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Steady shear viscosity measurements of viscoelastic fluids with the falling needle viscometer
Journal of Non-Newtonian Fluid Mechanics, 34 (1990) 351-357 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands
351
STEADY SHEAR VISCOSITY MEASUREMENTS OF VISCOELASTIC FLUIDS WITH THE FALLING NEEDLE VISCOMETER
NOH A. PARK J & L Instrument Corp., Norristown, PA 19403 (U.S.A.) YOUNG
I. CHO
Department of Mechanical Engineering and Mechanics, Drexel University, Philadelphia, PA 19104 (U.S.A.) THOMAS
F. IRVINE
Jr.
Department of Mechanical Engineering, State University of New York, Stony Brook, NY II 794 (U.S.A.) (Received
January
30, 1989, in revised form August
8, 1989)
Abstract Previous measurements by other investigators of the purely viscous properties of viscoelastic fluids using the falling ball viscometer have been shown to yield anomalous results. These occur because the ball falling through the viscoelastic fluid creates a stress field which requires up to one hour to relax to its stress free state before another ball can be dropped. This is experimentally inconvenient. To further investigate this effect for a variety of viscometers, time interval measurements were made on a viscoelastic fluid (AP-273 Separan) using falling ball, falling needle and rotating cylinder viscometers. Although the falling ball measurements showed considerable time interval effects, the falling needle and rotating cylinder measurements did not. Thus the falling needle and rotating cylinder viscometers can be used to conveniently measure the steady shear viscosity of viscoelastic fluids.
1. Introduction The falling ball viscometer has been widely used to measure the steady shear viscosity of Newtonian and purely viscous non-Newtonian fluids [1,2]. 0377-0257/90/$03.50
0 1990 Elsevier Science Publishers
B.V.
352 However, as discussed in [2-41, a major difficulty occurs when attempting to measure the shear viscosity of viscoelastic fluids by using the same viscometer. In the case of viscoelastic fluids, the terminal velocities of identical balls were found to be strongly dependent on the time interval between the introduction of two consecutive balls. In some cases, the terminal velocity of the second ball was found to increase by 50% when the time interval between drops was one minute. In order to obtain identical terminal velocity measurements for two balls it was necessary to increase the time interval to the order of one hour. These large time intervals are not only experimentally inconvenient but for any given fluid, the “safe” time interval is not known beforehand and must be determined experimentally. This adds to the experimental difficulties of the falling ball measurement technique. It is believed that the time interval effect described above occurs for the following reason. As the first ball descends through the fluid it creates a stress field which because of the time constant of the viscoelastic fluid requires a time interval to return to its zero stress state. Thus, the second ball experiences a different stress medium than the first one. The theoretical description of a steady non-Newtonian fluid flow around a slowly moving sphere has been reported elsewhere [5-81. A time-dependent viscoelastic fluid flow around a sphere was experimentally investigated [1,2], which demonstrated that the interaction between a sphere and a viscoelastic fluid was very complicated due to the memory effect of the viscoelastic fluid. However, a theoretical study of the unsteady viscoelastic flow around sphere has not been reported. In the falling ball viscometer the form drag is approximately one third of the total drag for Newtonian fluids and comparable to this for viscoelastic fluids. If this pressure drag is responsible for the time interval effect, then a viscometer which has a small or no pressure drag should not exhibit this effect. Thus, the object of the present study was to determine whether the time dependent phenomena observed with the falling ball viscometer is present in the falling needle viscometer having a small pressure drag compared to the viscous drag and in a rotating cylinder viscometer having no pressure gradients. 2. Experimental apparatus The falling needle viscometer (FNV) has been developed to measure the rheological properties of both Newtonian and non-Newtonian fluids [9-121. Although it depends upon the particular fluid under consideration, the FNV generally operates over a shear rate range of 10P4 < i, < lo2 s-l. The accuracy is greater at low shear when compared with rotating type viscometers.
353
Needle
Launcher
Drain
Valve
Fig. 1. Schematic of falling needle viscometer.
As illustrated in Fig. 1, the instrument consists of a slender hollow cylinder with hemispherical ends (the needle) falling under the influence of gravity through a fluid housed in a cylindrical container. The needle velocity, after having reached a’constant or terminal velocity, is determined by measuring the time it takes for the needle to travel between two lines inscribed on the outer surface of the circular cylinder. This may be done either visually for transparent fluids or automatically for opaque fluids by using Hall sensors a known distance apart. With a knowledge of the needle terminal velocity, the system geometry and the difference between the needle and fluid densities, it is possible to construct a flow curve of either shear stress or apparent viscosity versus shear rate. An analysis of the viscometric equations and complete details of the experimental procedure for the Falling Needle Viscometer are given in [lo]. The rotating concentric cylinder viscometer was a Rheotron model (C.W. Brabender) while the falling ball measurements were made by dropping balls instead of needles in the apparatus illustrated in Fig. 1. A special ball
354 launcher was constructed to ensure that the balls fell along the center line of the cylindrical container. Aqueous solutions of AP-273 Separan, 2,000 wppm in distilled water were used as the viscoelastic fluids. All measurements were made at a temperature of 25 + 0.05 ’ C at a shear rate of approximately 0.4 s-l. After the viscoelastic fluids were placed in the various viscometers a period of 30 minutes was allowed to elapse before any measurements were taken. The same time period was used between time interval runs. 3. Experimental results Using the falling ball viscometer, twelve identical balls were dropped at time intervals of 1, 2, 3, 10 and 30 minutes. The results are shown in Fig. 2 where the falling time of the first ball dropped divided by the ball falling time is plotted against the time from the start of the first run of a time interval series. As the time interval between drops is decreased from 30 minutes to 1 minute the falling time ratio increased by approximately 30% demonstrating a significant time interval effect in agreement with previously reported measurements [2-41. Even with a time interval of 30 minutes, a time interval effect of approximately 5% remains. For the falling needle experiments, six identical needles were dropped at time intervals of 2, 3, 5 and 10 minutes. In order to ensure that the needles were identical, they were first dropped in a standard Newtonian fluid (Cannon S-600). The results are shown in Fig. 3, where the dropping time for each needle is plotted against needle number. It can be seen from the figure that the dropping time varied by less than f0.3%, which is approximately the accuracy of the system.
1.4 TIME INTERVAL
to/t
0
50
100
150
TIME FROM FIRST BALL DROP (mid
Fig. 2. Time interval
effect for falling balls, AP-273 Separan,
2000 wppm,
T = 25 o C.
355
o
AVERAGE VALUE FALLING NEEDLE
DATA
a 1
0.25
___________________________-.---________________ __ 0
n
0
4
5
I
0 __..___________________.______________~________ _.
0
12
3
NEEDLE
6
7
fl%
8
9
NUMBER
Fig. 3. Needle falling times in a Newtonian fluid (Cannon S-600), T = 25 o C.
The results of the falling needle time interval measurements are shown in Fig. 4, where the ordinate and abscissa are the same as in Fig. 2. From Fig. 4 it is seen that, although there is a data scatter of approximately -t2%, no time interval effects are discernible. In the operation of the rotating cylinder viscometer, time intervals of 1, 2, 3, 5, 10 and 30 minutes were used. The results are shown in Fig. 5 where the cylinder torque (which is proportional to the shear stress) normalized by the torque reading for the first run in a time interval series is again plotted against the elapsed time from the beginning of the first run in a series. As was the case for the falling needle experiments, no discernible time interval effect can be seen.
1.2 TIME INTERVAL
0
10
20
30
40
50
60
TIME FROM FIRST NEEDLE DROP (min)
Fig. 4. Time interval effect for falling needles, AP-273 Separan, 2000 wppm, T = 25 o C.
356 1.2 TIME INTERVAL
1.1 -
to/t
f?ik+P~
1.0
0.9’
.
0 TIME
FROM
n 20 FIRST
.
’ 40
TORQUE
’ 60
MEASUREMENT
Fig. 5. Time interval effect for the rotating T= 25°C.
’ 80
(min)
cylinder
viscometer,
AP-273 Separan,
2000 wppm,
It seems apparent from the above results that both the falling needle and the rotating cylinder viscometers do not have a time interval effect as was the case with the falling ball viscometer. As a further check on the internal consistency of the experimental results, a flow curve was measured of apparent viscosity vs. shear rate with the viscoelastic fluid. Both the falling needle and rotating cylinder viscometers were used, since they cover different shear rate ranges. The flow curve results are shown in Fig. 6. It is seen that in the region of data overlap the agreement is quite satisfactory and that the two instruments working together are able to cover over seven decades of shear rate from 7 = 10P4 to lo3 s-i.
0
ROTATING
.
FALLING
SHEAR
RATE
VISCOMETER NEEDLE VISCOMETER
(l/s)
Fig. 6. Typical flow curve measured with the falling needle (RCV) viscometers, AP-273 Separan, 2000 wppm, T = 25 o C.
(FNV)
and rotating
cylinder
357 4. Conclusions The time interval effect on the measurement of the viscous properties of a viscoelastic fluid was experimentally investigated using three viscometers, i.e. falling ball, falling needle and rotating cylinder types. It was found that a ball falling in a viscoelastic fluid creates a flow disturbance which in some cases takes an hour to completely disappear (time interval effect). However, in the case of the falling needle and rotating cylinder viscometers, no such time interval effect could be detected. On the basis of these results, a flow curve was measured for a viscoelastic fluid using the falling needle and rotating cylinder viscometers with excellent agreement between the two instruments. It is concluded that the falling ball viscometer is not particularly suitable for measuring the viscous properties of viscoelastic fluids but that the falling needle and rotating cylinder viscometers can be appropriately used. Acknowledgement The Authors express their appreciation to Mr. Kujin Instrument Corp., for doing some of the measurements.
Lee of the J & L
References 1 Y.I. Cho, Ph.D. Thesis, Mechanical Engineering Department, University of Illinois at Chicago, 1980. 2 Y.I. Cho, J.P. Hartnett and W.Y. Lee, J. Non-Newtonian Fluid Mech., 15 (1984) 61. 3 Y.I. Cho and J.P. Hartnett, Lett. Heat Mass Trans., 6 (1979) 335. 4 Y.I. Cho and J.P. Hartnett, Paper presented at the society of rheology meeting, Boston, MA, 1979; J. Rheol., 24 (1981) 891 (abstract). 5 R.B. Bird, Phys. Fluids, 3 (1960) 539. 6 J.C. Slattery, AIChE J., 8 (1962) 663. 7 K. Adachi, N. Yoshioka and K. Sakai, J. Non-Newtonian Fluid Mech., 3 (1977/1978) 107. 8 Y. Kawase and M. Moo-Young, J. Non-Newtonian Fluid Mech., 21 (1986) 167. 9 N.A. Park, Ph.D. Thesis, Mechanical Engineering Department, State University of New York at Stony Brook, NY, 1984. 10 N.A. Park and T.F. Irvine Jr., Rev. Sci. Instrum., 59 (1988) 2051. 11 N.A. Park, T.F. Irvine Jr. and F. Gui, in: P.H.T. Uhlherr (Ed.), Proc. Xth Int. Congr. Rheol., Vol. 2, Australian Sot. of Rheol., Sydney, 1988 p. 160. 12 N.A. Park and T.F. Irvine Jr., Warme u. Stoffubertragung, 18 (1984) 201.
351
STEADY SHEAR VISCOSITY MEASUREMENTS OF VISCOELASTIC FLUIDS WITH THE FALLING NEEDLE VISCOMETER
NOH A. PARK J & L Instrument Corp., Norristown, PA 19403 (U.S.A.) YOUNG
I. CHO
Department of Mechanical Engineering and Mechanics, Drexel University, Philadelphia, PA 19104 (U.S.A.) THOMAS
F. IRVINE
Jr.
Department of Mechanical Engineering, State University of New York, Stony Brook, NY II 794 (U.S.A.) (Received
January
30, 1989, in revised form August
8, 1989)
Abstract Previous measurements by other investigators of the purely viscous properties of viscoelastic fluids using the falling ball viscometer have been shown to yield anomalous results. These occur because the ball falling through the viscoelastic fluid creates a stress field which requires up to one hour to relax to its stress free state before another ball can be dropped. This is experimentally inconvenient. To further investigate this effect for a variety of viscometers, time interval measurements were made on a viscoelastic fluid (AP-273 Separan) using falling ball, falling needle and rotating cylinder viscometers. Although the falling ball measurements showed considerable time interval effects, the falling needle and rotating cylinder measurements did not. Thus the falling needle and rotating cylinder viscometers can be used to conveniently measure the steady shear viscosity of viscoelastic fluids.
1. Introduction The falling ball viscometer has been widely used to measure the steady shear viscosity of Newtonian and purely viscous non-Newtonian fluids [1,2]. 0377-0257/90/$03.50
0 1990 Elsevier Science Publishers
B.V.
352 However, as discussed in [2-41, a major difficulty occurs when attempting to measure the shear viscosity of viscoelastic fluids by using the same viscometer. In the case of viscoelastic fluids, the terminal velocities of identical balls were found to be strongly dependent on the time interval between the introduction of two consecutive balls. In some cases, the terminal velocity of the second ball was found to increase by 50% when the time interval between drops was one minute. In order to obtain identical terminal velocity measurements for two balls it was necessary to increase the time interval to the order of one hour. These large time intervals are not only experimentally inconvenient but for any given fluid, the “safe” time interval is not known beforehand and must be determined experimentally. This adds to the experimental difficulties of the falling ball measurement technique. It is believed that the time interval effect described above occurs for the following reason. As the first ball descends through the fluid it creates a stress field which because of the time constant of the viscoelastic fluid requires a time interval to return to its zero stress state. Thus, the second ball experiences a different stress medium than the first one. The theoretical description of a steady non-Newtonian fluid flow around a slowly moving sphere has been reported elsewhere [5-81. A time-dependent viscoelastic fluid flow around a sphere was experimentally investigated [1,2], which demonstrated that the interaction between a sphere and a viscoelastic fluid was very complicated due to the memory effect of the viscoelastic fluid. However, a theoretical study of the unsteady viscoelastic flow around sphere has not been reported. In the falling ball viscometer the form drag is approximately one third of the total drag for Newtonian fluids and comparable to this for viscoelastic fluids. If this pressure drag is responsible for the time interval effect, then a viscometer which has a small or no pressure drag should not exhibit this effect. Thus, the object of the present study was to determine whether the time dependent phenomena observed with the falling ball viscometer is present in the falling needle viscometer having a small pressure drag compared to the viscous drag and in a rotating cylinder viscometer having no pressure gradients. 2. Experimental apparatus The falling needle viscometer (FNV) has been developed to measure the rheological properties of both Newtonian and non-Newtonian fluids [9-121. Although it depends upon the particular fluid under consideration, the FNV generally operates over a shear rate range of 10P4 < i, < lo2 s-l. The accuracy is greater at low shear when compared with rotating type viscometers.
353
Needle
Launcher
Drain
Valve
Fig. 1. Schematic of falling needle viscometer.
As illustrated in Fig. 1, the instrument consists of a slender hollow cylinder with hemispherical ends (the needle) falling under the influence of gravity through a fluid housed in a cylindrical container. The needle velocity, after having reached a’constant or terminal velocity, is determined by measuring the time it takes for the needle to travel between two lines inscribed on the outer surface of the circular cylinder. This may be done either visually for transparent fluids or automatically for opaque fluids by using Hall sensors a known distance apart. With a knowledge of the needle terminal velocity, the system geometry and the difference between the needle and fluid densities, it is possible to construct a flow curve of either shear stress or apparent viscosity versus shear rate. An analysis of the viscometric equations and complete details of the experimental procedure for the Falling Needle Viscometer are given in [lo]. The rotating concentric cylinder viscometer was a Rheotron model (C.W. Brabender) while the falling ball measurements were made by dropping balls instead of needles in the apparatus illustrated in Fig. 1. A special ball
354 launcher was constructed to ensure that the balls fell along the center line of the cylindrical container. Aqueous solutions of AP-273 Separan, 2,000 wppm in distilled water were used as the viscoelastic fluids. All measurements were made at a temperature of 25 + 0.05 ’ C at a shear rate of approximately 0.4 s-l. After the viscoelastic fluids were placed in the various viscometers a period of 30 minutes was allowed to elapse before any measurements were taken. The same time period was used between time interval runs. 3. Experimental results Using the falling ball viscometer, twelve identical balls were dropped at time intervals of 1, 2, 3, 10 and 30 minutes. The results are shown in Fig. 2 where the falling time of the first ball dropped divided by the ball falling time is plotted against the time from the start of the first run of a time interval series. As the time interval between drops is decreased from 30 minutes to 1 minute the falling time ratio increased by approximately 30% demonstrating a significant time interval effect in agreement with previously reported measurements [2-41. Even with a time interval of 30 minutes, a time interval effect of approximately 5% remains. For the falling needle experiments, six identical needles were dropped at time intervals of 2, 3, 5 and 10 minutes. In order to ensure that the needles were identical, they were first dropped in a standard Newtonian fluid (Cannon S-600). The results are shown in Fig. 3, where the dropping time for each needle is plotted against needle number. It can be seen from the figure that the dropping time varied by less than f0.3%, which is approximately the accuracy of the system.
1.4 TIME INTERVAL
to/t
0
50
100
150
TIME FROM FIRST BALL DROP (mid
Fig. 2. Time interval
effect for falling balls, AP-273 Separan,
2000 wppm,
T = 25 o C.
355
o
AVERAGE VALUE FALLING NEEDLE
DATA
a 1
0.25
___________________________-.---________________ __ 0
n
0
4
5
I
0 __..___________________.______________~________ _.
0
12
3
NEEDLE
6
7
fl%
8
9
NUMBER
Fig. 3. Needle falling times in a Newtonian fluid (Cannon S-600), T = 25 o C.
The results of the falling needle time interval measurements are shown in Fig. 4, where the ordinate and abscissa are the same as in Fig. 2. From Fig. 4 it is seen that, although there is a data scatter of approximately -t2%, no time interval effects are discernible. In the operation of the rotating cylinder viscometer, time intervals of 1, 2, 3, 5, 10 and 30 minutes were used. The results are shown in Fig. 5 where the cylinder torque (which is proportional to the shear stress) normalized by the torque reading for the first run in a time interval series is again plotted against the elapsed time from the beginning of the first run in a series. As was the case for the falling needle experiments, no discernible time interval effect can be seen.
1.2 TIME INTERVAL
0
10
20
30
40
50
60
TIME FROM FIRST NEEDLE DROP (min)
Fig. 4. Time interval effect for falling needles, AP-273 Separan, 2000 wppm, T = 25 o C.
356 1.2 TIME INTERVAL
1.1 -
to/t
f?ik+P~
1.0
0.9’
.
0 TIME
FROM
n 20 FIRST
.
’ 40
TORQUE
’ 60
MEASUREMENT
Fig. 5. Time interval effect for the rotating T= 25°C.
’ 80
(min)
cylinder
viscometer,
AP-273 Separan,
2000 wppm,
It seems apparent from the above results that both the falling needle and the rotating cylinder viscometers do not have a time interval effect as was the case with the falling ball viscometer. As a further check on the internal consistency of the experimental results, a flow curve was measured of apparent viscosity vs. shear rate with the viscoelastic fluid. Both the falling needle and rotating cylinder viscometers were used, since they cover different shear rate ranges. The flow curve results are shown in Fig. 6. It is seen that in the region of data overlap the agreement is quite satisfactory and that the two instruments working together are able to cover over seven decades of shear rate from 7 = 10P4 to lo3 s-i.
0
ROTATING
.
FALLING
SHEAR
RATE
VISCOMETER NEEDLE VISCOMETER
(l/s)
Fig. 6. Typical flow curve measured with the falling needle (RCV) viscometers, AP-273 Separan, 2000 wppm, T = 25 o C.
(FNV)
and rotating
cylinder
357 4. Conclusions The time interval effect on the measurement of the viscous properties of a viscoelastic fluid was experimentally investigated using three viscometers, i.e. falling ball, falling needle and rotating cylinder types. It was found that a ball falling in a viscoelastic fluid creates a flow disturbance which in some cases takes an hour to completely disappear (time interval effect). However, in the case of the falling needle and rotating cylinder viscometers, no such time interval effect could be detected. On the basis of these results, a flow curve was measured for a viscoelastic fluid using the falling needle and rotating cylinder viscometers with excellent agreement between the two instruments. It is concluded that the falling ball viscometer is not particularly suitable for measuring the viscous properties of viscoelastic fluids but that the falling needle and rotating cylinder viscometers can be appropriately used. Acknowledgement The Authors express their appreciation to Mr. Kujin Instrument Corp., for doing some of the measurements.
Lee of the J & L
References 1 Y.I. Cho, Ph.D. Thesis, Mechanical Engineering Department, University of Illinois at Chicago, 1980. 2 Y.I. Cho, J.P. Hartnett and W.Y. Lee, J. Non-Newtonian Fluid Mech., 15 (1984) 61. 3 Y.I. Cho and J.P. Hartnett, Lett. Heat Mass Trans., 6 (1979) 335. 4 Y.I. Cho and J.P. Hartnett, Paper presented at the society of rheology meeting, Boston, MA, 1979; J. Rheol., 24 (1981) 891 (abstract). 5 R.B. Bird, Phys. Fluids, 3 (1960) 539. 6 J.C. Slattery, AIChE J., 8 (1962) 663. 7 K. Adachi, N. Yoshioka and K. Sakai, J. Non-Newtonian Fluid Mech., 3 (1977/1978) 107. 8 Y. Kawase and M. Moo-Young, J. Non-Newtonian Fluid Mech., 21 (1986) 167. 9 N.A. Park, Ph.D. Thesis, Mechanical Engineering Department, State University of New York at Stony Brook, NY, 1984. 10 N.A. Park and T.F. Irvine Jr., Rev. Sci. Instrum., 59 (1988) 2051. 11 N.A. Park, T.F. Irvine Jr. and F. Gui, in: P.H.T. Uhlherr (Ed.), Proc. Xth Int. Congr. Rheol., Vol. 2, Australian Sot. of Rheol., Sydney, 1988 p. 160. 12 N.A. Park and T.F. Irvine Jr., Warme u. Stoffubertragung, 18 (1984) 201.