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Ind. Eng. Chem. Process Des. Dev. 1983, 22,633-635
New Types of Viscometer Plummets for Measuring Viscosity of Low Viscous Liquids under Pressure Stlg Claeroon, Sabz All, and James L. McAtee, Jr.' Chemlshv Department, hyb University, Wam, Texas 76798
A descrlptton of a fatting body viscometer with four plummets of different shapes for measuring the viscosity of less vlscous fluids under pressure is given. The calibration constant was determined for each plummet using standard liquids.
Introduction The time of fall of solids bodies of various shapes in a liquid has been made the basis of many different types of viscosity measurements. The falling sphere viscometer is a familiar example. The use of a cylindrical body which is allowed to fall through a liquid in a tube of radius only slightly greater than that of the falling cylinder has been described by Segel (1903),Pochettino (1914),Lawaczek (1919),Bridgman (1926),Jobling and Lawrence (1951), Steiner (1949),and h e r and Blott (1949). For any given spherical ball or cylinder, the travel or fall time of the falling body multiplied by the difference between the density of the falling body and that of the liquid is a linear function of the absolute viscosity of the liquid. In case of less viscous liquids, the linear function no longer holds since the rate of movement of the falling body is so great that the flow becomes turbulent. During a program of research pertaining to the viscosity measurement of dilute polymer solutions, clay dispersions and polymer-clay mixtures under high pressure, four new kinds of plummets made of aluminum have been designed which substantially increase the fall time and thus decrease turbulence. Krigbaum and Flory (1953)found that specific viscosity of polystyrene (M,, = 383000)in benzene (0.0925g/100 mL) at 25 "C was independent of shear rate up to 2750 s-l. Sherman et al. (1953)also observed that the inherent viscosity of polystyrene ( M , = 2.88 X lo5)in benzene (0.03-0.05g/100 mL) exhibited no non-Newtonian behavior at various rates of shear ranging from 500 to 1100 s-l at 25 "C. The use of these plummets as falling bodies for measuring the viscosity of dilute polymer solutions and low viscous fluids is, therefore, feasible. Description of the Viscometer The literature contains many descriptions of highpressure, falling ball type of viscometers (e.g., Flowers; 1914;Sage; 1933;Hubbard and Brown; 1943;Griest and Schiessler; 1958;McDuffie and Kelly; 1964). A brief description pertinent to the present work is given here. The viscometer tube of 0.625-in. i.d., 1.541o.d., and 24 in. length is made of steel and is closed at one end by a dead-end plug with multiple O-ring seal. Details of the pressure-locking system have been discussed by Claesson et al. (1970). The time of fall of the plummet under gravity is determined by simple electrical contact. There is a hole in the dead-end plug and one in the bottom cap. When the dead-end plug is in place and the bottom cap is attached to the viscometer tube, two electrical leads are inserted into the dead-end plug and the bottom cap. The leads are connected to a clock through a relay circuit. The dead-end plug is insulated from the bottom cap by a piece 0196-4305/83/ 1 122-06338O1.50IQ
of nylon that has been mounted in the bottom of the cap. The nylon insulator keeps the circuit open between the dead-end plug and the cap until the falling body makes contact with the plug which activates the relay circuit to stop the clock and lighta a neon bulb in the sensor circuit. After the fall, the plummet is returned to the starting position by inverting the viscometer. The fall time was measured 15-20 times a t each set of experimental condition. The temperature of the viscometer w u held constant by putting it in a constant-temperature water bath. The pressure is generated by compressing the top piston above the solution in the viscometer tube using a hydraulic jack and is measured by a Heiss pressure gauge calibrated against a dead-weight gauge. Figure 1 shows the photographs of the four plummets of different shapes. Type A has a cone at one end and a propeller at the other end. There are two holes at the side of the cone which are connected with a central hole. B is similar to A except that it has a flange at one end instead of a propeller. Plummets A and B are 1.125 in. long and the cylindrical portion between the base of the cone and propeller (flange in case of B) is 0.256in. in diameter and 0.512 in. in length. The diameter of the central hole is 0.138in. in both A and B. C is a cylinder with a propeller at either end and a coaxial hole, while D has flanges at both ends. Plummets C and D are 0.780 and 1.850in.in length, respectively, with the cylindrical portion between the propellers (flanges in case of D) 0.56 in. in diameter and a coaxial hole 0.196 in. in diameter. The diameter and thickness of the propellers or flanges of all the four plummets are 0.56 and 0.039 in., respectively. The plummets were coated with gold in order to protect them from corrosion and to improve the electrical contact, while the viscometer tube was coated with nickel, both inside and outside, to prevent rusting and to get a smoother surface. Calibration of t h e Viscometer According to Smith (1957),Lohrenz et al. (1960),and Irving and Barlow (1971),the viscosity for a right circular cylinder of radius rZ, falling vertically for a distance L in a tube of radius r3, is given by 7=V(pl
- ~ & - 2 ~ g [ (+r ,r3') 2 In
- (r32r22)1)/2L(rz2+ ~
(r3/r2)
3
(1) ~ )
where p 1 and p z are the densities of the cylinder and liquid, respectively, and g is the acceleration due to gravity. However, for a cylinder with a central hole of radius rl eq 1 becomes tl
= IT(pl - p2)(r2 - r I 2 ) g [ h 4 -r24+ rI4) In (r3,/r2)(r,2- r22)2]1/2L(r34 - rZ4 r14) (2)
0 1983 American Chemical Society
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Ind. Eng. Chem. Process Des. Dev., Vol. 22, No. 4, 1983 A
B
C
D
21 TOP view
Top View
B o t t o m view
Top View
B o t t o c : View
Top View
B o t t o m View
B o t t o m View
Figure 1. Photographs of the four plummets: (A) cone at one end and a propeller at the other end; (B) cone at one end and a flange at the other end; (C)a cylinder with propellers at both ends; and (D) a cylinder with flanges at both ends. Table I. Comparison of the Experimentally Determined Values of Viscosity with the Literature Values for Sucrose in Water at 20 "C plummet
A
B
C
D
concn, wt % 13.0 20.0 32.0 44.0 52.0 13.0 20.0 32.0 44.0 52.0 13.0 20.0 32.0 44.0 52.0 13.0 20.0 32.0 44.0 52.0
fall time, s
11.54 2 0.18 15.17 5 0.12 29.34 * 0.20 67.05 * 0.09 150.86 f 0.11 8.14 2 0.22 10.70 5 0.24 20.68 2 0.20 47.28 f 0.18 106.37 2 0.12 7.05 f 0.20 9.24 f 0.26 17.86 * 0.23 40.83 2 0.14 91.87 f 0.10 5.18 f 0.29 6.81 f 0.27 13.16 5 0.22 30.08 * 0.08 67.70 0.18
Vlit.9
cp
7)exptl,
CP
1.461 1.923 3.840 8.508 19.527 1.497 1.987 3.690 8.689 19.146 1.446 1.905 3.827 8.438 19.602 1.624 1.749 3.884 8.697 19.199
1.480 1.945 3.761 8.596 19.341 1.480 1.945 3.761 8.596 19.341 1.480 1.945 3.761 8.596 19.341 1.480 1.94 5 3.761 8.596 19.341
error, % -1.28 -1.13 + 2.10 -1.02 + 0.96 +1.15 + 2.16 -1.89 + 1.08 -1.01 -2.29 -2.06 + 1.76 -1.84 +1.35 +9.76 -10.07 + 3.27 +1.18 -0.73
By putting all the constants equal to K , eq 2 can be rewritten as
where K and A are constant and are dependent upon the geometry of plummet, bore length, bore diameter, plummet density, and angle of tilt. K and A can be determined from the slope and intercept of a plot of 7 vs. T(pl - p2), respectively. The values of K must be determined experimentally with great precision as the plummets are not cylindrical in shape as required by eq 2. The viscometer was calibrated at 25 "C and atmospheric pressure by measuring the fall time for liquids of known
0
40
80
120
T (6-h)
Figure 2. Calibration plots for the four plummets.
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Ind. Eng. Chem. Process Des. Dev., Vol. 22, No. 4, 1983 635
viscosity. The liquids used in this work were standard viscosity oils S-3and S-6 supplied by Cannon Instrument Co., 54 wt %, 50 wt %, 32 wt %, and 2 wt % glycerol in water and 92.28% ethyl alcohol. The viscosities of these liquids are known a t several temperatures, so the effect of temperature on the calibration of the viscometer could be determined. Figure 2 shows calibration curves for the four plummets in accordance with eq 3. The plots are straight lines over a greater part of the range. Using a leasbsquare method, the values of the calibration constant were found to be 5.8 X 8.2 X 9.6 X and 10.3 x cm2/s2 for the plummets A, B, C, and D, respectively. It was found by Sage (1933) that up to 172 bar any change in calibration due to pressure could be neglected. This view was further supported by Irving and Barlow (1971), who observed that the variation in the calibration constant for their falling cylinder viscometer was small up to a pressure of 10000 bar. From the measured fall time and the density of the liquid, it is simple to calculate the absolute viscosity from the calibration curve. The kinematic viscosity can then be computed from the absolute viscosity and the density. Irving and Barlow (1971) used two cylindrical plummets, made of soft iron, with hemispherical ends. The range of viscosity they could measure was 0.01-10 P and 10-3000 P for the solid and hollow cylinders, respectively. The viscometer designed by Stanley and Batten (1968), using a stainless steel ball as a falling body, could be used to measure the viscosity in the range of 0.03-300 cP under a pressure of 1380 bar. However, the use of their instrument is limited only to electrolytic fluids. A recent study of Claesson et al. (1982) on the viscosity of dilute solutions of polystyrene (M,= 209000) in toluene (0.0025-0.02 g / d ) indicates that plummet A can be used satisfactorily in the viscosity range of 2.5 to 0.478 cP at pressure up to 1057 bar. The viscosity of sucrose solutions was measured under atmospheric pressure and compared with the literature values edited by Weast (1973-74) in order to provide a check on the accuracy of the calibration. Table I shows the measured and literature values. There is a close
agreement between the results for the plummets A, B, and C. The discrepancy in the literature and experimental values of viscosity in case of plummet D, for low viscous sugar solutions, is probably due to short fall time which results in greater turbulance in the liquid emerging from the smaller annular gap between the plummet and tube. The fall time increases as the solutions become more viscous, which shows that plummet D would be appropriate for fluids having a viscosity of at least 3.00 cP using a viscometer of the present dimension. From Figure 2, it can be seen that a change in the surface conditions of the plummet changes the calibration of the viscometer to a marked extent. The present design may easily be modified to meet particular requirements.
Acknowledgment The authors are grateful to Robert A. Welch Foundation for the financial support of this research. Literature Cited Amner, J. W.; Blott, J. F. T. "Principles of Rheological Measurement"; Nelson: London, 1949. Brldgman, P. W. froc. Am. Aced. 1026, 61, 57. Claesson, S.; Maimrad, S.; Lundgren. B. Discuss Faraday. SOC. 1070, 66, 3048. Claesson, S.; McAtee, J. L.; Ali, S. "Abstracts of Papers", 38th Southwest and 6th Rocky Mountain Combined Regional Meeting of the American Chemical Society, El Paso, TX, Dec 1982. Flowers, A. E. froc. Am. SOC. Test. Meter. 1014, 1 4 , 565. Griest. E. M.; Schiessler, R. W. J . Chem. Phys. 1056, 2 9 , 711. Hubbard, R. M.; Brown, 0. G. Ind. Eng. Chem., Anal. Ed. 1043, 15, 212. Irving, J. B.; Barlow, A. J. J. fhys. E. 1071, 4, 232. Jobling, A.; Lawrence, A. S. froc. R . Soc. London, Ser. A 1051, 206, 257. Krigbaum, W. R.; Flory, P.J. J . f o k m . Sci. 1953, 1 1 , 37. Lawaczek, F. 2. VerelnesDeut. Ing. 1010, 63, 677. Lohrenz, J.; Swift, G. W.; Kurata, F. AIChE J. 1060, 6 , 547. McDuffie, 0. E.. Jr.; Kelly, M. V. J . Chem. fhys. 1064, 4 1 , 2666. Pochettino, A. Nuovo Cimento 1014, 7 7 . Sage, 8. H. Ind. Eng. Chem. Anal. Ed. 1933, 5 , 261. Segel, M. fhys. 2. 1903, 4 , 493. Sherman, L. J.; Sones, R. H.; Cragg, L. H. J. Appl. fhys. 1053, 24, 703. Smith, G. S. J. Inst. Pet. 1057, 43, 227. Stanley, E. M.; Batten, R. C. Anal. Chem. 1068, 4 0 , 1751. Stelner, L. A. Chem. Age 1040, 60, 638. Weast, R. C. "Handbook of Chemistry and Physics", 54th ed.; 1973-74; Section D-231.
Received for review August 4, 1982 Accepted February 15, 1983
