THE JOURNAL OF INDUSTRIAL A N D ENGINEERING CHEMISTRY
1130
Vol. 14, No. 12
T h e Drainage Error in Measurements of Viscosity by the Capillary Tube Method’ By Eugene C. Bingham and Henry L. Young LAFAYETTE COLLEGE, EASTON, PA.
I
F T H E viscometer already described2 is used for very
viscous materials, there are certain corrections to be considered which are ordinarily not necessary, presuming that a reasonable precision is desired of, say, 0.2 per cent. A drainage correction arises from the fact that the volume of flow is assumed to be the volume of a certain double coneshaped bulb which has been calibrated by means of some known liquid. If the unknown liquid does not drain as well as the calibrated liquid, the volume of flow will be too small, and vice versa. The drainage error may, of course, bc decreased to any extent that is desired by simply increasing the time of flow, but it is wasteful to have the time of flow for a single determination consume several hours if an equally good determination can be made in a few minutes by using a more suitable apparatus or previously determined correction terms. Happily, both of these alternatives are open to us. By using the plastometer , no drainage correction is necessary, and with the viscometer simple corrections may be made.
Experiments were made to determine‘ how, with a given time of efflux (15 min.), the drainage error varied with the viscosity of the liquid used. Our experiments indicate that the drainage error may be taken as a linear function of the viscosity. Castor oil, lard oil, linseed oil, and certain mineral oil mixtures were used. TABLEI-DRAINAGEERROR FOR A BULBHAVING A CAPACITY 0~24.42ML., USING CASTOR OIL AT 20’ Time in Min. Average Rate of Efflux Drainage Error t l/t Per cent
7.80 7.84 9.79 9.80 13.OS 13.08 18.41 18.38 27.63 27.46 48.16 47.88
0.128 0.102
..... .....
0.0765 0.0544
.....
0.0363
.....
0.0209
.....
1.40 1.46 1.27 1.36 1.20 1.15 0.91 0.97 0.80 0.74 0.51 0.55
’
As a result, we have prepared Table I1 to show the drainage corrections for liquids of different viscosities and for different times of efflux. I n using the table, suppose that a liquid of approximately 750 centipoises mas determined in a time of e a u x of 30 min. By interpolation of the table, the error due to faulty drainage is found to be 0.5 per cent. I n the formula for viscosity13 the volume of efflux is 0.5 per cent less than the actual capacity of the bulb; hence we obtain the final simple formu1al4 17 = 1.005 C p t - C’ p/t. If the material used is not a true fluid but partakes of the character of a plastic solid, it is evident that this table of corrections will not apply. Furthermore, a source of difficulty arises in that some liquids do not wet the walls of the bulb uniformly, so that the drainage is uneven. TAELE11-DRAINAGE CORRECTIONS FOR DIFFERENT VISCOSITIES AND TIMESOR EFFLUX IN PER CENT EFFLUX 10 15 30 45 60 100 150 Viscositv in Co. Min. Min. Min. Min. Min. Min. Min. 1000 1.2 1.0 0.7 0.6 0.4 0.3 0.2 500 0.6 0.5 0.3 0.2 0.2 0.1 0.1 100 0.1 0.1 0.1 0.1 0.0 0.0 0.0 1 0.0 0.0 0 . 0 0 . 0 0.0 0.0 0.0
-
oLrd:
I
02
I I ,I I I I I 0 3 0 4 0 5 O b 07 0 8 0 9 ~ ~ a ~ n frror k g c 1 1 1 Per C e n t
t IO
I 11
I
22
! 13
I
I
1.4
FIQ.1
I n our experiment, me have used double cone-shaped bulbs having the following volumes determined by means of mercury-2.50, 3.68, 8.80, 11.46, and 24.42 ml. Liquids of known viscosity were driven under known head through a capillary attached to the lower end of the bulb. The volume of the bulb being known and the volume of efflux found by direct weighing, the drainage error was determined by difference. As an example me give the values obtained for the 24.42 ml. bulb in Table I and Fig. 1. I n the figure the drainage error is plotted against the rate of efflux, which is taken as proportional‘to the reciprocal of the time in minutes (l/i). It is seen that in order to determine the viscosity of castor oil at 20’ with an accuracy of 0.2 per cent, it is necessary to make the time of flow about 2 hrs. unless a correction is made for drainage error. 1 Presented before the Division of Physical and Inorganic Chemistry at the 63rd Meeting of the American Chemical Society, Birmingham, Ala., April a to 7, 1922. 1 Bingham, “Fluidity and Plasticity,” lS’Xd, p. 76.
Leaving the question of the drainage error, the question may arise as to whether the heat developed within the capillary, due to the work done in overcoming viscous resistance, is sufficient to make an additional correction desirable. Take as an example one of our experiments with castor oil at 20°, using a pressure of 214 g. per sq. cm. and a volume of efflux of 7 ml. The work done amounts to 1,470,000 ergs, which is equivalent to 0.035 cal. Assuming a specific heat of 0.48, the elevation of the temperature of the oil on leaving the capillary should have been O.0lo, provided that no heat had been conducted out through the material of the capillary. This would affect the viscosity of the castor oil by only 0.08 per cent, which we must regard as negligible at present. In plastic flow much higher amounts of energy are absorbed, but the accuracy at present is not better than 0.5 per cent. It will evidently be practicable to make a correction for the heat developed as the necessity arises. 8
4
Bingham, “Fluidity and Plasticity,” 1922. p. 23. I b i d . , p. 74.
