High Temperature Viscometer N. H. SPE4R
AYf)
L. P. HERRINGTON, John B. Pierce Foundation, *Vew Huoen, Corm.
.ihigh temperature viscometer was developed in order accurately to measure viscosities of new heat transfer liquids currently under development. Instruments available either do not have the temperature range investigated or do not possess satisfactory accuracj- in this range. because high temperature viscosity standards are not available. The viscometer developed to fill this need is calibrated at ordinary temperatures, has a teniperatrire range to over 300" C., and measures with an accuracy better than 57'. Small volrinies ( i o ml.) of test liquids
THE
need for a simple and reliable viscometer which may be used to measure fluid viscosities a t high temperatures has become a11 increasingly important problem in the fields of lubrication and heat transfer. Very feiv data are available in the literature on viscosities of nonmetallic liquid substances above 125" C. This is caused, in part, by the lack of high temperature viscosity standards and lack of convenient apparatus. The extrapolation of liquid viscosities to higher temperatures is uncertain, because insufficient work has been done in this field to permit positive use of empirical formulas, and because of possible anomalous rheological behavior. The object of the work described here was to develop a practical viscometer, applicable to measurements to 300" C. or more, and to measure the absolute viscosity of liquids, particularly chemical heat transfer agents, reliably in this temperature region. I t was necessary that the apparatus be simple and flexible, and require only a relatively small volume of test liquid.
are required and no hazardous liquid baths are employed. Viscosity for three liquids are reported and data are compared with previous investigations. The unique features of the instrument are its simplicity, flexibility, and accuracy in viscometry at high temperatures. Physicists, chemists, and engineers have needed such an instrument for proper investigation of high temperature viscosities in the fields of heat transfer and lubrication, as well as for better scientific understanding of the effect of temperature on T iscosity.
Hubbard and Brotvn, in their technical paper, derive an equation of test for the rolling sphere viscometer: R =
+
5, d(D d) - 9K 42 ' L
(Sb
- S1)T sin
e
where = = g = K = d = D = L = 8 b = SL = 1' = e = ZL 7
absolute viscosity, poise 3.1416 acceleration of gravity, 980 em. per correlation factor (dimensionless) diameter of sphere, em. diameter of tube, cm. length of descent path, em. density of sphere (c.g.s.) density of liquid (c.g.s.) time of descent of sphere, seconds angle of inclination of tube, degrees
r-
METHODS OF MEASU-REMENT
There are three basic methods of measuring viscosity of liquids: rot.ationa1, falling body, and efflux timing. The rotational method consists of measuring either the torsional drag of a body while rotating in a liquid a t a constant speed, or the speed of a rot,ating body under constant torsional force; the body is immersed in the test liquid in both cases, and the viscosity is computed from the mathematical formula defining viscosity. The falling body method consists of timing the fall of a sphere or body through a given distance in the test liquid under gravitational forces, the viscosity being computed from Stokes' law. The efflux timing method (sometimes called tube or capillary method) consists of timing the flow of a given volume or mass of the test liquid through a dimensionally knovin orifice, the viscosity being computed from the Hagen-Poiseuille law for laminar flow in a circular tube. None of these methods is ideal. Each has its limitations, related to the physical nature of the apparatus, which results in apparatus constants that must be taken into account with varying degrees of accuracy before viscosity values may be obtained. Each method has specific advantages and disadvantages in application t o small volumes a t high temperatures. Complete consideration was given each method prior to the decision to uee a rolling sphere method, which is a variation of the falling body method. The variation requires modification of Stokes' law t o account for the translational effect of rolling and the proximity of the walls, so-called "wall effect.]' Many investigators have investigated this problclm, but it was only recently that Hubbard and Brown ( 4 ) , after a theoretical and experimental study, derived a satisfactorl-equation for this test method. The accuracy of their work is supported by a collation of their data and that of previous investigators, and by the excepbional agreement of the work described here.
I
i
4
Figure 1.
. TItiS/ON SCREWS 1 I
Diagram of Visconieter
Main assembly is metal block of high heat capacity, completely insulated
148
V O L U M E 23, NO. 1, J A N U A R Y 1 9 5 1 10-3 8
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6
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149 of the time of descent of the sphere. The viewing cuts were of the approximate diameter of the spheres, so that timing could be made upon complete interference of the light sources behind the viewing cuts. This was readily distinguished by coincidence of the leading and trailing edges of the sphere with the viewing cut, and permitted measurement of opaque liquids because of the greater light transmittance through the glass spheres than through the liquid. Care was taken to assure that the tube length w&s sufficient for good timing and permitted the sphere to attain a constant velocity of descent prior to measurement. The entire assembly was insulated with 2 inches ( 5 cm.) of ri id magnesia asbestos, and secured to a swivel. The swivel was tfen bolted to a wall, where vibratory characteristics were negligible, giving complete freedom of rotation of the entire apparatus. A bubble catcher was incorporated within the open end of the tube to eliminate bubbles from the testing area.
I
CORRELATION OF ROLLING SPHERE VISCOMETER
6
2 10-4
8 6 6
*
2
2
4
t
I 0
I
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h
I 80
5
60
2
;IO-6 U
‘
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i
-
VISCOSITY OF TETRA -ARYL- SILICATE
40 8 6 4
20 2
VI
2
p
10- 7 8
10
c e W
u e
a
t
HUBBARD- BROWN HOEPPLER BEYNlNG MARKWOOD
>
-
c
10-8 86
88
90
92
.94
96
98
IO
d/D
f;igii re 2.
A
$
Y
W
2
Correlation of Holling Sphere Viscometer I
.e
The corwlation factor, K , is shoivn to be a function of d / D by a graphical summary of experimental data. This plot shows a degree of random spread which may be expected because previous investigators did not havo the advantage of thP precision of apparatus available today. Prwision glass tubing became availa h k in this country in 1937 (Fischer & Porter Co., Hatboro, Pa.), and was ohtainahle at oiily one foreign plant prior t o that tinw, :it prohibitive prirw,
6
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t
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200
250
0-r
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4
I 2
-
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50
100
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APPAR
2
CALIBRATION A Y D TESTING
Four heating coils of Sichrome ribbon, wound on porcelain mandrels and insulated, were series-connected and positioned inside the metal block symmetrical to the tube. Two viewing cuts were drilled through the block to permit visual measurement
The calibration and test routine required by this apparatus is deceptively simple. The procedure merely consists of timing the descent of the sphere through the test liquid in the tube, while the
ANALYTICAL CHEMISTRY
150 Table 11.
Sb = 2.2236
Angle of Inclination, 21
Test 1 2 3 4 5
6 7 8 28
1
2 3 4 5 6 7
8
39
1
2 3 4
45
1 2
3 4
75
78
1 2 3 4 5 1 2 3
4
5
Wt.
Liquid Benzene Water Water H-7 oil Toluene Benzene Water H-7 oil Benzene Water Water H-7 oil Toluene Benzene Water H-7 oil H-7 oil Water Benzene Toluene H-7 oil Water Benzene Toluene Wat,er H-7oil H-7oil Toluene Benzene Water I€-7oil H-7 oil Toluene Benzene
3 3 3 5 1
3 3 5 3 3 3 5
1 3 3 5 5 3 3 1
5 3 3 1 3
5
D
1 3 3 5 5 1
3
Temp. O C. 20.6 23.6 30.1 34.8 36.3 35.7 35.6 28.3 20.6 23.6 30.1 34.8 36.3 35.7 35.6 28.3 29.3 27.9 28.0 28.6 29.3 27.9 28.0 28.6 28.5 33.0 29.3 34.0 34.2 28.5 33.0 29.3 34.0 34.2
SL G./cc.
0.8781 0.9974 0,9956 0.8189 0,8504 0.8620 0.9949 0.8233 0.8781 0.9974 0.9956 0.8189 0.8504 0.8620 0.9949 0.8233 0,8228 0,9963 0,8702 0.8587 0,8228 0.9963 0.8702 0.8587 0.9961 0.8202 0.8227 0.8527 0.8639 0.9961 0.8202 0.8227 0.8827 0,8639
B
u Poise
5’ X
Time 106 Sec. 0.0064 125.6 3.79 0,0092 192.6 3.90 0,0080 160.6 4.06 0.0483 925.6 3.72 0.0049 1 0 0 . 5 3 . 5 5 0.0052 102.3 3 . 7 3 0.0071 156.3 3 . 7 0 0.0580 1182.7 3.50 0.0064 98.5 4.83 0.0092 148.0 5.07 5.31 0.0080 122.7 0.0483 700.0 4.91 4.59 0.0049 77.7 4.84 0.0052 78.9 4.89 0.0071 118.2 4.57 0,0580 905.5 0.0562 650.5 6.17 0.0084 101.4 6.75 0.0052 61.4 6.26 0.0048 57.0 6.17 0 , 0 5 6 2 589.1 6.81 0,0084 8 9 . 7 7.63 0 0052 56.5 6.80 0.0048 52.4 6.71 0,0083 6 2 . 0 10.92 0.0507 340.8 1 0 . 6 1 0.0563 370.7 10.84 0.0050 3 6 . 3 10.05 0.0053 3 7 . 6 10.37 0.0083 6 1 . 9 10.92 0.0507 339.3 10.65 0.0563 367.6 10.93 0.0050 3 6 . 0 10.13 0.0053 3 6 . 8 10.59 V e a n weighted B
tube is inclined a t a known angle, and recording the liquid temperature before and after this descent. Physical dimensions were measured mechanically and K was measured by testing of viscosity standards. The correlation factor, K , was measured a t room temperature on five tube and sphere combinations for comparison with data of previous investigators (1, 3, 4,7 ) . These data are summarized in Table I and compared graphically with Hubbard and Brown’s summary of correlation factors in Figure 2. The mean deviation betn-een the values reported here and the curve by Hubbard and Brown is 8%. This is considered to be good, in view of the degree of control of dimensions in sphericity of available tubes and spheres. The calibration was unique, in that the equation: u =
The time interval has been given much attention by other investigators in view of slippage or “skipping” of the sphere a t too great an angle of inclination. Hoeppler (3) states that the fluid motion is turbulent when LIT > 6 and that the maximum velocity is realized when D2/da = 3. Hubbard and Brown ( 4 ) derive an empirical correlation for corrections due to skipping by consideration of a critical velocity, critical Fkynolds number, and critical resistance factor, and place the cause of the deviation as inertia of the fluid, formation of eddy currents in the flowing fluid, or combination of these causes. Block ( 8 ) states that the cause is inertia. In the present study no account was taken of turbulent flow, other than t o be sure laminar flow was realized. This was done by reduction of angle of inclination and coniparison of viscosity values obtained. The data recorded showed that no results were affected by turbulent flow, but that a general trend toward lower viscosity values did exist for larger angles of inclination. However, in no case did these values lie outside the range of experimental error.
Viscometer Calibration Data L = 17.145 (Weighted hlean) X 104 1 043
1.039
1.007
0.991
1,103
RESULTS
0.000105
60
and was further simplified by standardizing the calibration constant, B, with respect to the angles of inclination of the apparatus as B’, where
B’ = B X sin e The mean B values were obtained by classifying the viscosity standards used in calibrating into three groups and assigning weights to the groups by inspection. The H-7 standard viscosity oil was obtained from the National Bureau of Standards and was weighted 5, distilled water and C.P. benzene were weighted 3, and toluene was weighted 1. A statistical analysis of this weighting process was not deemed necessary. A detailed tabulation of correlation factor data is shown in Table I1 for tube and sphere combinations 1 t o 5. This combination was selected for testing because it gave the optimal time intervals for a given descent. The and the standard deviamean of the weighted B is 1.050 X tion is 1.2 X 10-6,
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200
250
300
--
-
8 MURPHY DATA
20 u)
VI W
-
g
10
P a
8e
L
I
COMPARISON OF MEASURED HIGH TEMPERATURE VISCOSITIES
I I
+ d)
42
.
40
3U t
B = K - g5~- - d ( D
I
80
B(Sb - SI)T sin e
was used, where
Test results on a liquid heat transfer agent, tetraaryl silicate, are shown in Figure 3. The curve shown was obtained by grouping and averaging, the mean deviation from the curve being lese than 7%. Viscosity measurements to 200” C. had been made on this liquid prior to this
1.098
6
c 4
> w
k
2
2 J
Pm 4
i 8 6
4
0
50
100
150
354
TEMPERATURE - c ° C .
Figure 4.
Comparison of Measured High Temperature Viscosities
V O L U M E 23, NO. 1, J A N U A R Y 1 9 5 1
151
study, using an efflux timing method. These data are also shown in Figure 3, and deviate from the curve by less than 2% in all cases. Viscosity measurements were also made on two additional liquids, diphenyl and Navy Symbol S o . 1065 oil, for comparative purposes. These data are shown graphically in Figure 4 in comparison with data by RIonrad (6) on diphenyl, and by Xurphy, Romans, and Zisman ( 6 ) on N.S. No. 1065 oil. The diphenyl obtained, the purest available, was found to contain solid impurities which restricted the descent of the viscometer sphere, and hence yielded apparent viscosity values higher than those of Monrad. The N.S. S o . 1065 oil was obtained through the courtesy of Zisnian, and was essentially the same as that reported on in the technical paper. The published values of specific gravity were used in this work. A summary of N.S. S o . 1065 oil viscosity data is given in Table I11 for comparative purposes. The comparison with published data, Figure 4, reveals a close parallelism with the absolute values reported here, which are about 8% lower than those reported by Murphy et al. This deviation may be caused, in part, by differences of oil samples used, and techniques employed by the investigators. This question can be settled only by additional high temperature viscosity measurements by other investigators on standard samples. C0NCLUS10.Y
Additional research is required and needed by science and industry in high temperature viscometry. The apparatus described is simple from the standpoints of construction, theory, and operation. I t is presented here in anticipation that additional
Table 111. hv. Temp., C.
N.S.
18
124.2 3:i7 142.0 154.6 2.86 1.92 183.8 1.63 19.5,6 1.29 218.4 1.0.5 243.4 0.79 275.2 0.60 297.5 Mean deviation, 7%
No.
23
3:i4 2.89 1.79 1.63 1.17 0.99 0.70 0.62
1065 Viscosity Data Summary
Angle of Fall, O 39 51 71 Viscosity, Cp. 3:65 3.06 2.07 1.79 1.41 1.22 0.84 0.70
5.03 3.50 2.99 2.87 2.28 1 . 9 7 2.01 1.72 1 . 5 4 1.36 1.10 1.04 0.92 0.81 0.77 0.67 4:06
73
AV.
Viscosity, Cp. 5.05
3.48 2.84 1.96 1.71 1.35 1.03 0.80 0.67
5.04
3.57 2.92 2.00 1.75 1.35 1.07 0.81 0.67
*0.27~ f f f
5.5% 3.0% 5.5%
5.7%
=t
* 5.9% * 6.4% 5.7%
* 3.9% *4.6
research and development will be done, in order to lessen the obscurity and uncertainty in the field of high temperature liquid viscometry. LITERATURE CITED ( 1 ) Benning, -L F., and Markwood, W, H., R e f r i g . Eng., 37, 243 (1939). ( 2 ) Block, R. B., J . A p p l i e d Phys., 11, 635 (1940). (3) Hoeppler, F., 2. tech. Physik, 14, 1G5 (1933). and Brown, G. G., IXD.ENG.CHEM.,ANAL.ED., (4) Huhbard, R. M., 1 5 , 2 1 2 (1943). (5) Rlonrad, C. C., “Condensation of Diphenyl Vapor and Application
to Xusselt’s Theory,” doctor of philosophy dissert,ation. University of Michigan, 1930. ( 6 ) Murphy, C. XI,, Romans, J. B., and Zisman. W. A.. Trans. Am. S O C . Mech. Engrs.. 71, 561 (1949). ( 7 ) Sp&,T’., Trans. C h e m E r t g r . Cons.. W o r l d P o w c r Conf., 2, 1 (1937) ‘
RECEIVED March 30, 1950.
Determination of Particle Density of Crushed Porous Solids Gas Flow Method SABRI ERGUN, Coal Research Laboratory, Carnegie I n s t i t u t e of Technology, Pittsburgh, Pa.
ASY properties of fixed beds and fluidized systems are related to the particle density and the specific surface of the solids that constitute the bed. A knowledge of the particle density, for example, is essential in the calculation of the effective void volume of a bed and in the determination of the effective specific surface of solids by gas flow methods. The estimation of the pressure drop and rates of heat and mass transfer which accompany every reaction in a bed requires knowledge of the void volume and the effective specific surface which can tie determined only when the particle density is knoltn. When a porous material is broken into smaller pieces, the particle density of the smaller pieces nil1 be greatrr than that of the original piece, owing t o elimination of pores in thr course of breakage. The increase will be more and more marked as the size of the particles approaches that of the pores. Khen the material is pulverized to the size of its smallest porcs, the particles are no longer porous. Accordingly, the particle density will approach the true density of the solid as the size of the particles is reduced. The particle density, therefore, is not A characteristic property of a porous material, because it changes with pnrticle size. It characterizes the material only when the size of the particles is specified with it. Although porous materials such as coke, activated carbon, sintered alumina, sintered magnesia, silica gel, and many other catalysts form the beds for numerous industrial operations, the dependence of the particle density on the particle size for these materials has not been generally recognized. Instead, an apparent density has been
A gas flow niethod has been developed for determining the particle density of crushed porous materials from gas flow rate, pressure drop, and bulk density measurements. The method is based upon the determination of coefficients a and b of the linear form of the pressure drop equation ( 1 3 ) at different bulk densities to which a given porous material may be packed:
IPILU,,, = a
+ bG
The particle density is obtained by the method of least squares as the intercept of either of the following linear relationships derived:
The method is self-checking in that i t offers t w o alternatives largely independent of each other. Its validity has been checked with nonporous solids by comparing the results with water-displacement densities. Results are reported for numerous cokes of different origin as well a3 size fraction, and possible applications of the method are discussed.
