Falling Ball Viscometry A n Instrument for Precise Measurements W . K. LIM, H.
W. JOHNSON, Jr., P. C. WILHELMSEN, and F. H. STROSS
Shell Development Co
., Emeryville,
Calif.
,The viscosity of liquids can be determined b y measuring the time required for a solid sphere or spindle to fall through a known distance in the liquid. A precise and convenient instrument employing this principle and featuring electronic timing uses small steel balls, which are commercially available at low cost and manufactured to rigid specifications. Performance data are given. The relative standard deviation of fall times when dropping and retrieving the same ball ten times is 0.05%.
T
viscosity of liquids is conventionally measured by means of capillary viscometers, in which passage of a measured volume of liquid under the influence of gravity is timed. The time of passage of the liquid through such capillaries is approximately proportional to the ratio of the viscosity, 7, to the density, d i , of the liquid under the same conditions; this ratio is known as the kinematic viscosity, Y , of the HE
7 Then = Y . The viscosity di of a liquid can also be calculated, over a considerable range of conditions, from the time of fall of a sphere through a known distance in the liquid, if the densities of the liquid and the sphere are known. The use of falling objects to determine viscosity, and the improvement in the accuracy and scope of the method, have been the subject of development during the past few years (1-7) Some instruments (1,2, 4)used an acoustical signal; others ( 3 , 5 )used a meter deflection, and one (6) used both a microammeter and an earphone. The smallest diameters of the metal balls used in the different instruments were between 1 and 3 mm. The best precision recorded was 0.3y0; that of nearly all the other instruments was substantially poorer. It is likely that the instruments were essentially limited in their range o precise nieasurement to liquids having viscosities eyceeding 200 centistokes. Recent advances in electronic timing and in the production of spheres of veq- uniform size, shape, and composition have suggested the possibility of improved precision and speed of
liquid.
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ANALYTICAL CHEMISTRY
determination for falling ball L iscometry over earlier attempts and possibly over other techniques. Preliminary experimentation bore out this idea. and a successful instrument was designed. This system is sensitive enough to measure fall times of 'IM-inch stainless steel balls with precision similar to that obtained in capillary viscometry. A schematic diagram is shown in Figure 1. EXPERIMENTAL
Apparatus. The sample is contained in a 12 X 240 mm. test tube (0.d. X length), situated axially within two sensing coils, which are 5 or 15 ern apart. The passage of the ball past each coil is sensed electronically, and the time for passage between the coils is indicated by a n electronic counter. All of the components except the electronic timing equipment are located in a main cabinet (Figure 2): constant tempeiature bath, temperature regulator, stirring motor, auxiliary heaters, cooling coil, temperature-limiting switch, sample-handling assembly, shielded lead-in tube, bridge resistors, ball dropping mechanism, and metal balls. The electronic timing equipment is mounted separately to avoid electrical interference. MAIN CABIXLT. The constant temperature bath is constructed from a cylindrical borosilicate jar, lagged with niagnesia and mounted inside a 16gauge steel cylindrical shield. The
Hallikainen Thermotrol temperature regulator controls a 130-watt heater and a second heater consisting of barewire winding around the ja,r to reduce t'he temperature gradient between the bath liquid and the ambient. Two manually controlled auxiliary heaters, a quick heater and a constant heater, are used at higher temperatures and in changing from one temperature to another. To assist further in quick temperature change, a 40-inch cooling coil is available. SAMPLE-HANDLISG ASSEJIBLY. The complete assembly (1, Figure 2) consists of a sample tube holder, sensing coils, lead-in tube, and bridge resistors. The sample tube holder maintains the sample tube axially a,ligned m-ith respect to the coils by nieans of two threepronged support rings. The units used to contain and shield the two sensing coils are machined from mu-metal and designed to accept 13-mm. 0.d. glass sample tubes. The sensing coils are made from 600 turns of 32-gauge enameled copper wire and are impregnated wit,h epoxy resin during the winding process. They are mounted in the mu-metal shield. The shielded lead-in tube is made from a section of brass tubing and wrapped with shielding foil in such a manner that, the lower end of the tube is also shielded. The bridge resistors are bifilar 100-ohm resistors mounted on insulated feed-through terminals on the lead-in tube. B A L L D R O P P I N G &\IECHANIShl. That shown in Figure 3 is designed for convenient handling and dropping of balls
Ball Dispenser
0
Samnlr r--
Balancing Circuit
Bridge Resistors
tolls
Pre-amp, Amplifier and Demodulator
Carrier Oscillator
! I
I Figure 1.
Block diagram of falling ball viscometer
Electronic Counter
Figure 2. 1. 2. 3.
4. 5. 6. 7. 8. 9. 10. 1 1. 1 2. 13. 14. 15. 16.
17. 20. 2 1. 22. 23.
Main cabinet
A
regulated. The sensing coils are designed to generate a large response in the bridge output when a ball passes through the field of either coil and must have a reasonably high Q value (ratio of reactance t o resistance). The coils are shielded with mu-metal cups and mashers to reduce the possibility of electromagnetic interference. The balls were sorted according to weight by means of a rapid microbalance-Cahn electrobalance-and those falling within a range corresponding to 0.1% of their nominal weiKht mere retained. For routine determinations, selected balls are used once and discarded with the sample. Data to evaluate the inherent precision of the apparatus were obtained by dropping and retrieving the same ball by means of a vacuum-operated ball dropper. This eliminates errors arising from differences between the spheres, and facilitates statistical treatment of the d a t a for assessing the performance of the instrument.
Sample-handling assembly Support for ball-dropping mechanism Pulley for stirrer Stirrer Cannon receptacle Shielded lead-in tube 1 00-ohm j z 1 % resistors Coaling coils Sample tube Sample tube holder 18, 19. Heaters Thermotrol-resistance thermometer Borosilicate glass jar Magnesia lagging M e t a l shield for borosilicate glass lor M e t a l cabinet Exhaust tube for cooling liquid to stirrer Stirring motor Heater control panel Temperature-setting dial of safety device to prevent overheating Sensing bulb for safety device
for routine determinations. The balls are stored in the ball reservoir and are individually dispensed by rotating a bronze spindle by M o o , then directed through the sample tube. X rack and Figure 3. Mechanical ball dispenser pinion permits t'he ball dropper to be moved vertically for convenience in frequencies. .A cathode follower, deThe operations of the ball droppers changing sample tubes. tector, electronically regulated power were observed by means of a highMETALBALLS. The balls are comsupply, and electronic counter capable mercially available at' low cost from speed camera, which followed the bali of measuring microseconds complete the L-niversal Ball Co., Willow Grove, Pa. during its fall. With the vacuum-type electronic instrumentation. (instrument grade), and are made from retriever-dropper, the balls did not drop 440 stainless steel. According to manvertically, but moved outward over RESULTS ufacturer's specifications they have a the edge of the retriever before drolq)ing. precision of 5 X 10-6 inch in sphericity Operational Considerations. T h e 'This random radial displacement, howand diameter. ever, was less than half the diameter ELFXTRONCTIMING EQUIPMEKT.constant temperature bath provides facilities for maintaining the temperaof the 1/32-inchbail. .I displacement The two sensing coils are combined ture of the sample being tested, equilof this magnitude has no significant with two resistors in a simple imibrating additional samples to the pedance bridge. A stabilized Wieneffect. The mechanical ball dispenser bridge oscillator provides the carrier proper temperature, a n d dissipating shown in Figure 3, which uses a ball voltage supply for the impedance bridge heat from the impedance bridge. guide, released the ball asially. Yo and for a balancing circuit. The balancThe temperature remained constant radial deviation was observed. ing circuit is adjustable in amplitude and within *0.003" C. for several days. Evaluation of Operating Conditions. phase, and is set to give t,he minimum The most critical feature of the T o find the conditions associated net bridge output when no ball is being sample-handling assembly is the imwith optimum precision, a study was dropped. This output is fed to a pedance bridge. The sensing coils are made to determine which adjustments ixeamplifier. A band-pass filter bevery sensitive to temperature changes a n d settings were critical, by varying tlveen the preamplifier and the highgain yoltage amplifier rejects unwanted and must be properly temperaturethe settings over a relatively wide VOL. 3 6 , NO. 13, DECEMBER 1 9 6 4
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range and noting a n y correlation between the setting and the measured fall times in the case of carrier voltage, carrier frequency, different sample tubes, centricity of ball path, saturation of the amplifier for prolonged periods, temperature of the balancing circuits, ball material, distance between sensing coils, and demodulator filter settings. I n all the tests the bath temperature was 25" C. CARRIER VOLTAGE.When the carrier voltage was increased, the noise increased along with the output signal, and the impedance bridge required more frequent balancing. Accordingly, to minimize noise and obtain the best bridge stability, the carrier voltage must be kept as low as possible but high enough to trigger the counter. The optimum carrier voltage for l/M- and 1/32-inch stainless steel balls was 4 and 2 volts peak-to-peak, respectively. CARRIERFREQUENCY. Carrier frequencies of 5000 and 10,000 cycles were compared with the normal frequency of 1500 cycles t o determine the effect of frequency on timing repeatability. I t was necessary to change the band-pass filters for each test frequency. As the frequency increased, the output signal amplitude to the electronic counter decreased, the bridge was more difficult to keep in balance, and the precision of fall times decreased. DIFFERENT SAMPLE TCBES. To find if slight differences in sample tube dimensions could affect observed fall times, a 1/32-inchstainless steel ball was dropped eight times in four different sample tubes of the same nominal diameter containing samples of the same oil. Although nominally of the same diameter, the tubes showed differences over a range of 0.5 mm. The observed fall times were independent of the sample tube used. -4ccordingly, it is not necessary to calibrate or select sample tubes. CENTRICITY OF BALL PATH. Tests were conducted to determine the effect of the departure from coaxial fall of a ball passing through the coils, as this might affect bridge response and thus timer operation. The tests were made with one ball having a diameter of l/32 inch and the vacuum-type ball retriever and dropper. The ball dropper was located in two positions: centered, and inch off center. Fall times were measured, and no significant difference was found between the centered and offcenter drops. Substantially greater departures from coaxiality might influence the fall times. SATURATION OF AMPLIFER FOR PROLONGED PERIODS.The test was carried out by lowering the vacuum ball retriever-dropper into the sample test tube. This greatly unbalanced the impedance bridge and created so large a bridge output that the amplifier was 2484
ANALYTICAL CHEMISTRY
Figure 4.
Oscillograms of output waveforms of different ball materials Horlzontal deflection. 1 sec./cm. left. Tungsten carbide ball, '/:pinch diameter Vertical deflection, 5 volts/cm. Center. Chrome alloy steel bail, '/:Z-lnch dlameter Vertical deflection. 5 volts/cm. Right. Stainless steel ball, '/:*-inch diameter Vertical deflection. 10 volts/cm.
saturated. This condition was maintained for varying periods of time; then the 1/12-inch stainless steel ball was retrieved, brought to dropping position, and released. Observed fall times were not significantly affected by saturating the amplifier for periods up to 2 minutes, much longer than would occur during routine determinations. TEMPER.4TURE O F BALANCING CIRCUITS. Sensitivity of the balancing circuits to temperature changes was tested by using a heat gun to heat the balancing circuits to approximately 50" C. An air blower then cooled the heated parts to ambient temperature. These heating and cooling cycles did not significantly affect bridge balance or observed fall times. BALL MATERIAL. Balls 1,'32 inch in diameter made of tungsten carbide, chrome alloy steel, sapphire, and silverplated sapphire were compared with the standard stainless steel balls. The output wave forms developed with a constant carrier voltage of 2 volts peak-topeak are shown in Figure 4 for tungsten
Figure 5. Viscosity calibration chart
carbide, chrome alloy steel, and stainless steel. There was no detectable response from sapphire and silver-plated sapphire balls. Balls inch in diameter made of stainless steel and tungsten carbide developed outputs of 36 and 9 volts, respectively, with a 4-volt peakto-peak carrier voltage. These two balls, and the three 1/32-inch balls represented in Figure 4, produced sufficient voltage to trigger the electronic counter. DISTANCEBETWEEN SENSING COILS. By increasing the distance between coils from 5 to 15 inches, the standard deviation of fall times was improved by a factor of 2 . While greater distances would clearly be desirable from the point of view of precision, 15 inches is the largest possible distance in the present bath. All performance data in this paper refer to the 15-inch spacing. DEMODULATOR FILTER SETTINGS. The position of the demodulator switch can affect precision. If inadequate filtering is used with high viscosity oils, random noise in the input to the
electronic timer can cause excessive error in the triggering. If excessive filtering is used with low viscosity oils, the triggering pulses are reduced in amplitude. This reduces the maximum rise time of the triggering pulses, and precise timing is not possible. The ol)t,imumsettings are determined esperimentally for a new instrument when put into service. Calibration. Departure from Stokes' straight-line relationship between fall times and the viscosities of liquids occ,urs a t onset of turbulence. Under present conditions, this is observed at viscosities below 40 to 50 cp., when the drag caused by turbulence tends to increase the fall times beyond those due to viscosity alone. The fall times, howeoer, remain repeatable, and the viscosity us. fall-time relationship can be defined satisfactorily by calibration down to shout 2 cp. The function (7.4487 - d J t against q , where 7.4487 is t'he density of the steel balls, dl is the density of liquid, t is the fall time, and q is the absolute viscosity, was plotted for liquids covering a considerable range of viscosities and densities. A single straight line was obtained down to the onset of turbulence; this and the
curvature arising beyond that point are shown in Figure 5. I n routine operation it may be desired to plot fall times directly against viscosity. Because of the relation espressed by Stokes' law, this function will be valid only for liquids of a single density. If the liquids to be tested cover a significant range of densities, the calibrations can be made available on a single sheet by plotting a family of curves representing the viscosity-fall time correlation obtained for different densities. Each curve then represents a calibration for liquids having a corresponding density. Alternatively, it is possible to construct a three-branch nomogram for the purpose. Performance. T h e falling ball viscometer was calibrated with standardizing oils of known viscosities a n d densities and with mixtures of these oils. The fall times were measured with a group of 10 balls with closely matching diameters and densities, each dropped once in each oil. The average relative standard deviation of the fall times for the set was O . l O l ~ o under standard testing conditions. By contrast, the corresponding standard deviation for a single ball dropped ten times was only 0.05%.
The set of balls evidently showed small variations in density, size, or sphericity, which account for the larger standard deviations. The variation can be further reduced by actually dropping the balls through a suitable long column of liquid and collecting those bracketed within a specified narrow range of fall times. ACKNOWLEDGMENl
We acknowledge the contributions made by Gordon O'Donnell and F. A. Olson. LITERATURE CITED
(1) Fidleris, V., Whitmore, R. L., J . Sci. Jnstr.. 36, 35 (1959). ( 2 ) Lana G. L., U. S. Patent 2.252.572 I
,
(August 1941). (3) McDowell, C. A., Walker, B. Y., Chem. I n d . ( L o n d o n ) 64,323 (1945). (4) Moore, L. P., Cuthbertson, A. C., IND. ENG. CHEM.,ANAL.ED. 2, 419 (1930). (5) Symmes, E. &I., Lantz, E. A,, Zbid., 1. 35 (19291. (6) 'Thompson, A . M., J. Sci. Instr. 26, 75 (1949). (7) Wertheim, R. A . P., Patent Oflice, London, Patent Spec. 758,199 (1956). RECEIVED for review August 18, 1964. Accepted October 1, 1964.
Structure and Behavior of Organic Analytical Reagents Formation Constants of Transition Metal Complexes of 2-Hyd roxypyrid ine-1-Oxide and 2-Merca ptopyridine-1-Oxide PENG-JOUNG SUN,' QUINTUS FERNANDOl and HENRY FREISER Department of Chemistry, University o f Arizona, Tucson, Ariz. The solution equilibra of 2-hydroxypyridine-1 -oxide and 2-mercaptopyridine-1 -oxide, heterocyclic analogs of hydroxamic acids, were studied to evaluate the effect of the nature of the donor atoms, the nondonor atoms in the chelate ring, and auxilliary ring systems in the metal chelate, on the analytical behavior of these reagents. The acid dissociation constants and the chelate formation constants of these two compounds with Mn(ll), Co(ll), Ni(ll), Cu(ll), and Zn(ll) were determined potentiometrically and spectrophotometrically. The significance of these results in the design of new analytical reagents is discussed.
T
of metal chelate formation equilibrium data in analytical chemistry arises from its use in predicting values of solution paramHE
IMPORTANCE
eters appropriate for analytical determinations. The extent of metal chelate formation depends not only on the value of the formation constants but also on the concentration of the free ligand species which in turn depends on the acid dissociation constants of the ligand. These considerations are clearly expressed in terms of the proton displacement constant, K p d ,which is the product of the overall formation conconstant, &, and the acid dissociation constant K , raised to the nth power where n is the number of ligands in the chelate. Thus, for the formation of copper acetylacetonate : Cu2+ 2Hacac Cu(acac)z 2 H +
+
+
. Ka2 (1) I n a series of related ligands chelate stabilities increase with ligand basicK D d
= Pz
ities-Le., pn increases as K , decreases (4). Inasmuch as K , appears to a higher power than pn in K p d , it is not too surprising to find that in such families of ligands, the less stable the chelate a ligand forms with a particular metal ion, the lower the pH a t which formation occurs. For example, the halogenated 8-quinolinols form metal chelates a t lower pH values than the parent compound and thenoyltrifluoroacetone (TTA) reacts with metal ions a t lower p H values than does acetylacetone. I n designing chelating agents for analysis then, the effect of structural changes on acid dissociation behavior as well as on metal complex formation must be taken into account. It will be of advantage to have reagents in which the K , as well as ' O n leave from the Department of Chemistry, National ~~i~~~ university, Taipei, Taiwan, China. VOL. 36, NO. 13, DECEMBER 1964 e
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