INDUSTRIAL A N D ENGINEERING CHEMISTRY
134
VOl. 19, N o . 1
Calibration of the Buret Consistometer’ By Winslow H. Herschel and Ronald Bulkley2 NATIONAL BUREAUOF STANDARDS, WASHINGTON, D. C.
ARIOUS methods for determining the consistency of a mushy material3 by forcing it through a capillary tube
V
call for flow-pressure graphs. Data for plotting these graphs may be obtained by making successive runs a t different pressures but this is unduly time consuming and auxiliary apparatus is required to keep the pressure constant during each run. The fundamental idea of the buret consistometer-obtaining a series of observations a t different rates of flow by permitting the hydrostatic head to vary-has been used by Cooke4 and by A ~ e r b a c h . ~The instrument requires no external source of pressure and serves as a convenient means for obtaining flow-pressure data on materials that are not too stiff. The object of the work here reported was to determine the best method of calibrating the buret consistometer and the degree of concordance attainable. The Consistometer
I n Auerbach’s apparatus (Figure 1) a buret 3 to 5 mm. in diameter was connected, through a capillary tube and a Utube, to a shorter limb ten times as large in diameter. Two stopcocks were so arranged that the apparatus could be filled and emptied without being removed from the bath. The buret consistometer in its simplest form (Figure 2), as used in our investigation, may be made by blowing a bulb on a capillary tube and joining half the bulb to the bottom of a n ordinary 50- or 100-cc. buret after the stopcock has been removed. This forms a trumpet-shaped entrance to the capillary tube and prevents an exact measurement of its length, as is possible with viscometers in which the ends of the capillary tube are cut off perpendicular to the axis. The latter construction, however, presents a more difficult glass-blowing operation. The temperatures employed in our tests were not far from those of the room. They were controlled by a water jacket consisting of a long glass tube, 6 cm. in diameter, to which hot or cold water was added as required. A stopper, perforated to admit air under pressure, which continuously stirs the water in the jacket, was inserted a t the lower end of the tube. A plumb bob, hung close to the consistometer, makes it possible to adjust the instrument to a vertical position. While the contents of the buret are coming to temperature flow is prevented by a piece of cork held over the lower end of the capillary. To make a run, the cork is removed and the descent of the meniscus is observed. Various methods of timing were investigated in order to obtain the maximum speed consistent with accuracy. Auerbach took readings a t equal intervals of time. This is objectionable because it necessitates the use of a specially graduated buret. We preferred an ordinary buret graduated in Presented before the Division of Petroleum 1 Received June 18, 1926. Chemistry a t the 72nd Meeting of the American Chemical Society, Philadelphia, P a . , September 5 to 11, 1926. 2 Published by permission of the Director, National Bureau of Standards 8 Bingham, Bur. Standards, Sci. Peper 278 (1916); Bingham and Murray, Proc. A m . SOC.Testing Materials, 18 (2), 655 (1923). Several authors, J . Phys. Chem., 29, 1201 (1925). 4 J . A m . Ceram. Soc., 7 , 651 (1924). 6 Zsigmondy Feslschrifl, suppl. to KolIoid-Z., 56,252 (1925); Kolloid-2 , S8, 261 (19261.
even cubic centimeters. Cooke’s method of timing was adopted. I n this method two stop watches are employed and readings are taken a t every fifth graduation, that is, after each successive 5-cc. portion has been discharged. I n detail, the method is as follows: Fill the buret t o about 2 cc. above the zero mark a t the top, and start watch No. 1 as the meniscus passes zero. After the first 5-cc. portion has been discharged, stop watch No. 1 and start watch No. 2 simultaneously. After the reading of watch No, 1 has been recorded and a n additional volume of 5 cc. has been discharged, stop watch No. 2 and start watch No. 1. Proceed in this manner until the last graduation has been reached.
This method of timing may introduce cumulative errors, but no difficulty was experienced on this account, even when readings were taken after the discharge of each cubic centimeter, as shown by a comparison of the total time obtained without stopping the watch with the sum of the times obtained as described. The possibility of cumulative errors is less with the method of taking readings on every 5-cc. portion.
n
Figure 1-Auerbach’s Consistometer
Figure 2-Consistometer as Used by Herschel and Bulkley
Cumulative errors can be avoided by the use of a “split second” stop watch. This is operated as follows: Start t h e two hands of the watch simultaneously and let them remain together until 5 cc. of the material has been discharged. Then stop hand No. 1 by pressing a second button, while hand No. 2 continues its course without interruption. After hand No.
INDUSTRIAL AND ENGINEERING CHEMISTRY
January, 1927
1 has been read, press the button again. Then hand No. 1 rejoins hand No. 2, wherever it may be, and continues t o travel with it. After a n additional 5 cc. volume has been discharged, again stop hand No. 1 and read. And so on.
With burets about 1 cm. in diameter allowing a n interval of 5 cc. between readings has the disadvantage that the average head causing flow must be calculated (by an equation to be given later) and cannot be taken as the arithmetical mean head, as may be done, except a t very low heads, when readings are taken after the discharge of each cubic centimeter. The use of the larger interval, however, has the following advantages: (1) When two stop watches are used the cumulative error in timing tends t o be reduced. (2) The labor involved, both in observation and in calculation, is reduced. An adequate number of observations at 5-cc. intervals may be obtained from a single emptying of the buret. (3) Accurate graduation of the buret cannot be assumed. Intervals of 5 cc. permit an accurate volumetric calibration of the buret. I n the commercial graduation of burets of the capacity used it is customary t o determine the length of buret required to discharge 10 cc. and to divide this length into ten equal parts. Errors as high as 1 per cent (Table 111) were found in graduations of 5 cc.
Calibration of Consistometer by Flow Tests
constants of the materials (suspensions and colloidal materials) for which the buret consistometer is primarily intended. The length of the capillary may be obtained with sufficient accuracy by direct measurement, but for the purpose of calculating the diameter it is convenient to write equation (1) in the form by the aid of which d may be calculated from data obtained by flow tests with liquids of known viscosity. Flow Tests o n Two Buret Consistometers Several consistometers were prepared in the manner previously described. Two, the approximate dimensions of which are given in Table I, were calibrated by flow tests. D i m e n s i o n s of Two Consistometers No. 1 No. 5 Caoacitv (cc 34 49 6iimet;r bf buret (cm.) 1.20 1.07 1.135 0.891 Nominal section of buret, So (sq. cm.) Measured length of capillary, I (cm.) 5.4 2.0 Inside diameter of capillary, d (cm.) 0.05 0.10 Outside diameter of capillary, d' (cm.) 0.6 0.6 Ratio l / d 108 20 T a b l e I-Approximate
The kinematic viscosities of the calibrating liquids, obtained with the Bingham viscometer, are given in Table 11.
The well-known equation for stream line flow o f a viscous liquid may be written ! ! = - r-gEd Lh = - cih czq P
where
= P
q =
Qt
128Lq
87rL
kinematic viscosity =
=
(/
viscosity (poises) density (grams percc.)
rate of flow (cc. per second)
diameter of capillary (em.) effective length of capillary (cm.) = measured length ( I ) end correction (A) g = acceleration of gravity = 981 cm. per m = coefficient of the kinetic energy correction, for which the constant value 1.12 is ordinarily assumed6 h = average hydrostatic head causing flow (cm.)
d
L
= =
+
As the volume discharged in the last timed interval may be less than 5 cc., i t is more convenient to insert the rate of flow, Q as ordinarily used for visp, in equation (1) in place of 7 cometers, where &, the volume discharged in the timed interval, is a constant. The average head, h, is usually calculated by Meissner's approximation formula
where hl is the initial and hz is the final head. Equation ( 2 ) is sufficiently accurate for the present purpose, and in general it may be used when neither hl-hz nor the kinetic energy correction is too large. A more accurate equation is available for use when necessary.' Calibration, in its simplest form, would consist merely of the determination of the instrumental constants C1 and Cz by means of flow tests with liquids of known viscosity. These constants, however, would not be enough t o determine the dimensions of the capillary nor to make possible comparisons with other methods of calibration. The dimensions of the capillary must be known in order to calculate the This designation of m is retained in accordance with common practice, though i t is somewhat misleading. The correction term allows not only for the kinetic or inertia resistance due t o acceleration, but also for the fact t h a t the true skin friction due to viscosity is not the same per unit length near the entrance t o t h e tube a s i t is farther on, where the distribution of velocity over the cross section has settled down to its final form. 7 Herschel, Bur. Standards, Tech. Paper 210, 230 (1922). 6
135
T a b l e 11-Viscosities
LIQnID
TEMPfRAToubURE O
F.
C.
Water 24 Water 20.2 KeroseneNo. 2 30 KeroseneNo. 1 28 MineralsealNo. 1 2 8 MineralsealNo. 2 2 8 500 sec. oil, Saybolt universal 25
'
of Calibrating Liquids KINEMATIC TENSION vlscoslTY Dvnes/cm.
V I ~ C O ~ I DsnsITY TY 'ISEs G./cc.
75.2 68.4 86 82.4 82.4 82.4
0.00914 0.01000 0.01457 0.01750 0.0552 0.0556
0.997 0.998 0.803 0.807 0.817 0.819
0.00917 0.01002 0.01815 0.02169 0.0676 0.0679
72.8 72.1 27.6 27.6 29.8 29.8
77.0
2.71
0.929
2.917
34.8
Surface tensions were determined by the D u Kouy apparatus.8 The first five liquids were used with consistometer No. 1 and the other two with instrument No. 5. The average times of flow, in seconds, as observed in the calibration of the two consistometers, are given in Table 111. T a b l e 111-Average
T i m e s of Flow in Two Consistometers
h'o. 1 KEROSENE
WATER
24OC. 20.2'C. Sec. Sec.
'OR'
Cc. 5.027 5.004 4.950 5.044 5.016 4.979 4.034
... ...
Fi:;
gt.2, z?':, Sec.
Sec.
Sec.
51.0 54.7 94.2 109.7 335.8 6 2 . 7 105.7 124.9 382.2 57.3 71.9 122.9 144.7 445.2 66.6 87.4 149.0 176.7 544.9 80.9 99.8 109.0 185.6 220.4 681.7 133.3 144.4 248.2 295.6 911.6 156.9 168.6 292.3 347.6 ...
.,,
...
,, ,
,
...
...
No. 5
... .
.
... ... , . .
.,. ... .. .
...
... ...
MINERAL 500SeC. C O R . Q SEAL OIL 28'C. 25OC. Cc. Sec. Sec. 5,009
4.973 5.018 4.983 5.026 4.988 5.020 4.976 5.012 3.996
4.4 4.7 5.3 5.7 6.7 7.7 9.3 12.2 17.9 26.9
139.0 152.1 174.2 196.8 230.0 273.6 346.5 459.5 709.8 1091.6
For each successive 5-cc. portion discharged the time of flow increased, as the head decreased. As the times of flow in the last line are for only 4 cc., the increase in time is irregular. The first column contains the corrected volumes of discharge obtained by the volumetric calibration of the buret. Corrections Required in Determining Mean Effective Diameter of Capillary After the burets had been calibrated volumetrically, two corrections were found to be necessary, in addition to the kinetic energy correction provided for in equation (3), -namely, a correction to the average heads calculated by equation ( 2 ) , to allow for surface tension effects, and a determination of the value m to allow for variations in individual 8
Klopsteg, Science, 40, 319 (1924).
INDUSTRIAL A N D ENGINEERING CHEMISTRY
136
instruments from 1.12, the mean or apprqximate value ordinarily assumed. It is known that the capillary rise in large tubes is small or negligible. Direct observation on a n inverted buret with the end opposite the capillary immersed in water showed that this was the case with the burets employed. If the diameter of the buret is not less than about 1 cm., therefore, the surface tension effect a t the upper meniscus may be disregarded, or it may be regarded as included in the calculated back pressure a t the outlet. For static conditions the capillary rise is given by the wellknown formula (4)
where y is the surface tension in dynes per centimeter, and CY is the angle between the liquid surface and the walls of the capillary. For a buret discharging into the air, d’ is the outside diameter of the capillary, or the diameter of the surface over which the liquid spreads as shown in Figure 2 . The back pressure due to surface tension may be found by equation (4) if cos CY is known. When equation (4) is used to calculate the capillary rise, cos CY is ordinarily assumed to have a value of unity for a liquid which wets the surface. Under conditions of flow in drops, however, the back pressure is not constant and cos a cannot be taken as unity. Just before a drop falls, for instance, the total surface tension forces are utilized in supporting its weight, and there is no back pressure. The next instant cos CY becomes a minimum, but only a small force is required to support the liquid remaining after the drop has fallen. Hartmanng found, by tests of flow through an orifice, that the mean effective back pressure could be calculated by equation (4) with cos CY equal to 0.5. Table IV-Heads for Two Consistometers ~
~
~~
No. 1 READIN MEASUREDAVERAGB HEAD HEAD cc. Cm. Cm.
0
37.02
5
32.59
10
28.17
15
23.78
20
19 32
25
14.93
30
10.55
34
7.02
30
...
35
...
40
...
45
... ...
49
A.0. 5
so
s
34 :?6
1:ooo
30.33
1.002
25.91
1.003
21.47
1.003
17.04
1.001
12.61
1.001
8.67
1,001
... ... ...
BEASURED HEAD Cm. 59.77 54.15 48.54 42.87 37.26 31.53 25.81
... ...
25.81
...
20.02 14.28
... ...
... .
.
I
8.40 3.69
AVERAGE HEAD ?! Cm. 3 56;91
1 :ooo
51.29
1.002
45.65
1.003
40.00
1.003
34.32
1.006
28.58
1.008
...
...
... ...
22.79
1.012
16.99
1.013
11.08
1.016
5.73
1.019
. . I
...
The back pressure may be determined graphically, in stream line flow, by plotting the rate of flow against the pressure. Correcting the pressure to allow for kinetic energy1° gives a straight line, which intersects the axis of pressure a t a point, p,, representing the back pressure due to surface tension. This graphicdly obtained value, p,, would, of course, include the surface tension effect at the upper meniscus, if appreciable, as well as that at the outlet. Results with the buret consistometers, however, agreed, as closely as could be determined by graphical methods, with Hartmann’s equation-i. e., with equation (4) where cos a is equal to 0-5.
* P h y s . Rcv.,2O,
728 (1922). The method of making this correction is explained in a paper by the authors presented before the Ametican Society for Testing Materials, June, 1926. 10
Vol. 19, No. 1
We therefore decided to use Hartmann’s method of correcting the average heads, as calculated by equation (2), to get the net effective heads causing flow. Table IV shows the measured heads obtained by the direct reading of lengths along the buret and the average heads calculated by equation ( 2 ) . O The ratio S3, the significance and use of which will be exp l a i n e d l a t e r , is a measure of the uniformity of bore of the buret. a= No.? The heads given in Table IV must be corrected for surface tension. Using t h e values in Table 11, t h e s u r f a c e tension correction is 0.25 em. for water, 0.13 cm. for the “500” oil, and 0.12 cm. for the other oils. Although these corr e c t i o n s appear alm o s t n e g l i g i b l e in comparison with the heads, t h e y were f o u n d t o be significant. If the diameter of the capillary were a 3-Buret No. 1 Determination of sufficiently small frac- Figure Coefacient of Kinetic ’Energy -_Correction tion of its length, the kinetic energy correction would be negligibly small and i t would not be necessary to determine m. The use of smaller capillaries, however, would greatly extend the time of testing and restrict the use of a given capillary to a comparatively narrow range of consistencies. It is therefore preferable to provide means, as in equation (3), for applying a kinetic energy correction when necessary. The buret consistometers used have somewhat irregular trumpet-shaped entrances to the capillaries and i t cannot be assumed that m will always have the constant value 1.12. On this account, and in order that even a t a high rate of flow the effect of any possible error in the value of m should be negligible, it was necessary to determine m for each instrument. A convenient method for finding the value of m has been described.” Briefly stated, if v is the average velocity I dP of flow (cm. per second) and Vis plotted against tL (the lr /* ratio of uncorrected to corrected or true viscosity), then m is given by 81
m=-
321 d tan 8
(5)
where 8 is the angle between the calibration graph and the fi’ 7gd4ph axis of abscissas. - = ,where p is the true viscosity M 12Ww obtained under such conditions that any possible inaccuracy in the assumed values n or X will cause a negligible error in the calculated viscosity. Figures 3 and 4 show how m is determined by the foregoing method, although there is a scattering of points, even after the surface tension correction has been applied, and some uncertainty where the lines should be drawn. Figure 3 shows that m must have a considerably higher value than 1.12 for buret No. 1. The value 1.78 shown in Figure 3 seems high, but it is within the limits of values referrred ~
11 Herschel, Proc. A m . SOL. T e s t i n g Materials, 19 ( Z ) , 680 (1919); Bur. Standards, Tech. P a p e r s 100, 112, 126.
I X D U S T R I A L A N D ENGINEERING CHEMISTRY
January, 1927
to by Bingham as determined by a n entirely different method from data of Poiseuille.lz Figure 4 indicates that for buret No. 5 m has a value more nearly equal to, probably somewhat lower than, 1.12, the commonly accepted value. The fact that the lines intersect the axis of abscissas a t a point below unity indicates a slightly negative value for A. As the length of capillaries could not be accurately measured, however, this negative value is probably without significance. After the corrected average head and the coefficient of the kinetic energy correction had been determined, t’hree methods were available for determining the diameter of the capillary from the data in Table 111. These methods, named for convenience from the authorities for the equations involved, are B (Bingham method), in which equation (3) is used for calculating d; A (Auerbach method) in which use is made of Auerbach’s equation for a viscous liquid; and D (Dryden method), in which a modified form of Auerbach’s equation is used and account is taken of the kinetic energy correction. Method B requires no further explanation. The others do. Auerbach used an i n s t r u m e n t in the form of a U-tube, but his equations apply equally well to the straight buret cons i s t o m u t e r . The method of deriving t h e e q u a t i o n shas been modified, however. B y combining e q u a t i o n s (1) and (2), neglecting the kinetic energy ‘OrCoefficient of Kinetic Energy Correction rection, and noting that Q = (hl - h2) So,the equation of flow for a viscous liquid may be written rgd4 T
128 L
(5)
So
=
CaT
137
studied the line would be concave upward. Curvature in this direction shows that the material in question is not to be classed as a true liquid. The converse is not necessarily true, however, for approximate straightness might result from the simultaneous effects of kinetic energy and departure from equation (l), if they happened to be nearly equal and opposite. If the kinetic energy correction is considered and equation (1) applies, then the more exact equation for (6) becomes log.
(a) +
YI
- YZ = C3 T
(7)
which may be obtained by combining equation (1) with the equation for average head.13 hi
h, = loge
- h2
($) + y1 - yz
where
+
y1=
(log.
n
- hz)’
(E) +
4-1
yz = r
c=
C (hi
‘/4
mgd4
h
2
Y1
(8)
- Yz)
-1 -1
256 ( $ ) * L a
Equation (7), in which C3 has the same value as it has in equation ( 6 ) , was used for determining the diameter of the capillary by method D. As equation (7) cannot be used until C has been calculated from a known or assumed value for d, equation (3) is to be preferred. Equations (6) and (7) apply only to true liquids which satisfy equation (1). For colloidal materials, Auerbach assumes the empirical relation14 q = k ( p ) ” or q = k’ ( g p ) * (9)
&
(6)
where hl is always the head a t the start of the run and is therefore constant, while hz is the head a t each successive graduation a t which observations are made. . T, the total time from the start of the run, must be obtained by addition if the method of timing by the use of two stop watches is employed. Equation (6) was used in finding the value of d by method A where the kinetic energy correction was negligible. h As it cannot ordinarily be assumed that the buret is of constant section, i t is necessary to use in place of T a corrected value, TI, obtained by multiplying T by the ratio where S is the average section of the buret from the starting point to the graduation a t which T is read and SOis the maximum section of the buret, assumed to be the nominal section. Values of this ratio are given in Table IV. If equation (6) applies, the time, T , plotted against the logarithm of the head, hz, should give a straight line, and if a material which is known to be a true liquid and to satisfy equation (1) gives a line which is convex upward, it follows that the kinetic energy is too large to be bored’ Even when the kinetic energy correction is insignificant, materials which do not satisfy equation (1) might give a line curved in either direction, though for such materials as have been
$’,
‘2 Bingham, “Fluidity and Plasticity,” pp. Book Co., 1922.
20, 23, McGraw-Hill.
Ratio of f i n o 1 to i n i t i a l head
Figure + D i a g r a m
for D e t e r m i n i n g Average H e a d f o r Plastic Materials
where is a constant of the material and o1 k , is an unknown function of another constant of the material and of the dimensions of the capillary. p is the pressure causing flow, expressed as grams per square centimeter, 18 This follows from Dryden’s equations, Bur. Standards, Tech. Paper 210, 230 (19221. . . 1 4 Nutting, Proc. Am. SOC.Testing Materials, 21, 1162 (1921); Ostwald, Kolloid-Z., 86, 99, 157, 249 (1925).
INDUSTRIAL A N D ENGINEERING CHEMISTRY
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of Caoillaries of Two Consistometers Calculated f r o m Flow Tests
Table V-Diameters
CALIBRATING
LIQUID
Water 24' C. Water: 20.20 C. Kerosene No. 2 Kerosene No. 1 Mineral seal oil Mineral seal Oil 500 sec. oil
1
d4
...
Dryden
d
dd
.,.
... .. , . .
0,088529
0.050%
...
1
I
No. 1 Auerbach
d
d4
Bingham
O.Osfifi22 O,OsfifiO2 0.06659fi O.Os6filO O,Osfi62O
0.0t6623 0.0~6622 0.0~6623 0,066595
0.066579
...
...
...
If p in equation (9) is assumed to be the average pressure corrected for kinetic energy, or if the kinetic energy correction is negligible, the average head for a material which satisfies equation (9) is given by
By combining equations (9) and (lo), log, ( T where
-
C,)
=
log,
C6
+ (1 - n ) log, P
cs=--
k(l c 4
=
- cj
(11)
SO
- n)
(
*,I
-
">
pl being the initial pressure. Equation (11), given by Auerbach, is difficult to solve and appears to be of value mainly as a check after the constants of the equation have been determined by other means.
Exeonent,
VOl. 19, KO.1
1
d
0.05073 0.05069 0.05068 0.05071 0.05072
... ...
No. 5 Auerbach d4
d
dc
..,
...
... ...
... ...
...
...
...
...
... o.oaim
... ... ...
o.iii60
Dryden
...
...
o.oaitix o.oai549
Bingham
d
d4
d
... ... ... ...
. . ... ...
...
o:iiie . 0.1116
...
... ...
...
o.0a'1;546 o.iii5 o . 0 ~ 1 ~ 5 1 0.1116
Table V gives the calculated diameters of the capillaries of the two consistometers as finally obtained. The values for each calibrating liquid are averages calculated from several runs of 7 observations each for consistometer S o . 1 and ten observations each for No. 5. The average diameter by both the Dryden and the Bingham method was 0.05071 for consistometer KO.1 and 0.1116 for S o . 5. Values of d 4 as well as of d are given because viscosities are proportional to d4. Method A was used only when the kinetic energy correction was almost negligible. Under these conditions the results agree well with those obtained by using the other methods. I n fact, under such circumstances method d might give more accurate results than the Dryden equation, which becomes very difficult to apply when the kinetic energy correction is small. I n calculating the results in Table V by method D, a value of 0.0507 was assumed for d for consistometer S o . 1, and one of 0.1116 for S o . 5, after these values had been determined by method B. d can be determined by method D only by successive approximations. This method, therefore, has been used merely as a check. The agreement between the assumed and the calculated values of d is a measure of the accuracy of the former, if methods D and B are equally reliable. From Table V it would appear that the concordance attainable by method B compares favorably with that of the Bingham viscometer, provided all necessary corrections are applied. The difference between the maximum value and the minimum value of d4, as determined by this method, was 0.4 per cent.
n
Figure 6-Correction
D i a g r a m f o r Average Head for Buret No. 5 Numbers on lines show reading of buret at end of timed interval
Figure 5, for determining the average head for a material which satisfies equation (9), is drawn from equation (lo), except for the upper curve, which is drawn from equation (2). For a given consistometer it is more convenient to obtain a correction to the arithmetical head by a diagram of the form shown in Figure 6, which gives the correction diagram for consistometer KO. 5. Within the range of values of n shown on the diagram, approximately, , --h , -h = h, - h
l + n 2
where ha is the arithmetical mean head and h is the average head, calculated by equation (2). That equation (12) is not of general application is shown by Figure 5.
P r e s s u r e y r a m s .per cm' Figure 7-Flow-Pressure
Graph for an Oil C o n t a i n i n g Soap
A buret consistometer calibrated as described may be used as a quick means of obtaining successive checks on viscositv determinations. the viscositv beine calculated v
INDUSTRIAL AiVD ENGINEERING CHEMISTRY
January, 1927
fromequation (1). If the values for L and m are taken as previously given and the values for d are taken as obtained by method B, the instrumental constants CI and C2will be as given in Table VI, which contains all constants necessary when employing the consistometer, either as a visoometer for ordinary liquids or for testing other soft materials. Table VI-Instrumental CONSTANT
Constants of Two Consisrometers No. 1
d (cm.)
0.05071 5.4 1.78 0.00002946 0.01312
L (cm.) m c1 c2
No $5 0.1116 2.0 1.07 0,001,363
0.02123
To exemplify the use of a buret consistometer in determining the consistency of a soft material, the results of tests made with instrument No. 5 on a n oil containing soap are shown in Figure 7 . As the lines in this graph are practically straight, the consistency of the material may be expressed, approximately a t least, by the yield shear value, f, and stiffness, S, as defined by the equations
where p is the pressure obtained as the intercept of the upper straight portion of the graph, prolonged, on the axis of ab-
'
- is also found graphically. 4 S and f are constants of the material. Both ordinarily increase as the resistance to flow increases. Taking values for d, L and C1from Table VI, and reading p = 5.5 arid p= 9 363, from Figure 7 , it was found that f = 75 dynes per sq. em. and S = 0.68 dyne-second per sq. cm. I n the absence of published data on the consistency of oils containing soap, comparison may be made with the results scissas.
139
of Porter and Gruse15 on worked cup greases. These investigators do not give values for f, but for their grease of 1 highest mobility, 0.217'6, the stiffness would be 0.217~ = 4.60, or about 7 times as great as that for the oil containing soap. It is not to be inferred from the foregoing example that equations (13) and (14) are applicable to all materials which do not obey equation (l), and reference should be made to our paper presented before the June, 1926, meeting of the American Society for Testing Materials for a method that is preferred for rubber-benzene solutions. However, whatever equations may be necessary to describe the consistency of a material after a flow-pressure graph has been determined, i t is believed that the buret consistometer is of general application, provided only that the material is not opaque nor too stiff to flow readily under hydrostatic pressure. Summary
The buret consistometer may be used for rapidly and accurately determining the flow-pressure graph of a viscous or other soft material. The value of the coefficient of the kinetic energy correction should be determined for each instrument. It may be necessary to check the graduations of commercial burets. A satisfactory correction for surface tension effects was made by subtracting from the average head half the capillary rise, calculated from the usual formula, with a diameter equal to the outside diameter of the capillary tube. The inside diameter of capillary was found by flow tests for two buret consistometers. The difference between the maximum value and the minimum value of d4 for consistometer No. 1, as determined by five calibrating liquids by the recommended method, was 0.4 per cent. The ordinary formula for stream-line flow may be used in the calibration, without resorting to the laborious calculations proposed by Auerbach. 15
THISJOURNAL,17, 9.53 (1925), Green, Proc. A m , Soc.
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Rubber as Lining for Grinding Mills' Solution of a Long-standing Problem of Chemical Grinding By B. W. Rogers? THE B. F. GOODRICH RUBBERCo., AKRON,OHIO
HE engineers responsible for the trial of rubber as a grinding mill lining in the mining industry had in mind the abrasion-resisting quality only, to OT ercome the severe wear and frequent costly renewal of steel lining. The early tests showed that rubber could, if installed under proper conditions, effect a very desirable saving in maintenance cost. Contrary to expectations, the rubber lining bettered the performance of mills by reducing consumption of power and grinding mediums and by increasing capacity and fineness of the product being ground. These indications later suggested tests which formed the basis of research to determine the reasons for the difference in performance between metal and rubber lining, when operating under parallel conditions. It was found that the light weight of the rubber lining as compared with steel or stone reduced power consumption and permitted loading the mill with 20 per cent increased
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Received July 26, 1926. Sales Engineer.
weight of grinding charge. Moreover, the rubber lining retarded the slippage of the grinding mediums against the shell, which was reflected in a more efficient agitation of the charge and a resulting increase in capacity and fineness. One series of tests included a photographic study of the operation of a laboratory mill with a glass front, which permitted visualization of the grinding action within the mill under varying conditions of pulp volume, density, lining material, and liner design. The photographs showed conclusively that slippage is detrimental to high efficiency. Slippage was not so pronounced in dry grinding operation as in wet, and it was observed that the nature of the material being ground had a strong influence on the action of the grinding charge. It was also observed that a corrugated lining helped to prevent slippage, and that a smooth rubber lining prevented slippage to a greater extent than smooth steel. This is accountable by the fact that the soft rubber allowed the individual pebbles or balls to indent the surface, forming a greater contact than the point contact of round grinding bodies resting on a hard lining.
