November, 1923
INDUSTRIAL A N D ENGINEERING CHEMISTRY
1109
T h e Standardization of Commercial Viscometers* By Madison L. Sheely ARMOURGLUUW O R K S , C H I C A G O , ILL.
to the fact that the differN DETERMINAThe need of the standardization of viscometers, and the advisaence in results of tests from TIONS involving visbility of expressing results in absolute units has been discussed. the lowest to the highest cosity there has been an The calibration, set up, and operation of a typical glass outflow grades is not great enough urgent need for the practical type of viscometer haoe been gioen, together wifh comparisons of clearly to define the many applicationof existing methoarious ofher similar types. grades which must be desods to the standardization of Data showing comparative results of viscosity determinations on i g n a t e d between them. commercial vis c o m e t e r s the oarious instruments are given. This so-called “spread” from which are in general use in A typical calibration of the MacMichael torsional oiscometer for one grad: of glue to the the present industrial laboa single range of viscosity has been studied and comparatioe data next is especially narrow on ratory and for theexpression have been included showing unexplained discrepancies in viscosithe low viscosity glues. For of results in terms which ties of glue solutions determined by this instrument and by instruthis reason mainly, other may be checked in other menfs of the capillary outflow type. instruments of v a r i o u B laboratorieswithin a reasonLiquids and solutions suitable for the standardization of commertypes, usually of glass and able limit of accuracy. cial types of viscometers haoe been briefly discussed. with a much longer capillary These instruments are gen(to increase the spread), a r e erally constructed of glass of varying shapes and dimensions, and the results of tests on commonly employed. It is with the typical calibration of them are never strictly comparable, owing to these variations several of these types, together with a typical calibration of and the impossibility of exactly reproducing the critical the MacMichael torsional viscometer, that this investigation dimensions in glass. To be sure, various methods of cali- is concerned. bration of most “standard” commercial instruments are CALIBRATION AND USE OF A VISCOSITY PIPET now available. We have, then, only to select the method A type of pipet studied is shown in Fig. 1. It is essenwhich i s most suited to the type of instrument available, and tially a 100-ce. pipet bulb with a somewhat larger bore tube by careful determinations on liquids of known viscosities, and funnel a t the top, and a 3-inch glass capillary, inside covering the range in which the viscometer is to be used, diametter about 0.25 to obtain a calibration curve for that particular instrument. cm., sealed on the botObviously, this method of calibration is the only one availa- tom of the bulb. The ble with instruments of the type where dimensions are not pipet was immersed known. in a water jacket con- VISCOSITY PIPETTE A calibration of this kind serves two definite purposes. sisting of an inverted I n the first place it expresses the results in absolute units, a ’-pound the 3EE CALIBRATION system which cannot be too highly recommended. The ex- bottom of which had CURVE FIGURE 11 pression of viscosity in arbitrary units, such as seconds of been cut off. The outflow or degrees MacMichael, or in relations such as the bath was heated with ratio of time of outflow to the time of outflow for water, a specially designed is entively inadequate and very confusing, especially with electrical heating unit instruments of the type described above. Secondly, the controlling accurately results may be duplicated in separate laboratories. Mate- the temperature withrials which are purchased on viscosity specifications may be in * O.l”C.,agitation accurately defined in this regard. Moreover, in the case of being effected b y fragile instruments, such as glass, where dimensions cannot means of a slow curbe accurately duplicated, it is essential to calibrate in order rent of compressed to duplicate results should the instrument be broken. Such air. instruments are a t present in use in many industrial laboThe general methratories. Calibration, then, especially in absolute units, od of procedure was is highly desirable. to bring the temperaThe viscometers of the short tube type most widely used ture of the liquid to for oils are the Saybolt Universal, Saybolt Furol, Engler, be tested slightly Redwood, and Barbey. The Saybolt Universal,2 Saybolt above or below the Furol,%Engler,4 and Redwood6 instruments have already desired temperature, been standardized as to their principal dimensions, within according to whether allowable tolerances, and thus have been made available as the temperature of standard instruments which when used with the equation for the determination was each type express results in the absolute unit of viscosity. above or below that of It has been found, however, that with certain classes of the room, and after FIG. 1 tests in industrial laboratories, such as the testing of glues, pouring into the pipet t o adjust it by means of an a?these standard instruments are not suitable, owing mainly curately graduated thermometer. A slight stirring was 1 Received M a y 21, 1923. effected by moving the thermometer up and down within * B u r . Standards, Tech Paper, 112 (1919). the pipet. When the desired temperature was reached, tlle t C h e m . Met. E n g . , 26, 1175 (1922). thermometer was withdrawn and the head adjusted to an 4 Bur. Standauds, Tech. P a p e l 100 (1917); 112 (1919). etched line, A , located on the upper tube, and the time 4 Ibrd., Tech. PaPer 210 (1922).
I
~~~~~~,,‘‘\”o”o~~
.
I N D UXTRIAL A N D ENGINEERING CHEMISTRY
‘>lllO
measured from this point to another etched line, B, a t the top of the capillary tube. The general equation for viscosity for any given instrument, the critical dimensions of which are unknown and depend on flow due to gravity, is in which p is the absolute viscosity in centipoises, y is t h e density in grams per cubic centimeter, t is the time of outflow in seconds, and A and B are constants of the given instrument. The first term,
e, is usually Y
designated as kine-
VOl. 15, No. 11
their positions with respect to the kinematic viscosity curve depending on whether they have a density greater or less than one; but when these values are changed over to the corresponding kinematic viscosities the continuous kinematic curve Phown is obtained. There are several methods2 of finding the two constants A and B in Equation 1. The method used in the calibration of these pipets consists in finding the time of discharge of two liquids of known widely different viscosities, These values of t, together with the known eorresponding values of p and y , are then substituted in Equation 1. The two simultaneous equations are then solved for A and B. In order to check the relation between kinematic viscosity and time thus found, several other solutions of intermediate, known viscosities were run and found to check remarkabIy well with the values calculated. (Fig. 2 and Table I) The liquid of lower viscosity must be so selected that the type of flow is still viscous-that is, in straight-line motion, since the equation does not hold true when the flow is turbulent. TABLSI-VISCOSITIES
O F SOLUTION9 COMPARED WITH CALCULATSD
DETERMINED WITH PIPET 1 ( A = 0.1807; B = 54.0) Temgerature Kinematic C. Seconds Centipoise5 Viscosity Calculated Error Medtctnal P a r a f i n Oil 30 104.0 15.15 18.27“ 18 27 0.00 45 64.8 8.96 10 92 10.89 0.03 60 46.2 5.87 7.22 7.18 0.04 25 Per cent Glycerol 20 23 9 2.18 2 . 06a 2 06 0 00 45 Pev cent Glycero2 20 32.8 4.69 4 22 4.27 0.05 Water 30 19.2 0.80 0.81 0.66 0.15 60 Per cent Sucrose 65 43.0 8.34 6.61 6.52 0.09 60 48.2 9.83 7.77 7.58 0.19 55 56.2 11.67 9.26 9.20 0.06 50 65.0 14.01 11.03 10.89 0.14 45 77.0 17.18 13.49 13.20 0.29 40 Per cent Sucrose 60 22.8 1.98 1.71 1.76 0.05 40 27.2 3.25 2.78 2.94 0.16 35 28.8 3.76 3.22 3.33 0.11 30 30.6 4.38 3.74 3.76 0.02 25 33.5 5 19 4 42 4.44 0 02 20 37 2 6 20 5 27 5.27 0.00 15 42 0 7.47 6 34 6.31 0.03 44 11 Per cent Ethyl Alcohol ( b y Weight) 30 24.6 2.02 2.18 2.25 0.07 60 Pev cent Glycerol 20 55.0 10.31 8.86 0.10 8.96 Castor Oil 40 1349.4 231.0 244.0 243.7 0.30 _. a These two values were used in calculating the A and B constants in Equation 1. VISCOSITIZS
FIG. 2
matic viscosity-that is, absolute viscosity divided by the density. It has been found that when known kinematic viscosities are plotted against seconds of outflow of these liquids (Fig. 2 ) a smooth curve results. It will be noted that wrth this particular type of pipet, as with most other c Immercial viscometers, the curve bends slightly near the lower end and approaches a straight line at the upper end. This deviation from the straight line is due t o the correction for the effect of the kinetic energy, which is the energy required to set the liquid in motion as distinguished from the actual energy required to overcome viscous resistance in the capillary, When equivalent volumes are delivered over variable periods of time, this correction increases as the time B of outflow decreases. The third term, ,; of Equation 1
To determine the absolute viscosity, then, of any unknown liquid, it is necessary to determine the time of discharge and from a calibration curve or by calculation from the A and B constants in Equation 1 to obtain the kinematic viscosity. This value multiplied by the density a t the temperature of the test gives the absolute viscosity in centipoises. PIPETTE “2
represents this kinetic energy correction. With liquids of high viscosity it becomes negligible and Equation 1 may be written !! = & Y
(2)
which indicates that kinematic viscosity in these cases is directly proportional to the time. It will be noted also on Fig. 2 that when seconds of outflow of the same liquids at the various temperatures are plotted against the absolute viscosity in centipoises, for each of the three calibrating liquids used three separate and distinct curves a r e obtained,
FIG.3
A graphical method for the determination of the A and B constants in Equation 1 for any given instrument has been
I N D U S T R I A L A N D ENGINEERING CHEMISTRY
November, 1923
evolved by Higgins.6 He combines Equations 1 and 2
.and plots the values
P 1 against yt
The data given in
t2'
Table 1for Pipet 1 were used in plot,ting these values in Fig. 3. The A factor, then, is numerically equal to the intercept of the line on the axis of ordinates, while the B factor is equal to the tangent of the angle which the straight portion of the line, extended to the axis of abscissas, makes with that axis. This method has the advantage that it aids in selecting a suitable calibrating liquid for the low point on the curve, as it is thereby possible with most types to obtain a series of points near the lower end which will indicate where the straight line begins to break, giiing high values for FIG.4
to bend upwards.
rt
and causing the line
From the value of
A
t*'
a t which this
break occurs, may be calcuIated, approximately, the number of seconds of outflow below which . t h e instrument may n o t > b eused and which is near the region of critical velocity-that is, the region of change from viscous to turbulent flow. The position of this region varies with the dimensions of the capillary, but in general the shorter the capillary the lower will be the velocity a t which turbulence begins. It is of utmost importance in the calibration of any instrument of this general type to determine, at least approximately, this region of change of flow. It may not be possible to obtain the exact point, but a point well below t,he critical velocity may easily be selected for use in determining the constants. This, in fact, was the manner in which Pipet 1 was calibrated, as only one point (for water) above the critical velocity was obt,ained and the exact point a t which the critical velocity was exceeded was not accurately determined. With velocities above this region, only the particles nearest the walls of the capillary a,re moving in parallel motion, while the main volume is in violent, turbulent action. When the value of the expression
vdr
-,
P
generally known as
Reynold's criterion, exceeds a certain figure which is characteristic of each type of viscometer, the change from parallel to turbulent flow has taken place. An attempt has been made to calculate the value of this criterion for the region of critical velocity, but owing to the non-uniformity of the, diameter of the glass capillary and other dimensions, antapproximation only could be arrived at. For Pipet 1 this region lies near to the value
vdr = 12.00, p (in cp.) which is less than the value 20.00 generally used with the' long tube instruments, since the capillary is only 30.5 Collected Researches, The National Physical Laboratory, 11 (1914).
1111
a
diameters in length, and is greater than the value 8.00, which is the value calculated for instruments of the short tube type, such as the Engler and Saybolt,4 where the ratio of length to diameter is about 7. If only a limited degree oE accuracy is desired, the point of critical velocity may be obtained by calculating the A and B constants from a series of low points and a single high point and selecting the pair which will give a correct calculation for a value on the curve immediately below the selected point. For instance, if values for A and B are calculated from a 45 per cent solution of glycerol and a suitable high point and these values suffice to calculate the krlown viscosity of a 40 per cent solution of glycerol, then it is reasonable to assume that the A and B values are correct. The constants, however, may not be used t o calculate viscosities above the critical velocity. About forty pipets of the type described above have been calibrated in this manner, a n d solutions of unknown viscosities have been evaluated to am accuracy of less than =t0.1 centipoise. Table I1 gives a series of viscosity determinations on glue solutions (12.5 per cent, 60" C.) on two pipets calibrated by this method. Portions of the same solution were used with each pipet in order to eliminate any error due to concentration or method of preparation. Pipet 2 was of the same type as Pipet 1, but the running time was considerably less, TABLS 11-VISCOSITY OF GLUESOLUTIONS DETERMINED B Y Two PIPETS Glue, No. 1 3 5 7 9 11 13 15 17 19 21
Pipet 1' CP.
Pipet 2 CP.
15.86 13.73 11.83 10.26 8.64 7.40 6.32 5.28 4.46 3.74 3.17
15.97 13.72 11.88 10.11 8.59 7.42 6.24 5.35 4.50 3.73 3.18
a
Difference CP G.?! 0.01 0 . os 0 16 0.05
n.02 0.W 0.07
0.04 0.01
0.01
I n order to determine F 4 0 the suitability of apipet for a given range of viscosity, two other pipets of radically different design were calibrated. ~ l ~ r l P , = - A NGLUE co, The Powell pipetshown in Fig. 4 consists of a cup-shaped glass vessel with attached glass capillary 5l6/16 inches in length, the whole surrounded by a glass water bath. The initial head was adjusted by means of an etched line on the upper part of thecupand thevolume ST'. C A L , B R A T , O N delivered war3 measured Lbi
