CONCENTRIC=CYLINDER MOTOR-DRIVEN VISCOMETER RICHARD H. WILHELM AND DONALD M WROUGHTON Princeton University, Princeton, N. J.
T
HE present form of viscometer was developed during the course of a study of the properties of several suspensions as they relate to flow resistance in pipes. Although a large variety of viscometers (1, 4, 7, 8) is available, few are suitabIe for use with suspensions. The viscometry of such materials was well reviewed by Hobson ( 5 ) . In several recent investigations (3, 6) a weight-driven concentric-cylinder visqometer of the Stormer type was favored for suspension measurements. This type of instrument may be operated at a series of different constant speeds and can therefore be used to detect a deviation from Newtonian behavior-that is, a variation of apparent viscosity with rate of shear. The concentric cylinder arrangement was chosen as a basis of the present study. However, during the course of early experiments with a weight-driven instrument, some difficulty was experienced with settling, due to the intermittent method of operation. Therefore it was decided to construct a continuously operating viscometer by driving the inner cylinder with a motor, torque being the measured variable. Under the constant conditions that may be obtained with this modified viscometer, the lowest speed for operation without the occurrence of settling can readily be detected. Furthermore, since the viscometer operates continuously upon a given sample of material, a variation in properties with the amount of stirring, such as occur with thixotropic suspensions, may also be detected. T o compare the flow behavior of suspensions with that in pipes, the range of operation of the viscometer was purposely extended into the turbulent region. The specific application of the viscometer to suspensions will be reported later. This paper deals with its calibration and use with true liquids.
propeller at the center to counteract settling of solids. The addition of paddles increased the torque reading of the instrument by about 6 per cent. Driving motor, J , is supported by an overhead beam, m. The motor is a Westinghouse, style 577,774, 100-volt a. c. or d. c., of about one seventy-fifth horsepower. (The exact rating was not given by the manufacturer.) It is series-wound, and the speed is controlled by an external resistance. The supporting beam carries hardened steel knife edges, n, set in exact alignment with the center of the motor shaft. These knife edges rest in agate V-bearings, 0, taken from a platform balance. End thrust is taken care of by needle points ground on the ends of one knife edge. These points bear against small vertical hard-steel plates,
The design of a motor-driven concentriccylinder viscometer is presented. The essential features of the instrument are continuous operation at a series of speeds, dynamometer mount of the motor which eliminates friction to a large degree, and accurate speed measurement by means of a simple stroboscopic device. The viscometer was calibrated in both the viscous and turbulent ranges by means of glycerol-water solutions. This calibration is presented as a specific friction factor vs. Reynolds number plot. The necessity of providing baffles on the wall of the outer stationary cylinder for stable operation, as well as the influence of these baffles on the shape of the calibration curve, is pointed out. The instrument was developed to measure properties of certain suspensions, but it is also useful for measuring the viscosities of liquids. This paper deals with the latter application.
Description of Viscometer The viscometer is shown in detail in Figures 1 and 2:
All parts are made of brass except as otherwise noted. Four rods, a,set in the corners of heavy square plates, b, constitute the supporting frame. The lower plate is solid except for four screw holes through which liquid may be drained. These holes are closed by wing nuts and gaskets (not shown). The outer cylinder, c, which serves as a container and has an operating capacity of about 1100 cc., is soldered to the bottom plate and passes through the top plate. A short overflow spout, d , determines the liquid level. Two triangular rods, e, are fixed, diametrically opposite ,to the inner wall of the outer cylinder. The necessity for these baffles will be pointed out later. Two of the rods, f, which are part of the frame, extend above the top plate to serve as guides and supports for raising and lowering the head, g. The head, a heavy plate, is fitted with short sleeves, h, around the vertical stee! rods, f. I t supports the rotating cylinder, i, and the motor, J . The head assembly may be raised to allow ready access to the outer cylinder for purposes of filling and cleaning. The rotating cylinder is supported by two SKF No. 13,301, small self-aligning bearings, k. Both ends of the cylinder are closed to prevent solids from depositing on the inside as a result of centrifugal action. The cylinder and shaft are finely machined. The bottom of the cylinder is equipped with two small blades, I, at the circumference and a small screw
p , set at the ends of the agate bearings.
Electrical connections to the motor are made through platinum wires, q, dipping into small mercury cups also set in line with the agate supports. Connections to the mercury cups are made with battery clips. The motor, together with its supporting frame, is free to pivot on the knife edges through a considerable arc. A long pointer, r, is fixed to the end of the motor support which projects over the headplate. This pointer indicates a position on a scale, s, on the frame. The entire motor support is properly counterbalanced by a fixed weight, t, so that it always remains in an upright position when the motor is a t rest. The pointer, 482
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however, is threaded a t the lower end and is provided with a small weight, u, which may be moved up and down t o change the sensitivity of this motor balance. Fixed to the pointer in line with the knife-edge bearing is a horizontal graduated scale, v, reading from 0 to 10. Stirrup-type weights of 0.5, 5.0, and 50 grams are suspended from this scale beam to weigh the torque developed. The motor is connected to the rotating cylinder by 3:l bevel gears, w. The larger gear, on the cylinder shaft, acts as a thrust bushing which places the entire weight of the cylinder on the top bearing. Any retarding forces in the liquid acting on the rotating cylinder are transmitted through the gears to the motor and cause the motor assembly to rotate about its center line on the two knife-edge supports. The torque necessary to return the pointer to the center position is measured on the scale and becomes 8 measure of the viscous drag on the cylinder. The speed of the motor is controlled by an external resistance and is measured by means of a stroboscopic disk, z, fitted to the end of the motor shaft. On this disk a single white radial line stands out from a black background. A neon bulb, with diskshaped electrodes placed back to back, is held close to the motor by a clamp in such a position that light from only one electrode will fall on the stroboscopic disk. The bulb is connected to an alternating-current line through a small peaking transformer which permits short neon discharges, producing sharp definition of the stroboscope line. The frequency of the supply current and the number of lines apparently seen on the disk while it is in motion are sufficient to give the speed of rotation. By means of a 60-cycle a. c. supply for the light, the speed of the disk for each pattern of lines which may be seen in an apparently stationary position is as follows: No. 8* 7* 6
5 9*
R. P. M. 450 514.3 600
720 800
No. 4 7* 3 8*
R.P.M. 900 1028 1200 1350
No. 5 7* 9*
2
R.P.M. 1440 1543 1600 1800
The peaking transformer is not absolutely necessary, but it is difficult to see those patterns which are marked * without it.
FIGURE 1. PERSPECTIVE VIEW OF MOTOR-DRIVEN ROTATING VISCOMETER
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Although some patterns are repeated at several different speeds, by using the prime speeds of 1800, 1200, and 900 r. p. m. as speeds of reference, no confusion results. A few speeds below the range included in the table were measured by counting revolutions in a definite time interval.
Suggested Modifications During the course of construction and operation of the viscometer, several possible modifications of the instrument were thought of: Although the large mass of liquid in the viscometer permits a simple manual adjustment and control of temperature, the installation of a water jacket connected to a constant temperature bath would be a convenience and would increase the precision. Operation a t only one speed is necessary when the viscosity of a liquid rather than a suspension is being measured. For this purpose a synchronous motor would be indicated. It may be possible to operate with a cup of smaller capacity than at present and still maintain precision in the torque readings by properly changing the gear ratio. The range of the instrument may be extended by using different sizes of rotating cylinders. Thus, the limit of viscosity which can be measured with the 3-inch rotor, when operating with pure liquids and with the motor now in use, is about 1 to 200 centipoises. A 2-inch rotor of the same length was found satisfactory for liquids with a viscosity of about 50 to 1000 centipoises. The range of any given rotor may also be extended by the use of a more powerful motor. A less destructible pivot for the motor assembly may be constructed by using small ball bearings a t each end of the motor shaft instead of the present agate sup orts, the scale, pointer, and other parts remaining the same. %his would decrease the precision, however, since the friction in these two bearings would be greater than for agate pivots. Although readings can be taken rapidly with the present arrangement, the addition of a chainomatic device in place of small weights would be a convenience.
FIGURE 2. DIMENSIONED SIDEVIEWOF MOTOR-DRIVEN . ROTATING VISCOMETER
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was done with the 3-inch rotor in place. Ten glycerol-water solutions, with viscosities ranging from 1 to 194 centipoises, were used as standards. The viscosities of the standard glycerolwater solutions were determined in Saybolt and Ostwald viscometers. The Saybolt calibration was checked with an A. P. I. standard alpha oil; the Ostwald, with water a t 25" C. The former was used to standardize glycerol solutions with viscosities greater than 30 centipoises, the latter for less viscous solutions. It was preferred to standardize the solutions in this manner rather than rely upon specific gravity-viscosity data ( 2 ) . Temperature corrections were made by using Sheeley's table (9) for interpolation. The torque vs. speed data for several solutions are plotted logarithmically in Figure 3. Curve A for the most viscous solution has a slope close to 1.0. This indicates that viscous flow exists according to Equation l:
T
=
~ M N
(1)
As the glycerol solutions become more dilute, a departure from viscous flow is noticeable. This is indicated by an increasing ' Courtesy, E . L . Luaces Associates slope from A to K , the latter being the ADSORPTION SYSTEM FOR EXTRACTING GASOLINE FROM NATURAL GAS curve for water. Squires and Dockendorff (IO) presented a convenient means of correlating data from concentric-cylinder Operation viscometerslwhen these are used either in the viscous or turbulent ranges. Their method will be followed. It conThe viscometer was first prepared for operation by bringsists essentially of establishing the calibration curve for a ing the motor system into balance with the rotor turning a t specific instrument as a friction factor vs. Reynolds number 200 r. p. m. in air. Adjustments were made with the plot. weights, y, a t the ends of the balance arm to bring the pointer The friction factor may be defined as t o a zero position. This procedure eliminates the friction of the gear and bearings from the readings a t low speeds. f = T/Dl'Dz'LsN' (2) T h e friction readings, when the cylinder speed was increased t o 600 r. p. m., were generally less than one unit of torque. Friction losses remained constant from time to time when the and the Reynolds number bearings were kept clean and well oiled. The sensitivity of as the dynamometer balance was adjusted by moving weight u up or down until the effect of the 0.5-gram weight in the unit position on the scale beam was readable. This is Re = Ns(D22 - Dl')/Z (3) about the limit of sensitivity, using the motor and power supply available, because of momentary fluctuations in readings caused by voltage variations and consequent speed For any instrument of changes. fixed dimensions, a specific To introduce liquid into the containing cylinder, the head friction factor and specific assemblv was first raised out of the way. Following this, the Reynolds number may be rotor was lowered into the liquid, the excess of which drained used. from the spout. During operations the spout was closed. The motor was brought to several speeds by means of a n f' = T / s N 2 (41 external resistance, and a t each of these speeds the torque Re' = N s / Z (5) was weighed much in the manner of an analytical balance. The readings were found to be completely reproducible for liquids within one unit of torque. The practical torque For the present instrurange for the 3-inch rotor extended from 20 to 550 units. ment all glycerol-water calibration data were plotted FIGURBI3. TORQUE us. Calibration in Figure 4 as f' vs. Re'. SPNEDCURVESFOR GLYCEROL-WATER SOLUTIONS One smooth curve resulted Because of end effects, the presence of paddles on the Z 8 which correlates viscometer rotor, and baffles on the stationary cylinder wall, viscosities A 194 1.240 flow data in terms of four cannot be calculated from the dimensions, torque, and speed B 109 1.232 C 53.5 1.217 variables-torque, speed, d a t a for the instrument. It is therefore necessary to caliE 19.3 1.184 viscosity, and density. brate the viscometer with liquids of known 'viscosity. This K 0.93 0.998
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FIGERE 4. CALIBRATION CURVE FOR VISCOMETER WITH BAFFLES Specific friction factor is plotted against specific Reynolds number.
Use of Calibrated Viscometer
Baffles and Stability
To determine the viscosity of a liquid, the torque developed a t any known r. p. m. is measured in the viscometer. With this information, together with the density, the friction factor T / s N z is calculated. The Reynolds number corresponding to this friction factor is then taken from the calibration curve, and from it the viscosity can readily be computed. This procedure was followed in measuring the viscosity of two oils a t 25" C. I n each case, however, the viscometer was run a t ten speeds. The data are given in Table I. The viscosities were about 2.5 per cent lower than the corresponding values found with a n Ostwald pipet. Because of the nature of the calibration curve, it would be expected that the accuracy would be greater in the viscous region and less farther out in the turbulent range.
Before the installation of the two triangular baffles, which are now part of the viscometer, unstable operation was encountered. This took place in the turbulent range only, with liquids of about 60 centipoises or less. Dependent upon the sequence of operation, it was possible to obtain different torque vs. r. p. m. readings. The following table shows two sets of readings with a solution of 30 centipoises a t 25" C.:
TABLEI. CHECKOF CALIBRATION 8
0,8591
0.8483
k
N
T
*x sNZ
10'
NZs
Z
Heavy Oil: Viscosity b y Pipet, 15.5 Centipoises 600 514 480 450 400 343 300 267 240 200 Average Error, %
14.7 15.1 15.0 15.0 15.3 15.6 15.3 15.3 15.2 15.0 15.15 -2.3
Light Oil: Viscosity by Pipet, 6.97 Centipoises 74.0 172 65.5 131 59.0 119 54.0 108 49.0 88 43.0 68 38.0 55 33.6 46 30.0 39 26.0 29 Average Error, %
-2.6
Speed, R. P. M. 480 400 300 240
High Torque 273 208 135 96
Low
Torque 250 191 125 90
Speed, R. P. M. 200 171 150
High Torque 72 56 45
Low Torque 69 53 42
The higher set of torque readings was obtained after accelerating the rotor rapidly from rest to a high speed, 600 r. p. m. Provided that the rotor was not completely stopped a t a n y time, these torque readings were reproducible by operating a t will up and down the speed scale. The lower and equally reproducible set of torque readings was obtained by starting the rotor very slowly from rest and increasing the speed carefully. The insertion of a rod into the annular space between the cylinders while the instrument was in operation and then withdrawing this obstruction caused high torque readings to decrease to lower values. Thereafter the low values were stable. Only by rapidly accelerating the rotor was it possible to revert to high torque readings. The effect of inserting and withdrawing a 0.25-inch round rod into the annular space between the cylinders is shown in Figure 5. The liquid level was a t the top of the rotor, the rotor speed was 480 r. p. m., the liquid viscosity was 30 centipoises. The rotor first was accelerated rapidly to bring about a high torque reading, A . The rod was then inserted through a hole in the headplate and was advanced one inch a t a time from the surface of the liquid to the .bottom of t h e container. The torque decreased along path ABC. When the rod was removed, the torque reading did not return to t h e former high value but decreased still farther along CBD. Any
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further introduction or removal of the rod caused the torque to follow along path C B D . I n order to repeat the cycle and again start with a high torque reading as a t A , it was first necessary to accelerate the rotor rapidly. TOP OF ROTOR
3
5
result was that the sharp change from viscous to turbulent flow in the absence of baffles was converted to a gradual transition when baffles were used. For a viscometer this gradual transition is desirable. It may be concluded that a rotary-type viscometer may be unstable in the turbulent range, that the introduction of baffles will lead to stable operation, and that the baffles will affect the shape of the Reynolds number us. friction factor calibration curve.
7 2 z
Acknowledgment
B
ss4 -
The authors wish to acknowledge their indebtedness to E. P. Culver for valuable suggestions concerning the design of the viscometer; to W. Grove for his careful machine work in constructing it; and to J. R. McGaw, Jr., and J. H. Morris for assistance in developing it.
BOTTOHOF b ROTOR
E
& ! BOTTOM OF CONTAINER 240
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250
270
260
Nomenclature
260
TORQUE
T = torque measured with the viscometer, arbitrary units
FIGURE 5. EFFECT OF INTRODUCTION OF BAFFLE ON TORQUE OF VISCOMETER IN AN UNSTABLE REGIONOF OPERATION Viscosity of liquid, 30 centipoises; speed, 480 r. p. m.
rotor
Two processes appear to be included in the above experiment. The insertion of the rod first changed the type of flow in the annular space from an unstable to a more stable form with a consequent decrease in torque (path A B C ) . Secondly, in the presence of stable flow conditions the insertion of the rod caused an increase in torque. This latter obstruction effect accounted for a further decrease in torque when the rod was withdrawn after stable flow had been achieved (path
CBD). I n the final form of the viscometer two baffles were attached to the inner wall of the stationary cylinder. These not only permitted the viscometer to operate in a stable manner over its entire range, but also affected the shape of the calibration curve as shown in Figure 4. The addition of baffles raised the position of the viscous flow curve. I n the turbulent or unstable region the rise in torque because of the obstruction effect of the two baffles approximately counteracted the lowering of the curve due to a change to stable flow. The net
(1 unit as measured = 0.334gram cm.) N = rotor speed, r. p. m. (rotor speed is that of the motor, which is measured with the stroboscope) k = a constant P = viscosity, poises z = viscosity, centipoises L = length of cylinder over which viscous drag is being measured s = specific gravity D1 = diameter of inner cylinder D, = diameter of outer cylinder
Literature Cited (1) Barr, Monograph on Viscometry, London, Oxford Univ. Press, 1931. (2) Bingham, E. C., “Fluidity and Plasticity,” New York, MoGraw-Hill Book Co., 1922. (3) Craft, B. C., and Exner, J. D., Trans. A m . Inst. Mining Met. Engrs., 103, 112-15 (1933). (4) Higgins, E. F., and Pitman, E. C., J. IND.ENG.CHEM.,12,587-90 (1920). (5) Hobson, G . D., J . Inst. Petroleum Tech., 21, 204-20 (1935). (6) Lewis, W. K., Squires, L., and Thompson, W. I., Trans. Am. Inst. Mining Met. Engrs., 114, 38-52 (1935). (7) Middleton, G., Ind. Chemist, 12, 131-3 (1936). (8) Riggs and Carpenter, J. IND.ENG.CHEM.,4,901 (1912). (9) Sheelev. M. L.. Ibid.. 24. 1060-2 (1932). (10j Squires,’ L., and Dockendorff, R.‘L., IND. ENG. CHEM.,Anal. Ed., 8, 295-7 (1936).
STILLHEADSAND CONTROLS IN A WHISKY DISTILLERY Courtesy,
E . B . Badger & S o n s C o m p a n y
