moved a t definite time intervals.
ANALYTICAL EDITION 211
F i g u r e 3 . Effe c tof Time
The curves in Figure 3 give the turbidim eter reading, R, against the time, t, in minutes. As the turbidity of the solu
tion increases, R decreases—th a t is, R is really a measure of the transparency of the solution and is inversely proportional to the turbidity. The curves in Figure 3 were selected from several hundred experiments, in which all the emulsions were prepared in the new emulsifying equipment mentioned above.
They illustrate a relatively low emulsifying efficiency as in curve A, a fair efficiency as in B, and a high efficiency as in C.
I t will be noted th a t R, in A, Figure 3, shows an initial de
crease, passes through a minimum, and then increases slightly. The final value of R is only slightly larger th an th e value for the first sample withdrawn. In the case of B, th e , Fig u r e 2. Effe c tof Dilution
The standard first used was an emulsion of the same type as the one being measured. To eliminate the inconvenience due to the change in turbidity of this standard, a standard was pre
pared after the method described by Kleinmann (34). A mixture of talc and collodion was painted on the glass disk in the bottom of the colorimeter cup. This standard gave constant readings for several weeks, but eventually became brittle and cracked, requiring replacement.
The problem of finding a truly permanent standard was finally solved by using a glass disk enameled on one side. A piece of
“ flashed” enamel glass was procured from the Pittsburgh Plate Glass Company, and disks were cut out and ground to fit the colorimeter cup.
Four thicknesses of the enameled glass were used to give a density which brought the readings for the most usual emulsion to the center of the colorimeter scale—i. e., between 15 and 35 divisions. The thickness of the glass disks was reduced by grind
ing off some of the clear glass. The ground finish had no effect on the turbidity.
Those emulsions which had relative turbidities outside the 15 to 35 range were generally colored, particularly in the higher range. To minimize this color difference a blue filter was placed in the colorimeter eyepiece.
A rough check was kept on the constancy of the values obtained by comparing a previously prepared emulsion, whose relative turbidity was known, with the glass standard before and after each set of measurements. Thus, any variation due to a change in the instrument, itself—e. g., the intensity of the light—could
be detected. .
The emulsion was an orange oil, 5 per cent by weight, in distilled water. Lecithin, in the amount of 10 per cent by weight of the oil, was used as a stabilizing agent. _
The oil, actually orange terpene, was obtained from McConruck
& Company, Baltimore, Md., and was kept under nitrogen in a brown bottle to prevent oxidation by light or air. The American Lecithin Company kindly supplied vegetable lecithin “S”, which contains approximately 70 per cent of lecithin.
212 INDUSTRIAL AND ENGINEERING CHEMISTRY VOL. 12, NO. 4
Fig u r e 5. Em ulsio n Treatedin Hom ogenizer
As the radius becomes smaller than the wave length of the incident light, the scattering of the light becomes more im
p ortant than reflection. Thus, the turbidity decreases with decreasing radius according to Rayleigh’s law.
r , r AnxF1 ,, , , (D' — D)* kiCxr3 ,as I . / h = — (1 + cos 8) -— Di = — (6) ki is a constant. Other symbols are as in Equations 4 and 5.
4 0 5 0 6 0 Fig u r e 7. Effe c t of Te m p e r a t u r e
on Tu r b id it y
E a c h s a m p le tre a te d 120 m in u te s a t te m p e ra tu re s in d ic a te d
Fig u r e 4. Tim e Re q u ir e d to Cream
minimum occurs a t smaller t than in A. As t increases, R in
creases more rapidly than in A. In the curve denoted by C the minimum has occurred prior to the first reading and, hence, does not appear on the figure. Furtherm ore, the in
crease of R in C is still greater than in B. Thus the final samples are much less turbid than those removed a t the beginning.
From a theoretical standpoint the turbidity should increase as the particle radius decreases, according to the equation:
I g k l C x / . I
T = “ 7 “ ®
1 o r 7, = intensity of scattered light / 0 = intensity of the original beam C = concentration of the emulsion
x = depth of the emulsion layer r = radius of the reflecting particles ki = a constant
1 5 3 0 6 0 9 0 1 2 0 1 5 0 1 8 0 M I N U T E S
Fi g u r e 6 . Em u l s i o n Tr e a t e d i n Co l l o i d Mi l l
Since R varies inversely as I,/Ia, it is apparent from E qua
tion 6 th a t w ith steadily decreasing radius, R should decrease to a minimum and then increase precisely as in the curves of Figure 3.
Thus, for two samples to the left of the minimum in Figure 3, the most turbid (lowest R) may be said to have the smallest average particle radius. However, in the size region to the right of the minimum the reverse is true.
These conclusions were checked qualitatively by correlating the turbidimeter readings w ith the time required for the samples to cream and, for the larger particles, with the size as measured microscopically.
One would expect th a t to the right of the minimum, th e higher R the more stable the emulsions would be—th a t is, they would take longer to cream. In Figure 4 the log of th e creaming time in hours is plotted as ordinate against th e
APRIL 15,1940 ANALYTICAL EDITION 213 time of treatm ent for the 5 per cent emulsions, A, B, and C
being the same as in Figure 3. In each case the samples having the higher values of R showed greater stability.
Figures 5 and 6 show the relation between the turbidity of orange oil emulsions and the time of treatm ent in a homo- genizer and a colloid mill, respectively.
Experimental results indicate th a t the orange oil on oxida
tion tends to emulsify more readily. Since the oxidation proceeds more rapidly a t higher temperatures, care must be taken to keep the temperature as constant as possible.
Figure 7 shows the effect of temperature of the oil during émulsification on the turbidity of the resulting emulsion.
Here values of R for 120-minute treatm ent are plotted against temperature of treatm ent for samples which were prepared
However, the following seems to give a satisfactory standard : 5 grams of a mixture of carbon tetrachloride and gasoline variables. Furthermore, the results can be compared quanti
tatively w ithout spending a prohibitive length of time.
S u m m a r y
The apparatus and procedure for a new method, based, on turbidity measurement, of determining emulsifying efficiency are described, together with a convenient standard emulsion.
The new method is compared with microscopic examina
tion and w ith the measurement of the time of creaming of the emulsions. Results on a colloid mill, a homogenizer, and a new type of emulsifier are presented.
A bibliography on methods of particle size analysis ap
plicable to the study of emulsions and suspensions is included.
L ite r a tu r e C ite d