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V O L U M E 25, NO. 6, J U N E 1 9 5 3
I
I
1
I
I
I
I
1
1
u)
Table 111. Analyses of Solutions of Anhydride Mixtures
W
:zoo -
n
Anhydride Mixture Solution 1 phthalic maleic Solution 2 phthalic maleic Solution 3 phthalic maleic
I
8K -01 1 5 0 F 2 W
U U
3 100
Amounts (Grams/4O Ml.) Added. Found 0.0461 0.0443 0,0451 0,0472 0.0335 0.0356 0.0953 0.0938 0,0525 0.0496 0.0677 0.0689
-
Relative Error, % -1.8 f4.7 +6.3 -1.5 -5.5 f1.8 Av. f 3 . 6
0
z
2
In
3
-
50-
n
I
0 0
I
0.5
10
1.5
2.0
Figure 1. Polarograms A.
Phthalic anhydride
B. Mixture of phthalic anhydride and maleic anhgdride
polarographic m-ave of a solution of 0.01280 mole per liter of phthalic anhydride. Curve B is the wave of the same solution of phthalic anhydride to which maleic anhydride was added. The wave height, hl, of the 0.01280 M phthalic anhydride, when present alone in the electrolytic solution, is equal to hz, the wave height of phthalic anhydride in the presence of 0.01647 ill maleic anhydride. This suggested the possibility of determining these two anhydrides when present together in mixtures. Curiously enough, mixtures of the two anhydrides do not produce the maximum obtained from solutions containing only one (Figure 1). To test the possibility of analyzing a mixture of anhydrides having distinctly different half-wave potentials, a solution (0.3 M lithium chloride, 50-50 benzene-methanol) containing weighed amounts of both phthalic and maleic anhydrides was prepared. The polarogram obtained with this solution resembled curve B ,
Figure 1, in having two distinct waves, one a t -0.75 volt due to the maleic anhydride and the other a t -1.16 volts due to the phthalic anhydride. From the proportional increases in the respective wave heights caused by adding weighed increments of phthalic and maleic anhydride, the quantities of phthalic and maleic anhydrides originally present in the mixture were calculated. Table I11 shows the results obtained using three solutions of mixtures of varying amounts of phthalic and maleic anhydride. These data show that it is possible to estimate the amounts of each of these anhydrides, when present together, with a relative percentage error of Z!Z 4%. ACKNOWLEDGMEhT
Determinations of the anilic acid numbers of the acid anhydrides were made by R. E. Koos; the butyl ester of aconitic acid anhydride was prepared by M. L. Fein and E. H. Harris, Jr. LITERATURE CITED (1)
Kappelmeier, C. P. -4., and van Goor, W. R., Anal. Chim. Acta,
(2)
Lewis, W.
2. 146-9 (1948).
k., and
Quackenbush, F. E'., J . Am. Oil Chemists
SOC., 26, 53-7 (1949). (3)
Lingane, J. J., and Laitinen, H. A , , IND.ENG.CHEM.,ANAL.ED., 11,504-5 (1939).
(4)Willits. C. O.,Ricciuti, C.. Knight, H. B.. and Swern, D.. AKAL. CHEM., 24,785 (1952). RECEIVED for review August 31, 1951. Bccepted March 26, 1953.
Anomalous Flow of liquids through Capillaries and Measurement of Viscosity G . F. N. CALDERWOOD, H. W. DOUGLAS, AND E. W. J. MARDLES Royal Aircraft Establishment, Farnborough, England
T
H E method of determining, by means of capillary viscometers, the viscosity of liquids, in centimeter-gram-second units, relative to that of water [LOO19 centipoises a t 20.00" C. (6)],used as the standard calibrating liquid, involves a possible error owing to the unique surface tension properties of water, the surface tension of water being about twice that of oils and other organic liquids. The design of the master or secondary viscometer with longer length capillaries than in the ordinary routine type of standard viscometer is such as to minimize, within a prescribed tolerance, any error due to surface tension differences. The standard method demands scrupulous cleaning of the viscometer with chromic acid mixture and rinsing, prior to the measurement of flow time. This cleaning is performed presumably, apart from removal of dust fibers, etc., to ensure a low contact angle of the water with the glass surface. Care is required to ensure that high contact angles are avoided, otherwise a meniscus resistance, the Jamin effect, comes into operation and may afiect precision. This meniscus resistance
becomes relatively large in microviscometers which are also adversely affected by another disturbing factor caused by the reversal of liquid flow a t the meniscus. Lillard, in a recent paper ( 4 ) , described a micromethod for determining the viscosity of oils by noting the rate of flow of an index of liquid in a tilted capillary tube. He used 0.04 ml. of liquid and claimed i~ 1% accuracy. Other workers ( 7 , 8),using this method of a column of liquid in a capillary, obtained with mercury a value 6% higher than the usually accepted coefficient of viscosity and attributed the difference to electrification a t the walls. During flow through a capillary, a drop rotates from the walls inwards so that the Poiseuille equation needs modification to allow for the reversal of flow a t the menisci. The importance of this can be shown by noting the apparent viscosity of an oil using columns of different lengths. With short lengths the apparent viscosity becomes abnormally high, reaching two or three times the normal value. The viscosity results given in Table I and Figure 1 were obtained. I n an experiment a t 20" C. with
ANALYTICAL CHEMISTRY
936
Several precautions must be taken in order to obtain the high precision required in the standard U-tube method of determining the viscosity of liquids (in centimeter-gram-second units) relative to that of water at 20" C., as the sole calibrating liquid. In microviscometry these precautions become of considerable importance. Unless viscometers are scrupulously clean, the flow time of water is complicated by the meniscus resistance (the Jamin effect) and by change in the average head of hydrostatic pressure caused by different contact angles. In microviscometrg the Poiseuille equation needs modification to allow for the reversal of flow at the menisci; unless the length of liquid is at least a hundred times the diameter of the capillary, abnormal values are obtained, especially at low rates of movement.
different lengths of silicone fluid (1 00 centistokes), rhosen because of the known low value of the Jamin resistance-less than 1 dyne per centimeter-in a tilted capillary 0.015 cm. in diameter, graph\ relating rate of flow and the force, in dynes, acting-calculated from the weight of liquid column and the sine of the angle of tilt from the horizontal-were first obtained and then the viscosity \\-as obtained from the slope of the graph? foi tiiffrrent liquid lengths.
The graph shown in Figure 1 is for the above equation and it will be seen that the results obtained closely fit the curve. Graphs relating the rate of flow of a column of mineral oil x i t h the force acting are curvilinear so that the apparent viscosity of ii length of oil moving down a tilted capillary depends on the rate of flow. The apparent viscosity values shown in Table I1 IVPIY obtained a t different rates of flow with a mineral oil having a viscosity of 100 centistokes. The abnormally high viscosities obtained with a column of mineral oil of length greater than 200 diameters moving down a tilted tube a t slow rates cannot be ascribed to the reversal of flow a t the menisci. The only explanation is that the Jamin ]'esistance is operative. Although it is generally considered that the Jamin meniscus resistance is nonexistent with organic liquids and water in freshly cleaned glass tubes, the resistance can be easily demonstrated with a liquid such as n-heptane; thus, for example, with a chain of 26 droplets of ?-heptane moving down a tilted capillary 0.056 cm. in diameter, the relation shown in Table I11 between .f, fowe in dynes, and u, rate of movement in centimeters X pc>r second, was obtained. Although n-heptane is a liquid of Xewtonian flow, yet the system of droplets is non-Sewtonian, behaving in an interestiiig rheological manner s h o n h g yield value and stress thixotropy. -4lthough the yield value (Jamin resistance) with a silicone fluid was found to be of the order 0.1 dyne and the graphs relating the flow rate of a column of liquid with force acting were nearly rectilinear yet the apparent viscosity was doubled by breaking the column into seven portions and the flow became non-Sew-
1
&-
,I
a?
.-X,.
.;-
1 .o P.0 3.0 4.0 APPARENT VISCOSITY: TRUE VISCOSITY, Y ' / V
Table I. Apparent Viscosity of Different Lengths of Silicone Fluid Moving through a Capillary
Figure 1. Variation in Apparent Viscosity of a Length of Liquid Moving in a Capillary, v' = v(l 4.5dll)
+
l / d . Length of liquid column divided by capillary diameter Y'. Apparent kinematic viscosity in centistokes 130 69 40 14.4 6.6 102 106 111 146 171
0 Silivonr fluid,
100 vrniirtoker: cupillnrg diamrter, 0.09 cm. Silicone fluid, 100 centi-tokes; capillury dinmeter, 0.20 c m .
X Silironc fluid, 20 ccntistukes; cnpillary diameter, 0.20 cm. 1 3linerul oil, I68 centistokes; capillary diameter, 0.09 cm. 1 Mincral oil, 18 ccntirtokea; capillnr) dinmeter, 0.18 c m .
Figure 1 also includes some values obtained with different lengths of mineral oil but with these the graphs relating rate of flow and the force acting were curvilinear; and tangents a t corresponding rates of shear were used for obtaining the viscosity. However, the results were closely similar to those found for the silicone fluid. The liquid column lengths are expressed in capillary diameters and it will be seen that liquid lengths of a t least 100 diameters are required to obtain a practical reading for viscosity. With a length of 5 diameter? the apparent viscosity is about twice the normal value. It has been possible to obtain an empirical equation describing the relation-namely, Y'
=
Y
(1
+ 4.5 d / l )
where V' is the apparent viscosity of a length, I , of liquid in a capillary of diameter d , in terms of the true viscosity, v.
i!'
3 3 193
Table 11. Apparent Viscosity of a Length of Mineral Oil Length. > 200 diameters, a t different rates of movement in a caiiillary 0.043 cm. in diameter Rate of movement, cm. X lO-3/sec. 0.5 0 25 10 5 2 1 v 103 112 131 183 325 681 Y'
u.
~
Table 111. Rate of Flow of a Chain of 26 Droplets of n-Heptane at Different Rates of Shear f
z
0 25
4
0 5 5 5
1
2 42
11
3 210
Table IV. Relation between Rate of Flow and 4pparent Viscosity for a Slstem of 20 Droplets of Mineral Oil in a Cnpillarj Tube Mineral oil 169 centistokes Rate of flou cm x 10-3isecond .4pparent viscositk in centistokes u 421 192 62 21 3511 460 530 680
z
Y'.
11 750
5 25 1360 2800
V O L U M E 25, NO. 6, J U N E 1 9 5 3
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surfaces tend to pick up hydrophobic films by adsorption and deposition. Contrary to what might be expected, the resistariw of the receding meniscus is greater than the advancing meniscus although the latter is moving over a relatively di Some experiments were done on the Jamin renistance of water in clean tubes of n-ide bore comparable with thc side arm or bulb of a L?-tube viscometer. Water was added through a fine capillary passing beneath the meniscus which was observed through a mi(-roscope. It was found that the meniwus flattened and the periphery rcniained stat,ionary for a while until a sufficient weight 1 P 3 of water, corresponding to the 5 to 25 dynes per centimeter of the meniscus resistance, had been added to hegin movement of the Figure 2. Relation between Flow Rate a n d Force i n Ilynes for 11-Cm. Length of Liquid i n Glass Tube 0.18 periphery. When water was xithdrawn from the t u l x through C m . i n Diameter the capillary the meniscus deepened and assumed its normal 1. n-Heptane 4. A fluorocarbon shape, then became further distorted until the periphery began to 2. Chloroform 5. Benzene 3. 4hsolute alcohol 6. Silicone fluid, 20 centistokes move erratically. Some results are shown in Figures 3 arid 4 for 7. Carbon disulfide the movement of the meniscus periphery with different amounts of water added or withdrawn. The Jamin resistance with \\.:iter on glass increitsed considerably with drainage, timr, of standing, and presencr, of hydrophotiic films. / Tests have I)clen pt.1.I' formed on the floiv timw /' ,/' i/' of n a t c r and SU('rO*iesolutioiis iii stundard visconi*/*'/./ eters both n-ith a wxttiiig L$ / agent ( 1 ) and n i t h a hyI . I drophobir film present. I ' ,**ey' Difference.q outside the ./ ; , .. %* *d prescribed awuracy of -0.2 0 0.9 0.4 0.6 0.15% were ohtainetl in VOLUME OF WATER ADDED, ML. 0.2 0.4 0.6 VOLUME OF WATER ADDED, ML. s e v e r a l instances. .isFigure 3. hlovement of Periphery of Water suming, through lack of Figure 4. Movement of Periphery of Water \Ieniscus i n Glass Tube 1.8 C m . in Diameter Meniscus i n a Freshly Cleaned Master Visa n increase 1. Freshly cleaned 3. With trace of oil cometer in the Jamin resistance 2. 4fter atanding 1 hour on walls of 25 dynes per centinieter and an approximate tonian. With a length of 100 diameters of a mineral oil, 169 periphery of 6 em. for the two menisci iu the h l h and rid? wntistokes, broken into 20 droplets of equal size, the apparent arm of a viscometer, the total increased resistance of t h r nimiwi osity a t different rates was found to be as shown in T a N e I V . is 150 dynes, corresponding to a loss in hydrostatic head of ahout These large divergences in viscosity values from the normal 0.5 mm. Gilbert (2) recommends for viscometers, a?;for pipets, ot,taiiied with broken lengths of liquid with numerous menisci a thin coating of a proprietary water-repellant material on the serve to emphasize the fact that the same divergences can exist walls for the purpose of ensuring complete drainage. He points out that in a tube with a Desicoted glass surfacte the water with a single column of liquid with two menisci, only to a smaller extent. In Figure 2 are shown some graphs relating the rate of meniscus is flat and t h a t the aqueous meniscus ha. a high startflow of' a column of liquid of Sewtonian behavior through a capiling friction. This higher meniscus friction and the change in lary with the force, in dynes, acting. The graphs, with the exaverage hydrostatic height due to the shape of the meniscus muqt (3eption of that for silicone fluid, are curvilinear and intercept the be considered in any viscosity calculation when high precision is Iorce axis. required. With vapillary viscometers there is always the danger that a With a S o . 1 British Standard viscometer a t 20" C., the time Iiuhtile or a droplet in the tube above the upper bulb may be of flow of water in a freshly cleaned viscometer was 299.8 secaondp present. Under these conditions the flow times tend to increase; while in the same viscometer, after rinsing with a benzene s o h P O , in the standard method, instructions stipulate t h a t bubbles tion of oleic acid, draining, and drying, the time of flow at the i i i u * t be absent. increase of same temperature increased t o 302.1 seconds-an about 0.7%. A similar experiment in the master viscometer VISCOMETERS AII-D JAMIN EFFECT WITH WATER indicated a n increaPe of ahout 0.2y0 in the flow time. Jamin ( 3 ) , in 1860, reported t h a t a chain of water droplets LITERATURE CITED c~)ultl withstand considerable pressure without movement. (1) Barr, G., Proc. P h y s . SOC.,5 8 , 575 ( 1 9 4 6 ) . I,iitcl, Smith and Crane (5) concluded from their experiments (2) Gilbert, P. T., Scirnce, 114, 637 ( 1 9 6 1 ) . that careful cleaning and avoidance of contamination render a (3) Jamin, J., Compt.rend., 50, 172 ( 1 8 6 0 ) . vapillary containing droplets incapable of sustaining pressure. ( 4 ) Lillard. J. G., ANIL. CHEM.,24, 1042 ( 1 9 5 2 ) . 13.1. using the tilted tube and other methods the authors have ( 5 ) Smith, W. O., and Crane, AI, D., J . Ana. Chem. Sac., 52, 1345 (1930). alnxys found a Jamin meniscus resistance with pure water and (6) Swindells, J. F., Coe, J. R., and Godfrey, T. B., J . Research sugar or glycerol solutions in glass and silica tubes of from 0.04 S a t l . Bur. Standards,, 48, 1-31 ( 1 9 5 2 ) . t o 1.8 cm. in diameter after careful cleaning, the values varying (7) West, G., Proc. Rou. Soc., A86, 20 ( 1 9 1 1 ) . from 5 to 25 dynes per centimeter according to the glass and ( 8 ) Tarnold, G. D., Proc. Phys. Soc., 50, 5 4 0 ( 1 9 3 8 ) . degree of drainage. If the resistance is absent immediately after RECEIVED for review October 24, 1952. Accepted March 30, 1953. Perini.. rlwriing, it quickly builds u p eeperially in an oil laboratory where sion t o publish has been given b y the Chirf Scientist, LIinistry of S i i ~ i ~ ~ I \ - .
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