Rotational Viscometer for Rapidly Settling Suspensions ASITESH BHATTACHARYA and A. N. ROY lndian lnstitote o f Technology, Kharagpor, lndia
by a system of weights and pulleys, and t h e number of revolutions ic noted when a steadv state is attained. T h e value of viwcositv of fluid i. obtained from the relation ( I )
i simple. sensitiie, and s t u d ) rotational \iscometer of the concentric cjlindrical tjpe has been developed to determine the apparent viscosities of some quickly settling suspensions of fine13 powdered solids in liquids. The essential features of this design include continuous operation at different speeds, pro\ision for draining out of contents, and a simple mechanical arrangement to measure the torque deFeloperl on the stationarj cs1intlrr. The \iscometer was calibrated against standard gl?rerol-\rater solutions, the determinations heing carried out in the turbulent range. and the data correlated as a plot of specific friction factor us. specific Re) noltls nuniher representing the calibration curie for this instrument. The design of the instrument, valihration with some liquids of linoitn Fiscositj, and its application for the measurement of apparent viscosi t ? of some rapid]? settling suspensions are presented.
I
rvhere I T - is the applied load, w is the equivalent of the friction i n t h e rotating system, R is t h e radius of t h e pulley, and h is t h e length of t h e inner cylinder of radius r1 inside a container of radius r? rotating a t uniform angular velocity a. Owing t o t h e presence of paddles and baffles which give rise t o end effects, viscosities cannot be calculated from the speed, torque. and dimension d a t a using Equation 1, which in the simplified form is
T =
S TIIIC course of studies on the flow of solid-in-liquid suspensions in vertical columns (Z), great difTic.ultj-n-as experienced
in tlrterniining the apparent viscosities of Eome slurries in which there w:ts rapid settling out of the finely divided solids from t h e liquid medium. Trials in rotational viscometers of the Couette type ( 3 )ivith t h e cup as the rotating member proved unsuccessful, oiving t o quick phase separation under the influence of centrifugal force. .Attempts xvere made t o determine hy allowing a constantly stirred slurry t o flow through a known vertival length b>- siphoning techniquc. T h e time required for the flow of a definite volume of sluri.>- \v:is determined and the value of viscosity n-as calculated in the usii:il way. T h e results did not show any marked deviation from t h a t obtained in the rotational viscometrr: hoivever. this nirthod w : ~regarded ~ theoretically iinsouncl and involved consider:tble experimental difficulties, p:irticnlarly with slurries of high solid content. I t vias. therrfore. found necessarj- t o design and construct a vontinuously operating concentric. cj-lindrical viscometer in which the inner cJ-linder. driven by a motor. acted as a stirrer. T h e value of viscosity was deterniinrtl from the measurement of t o q u e developed on the outer cylinder, hj. a simple mechanic:il :irr:ingenient. THEORY
Rotation:il viscometers are fundamentul in nnture and permit relative as 11-ell :is absolute measurement of viscosity of fluids. Such instruments essentially consist of two concentric cylindersthe outer cup or container, and the inner spindle or bob. Theoretically it is immaterial which of t h e cylinders is rotated, b u t in practice the choice depends on t h e nmynitude of the couple generated-that is, the value of viscosity. T h e determination of apparent vi.v~osityof quickly settling suspensions is a difficult problem, a:: none of the conventional rotational vifconietera are suitable for thiq purpose. Wilhelni :ind others (6). however, designed a n instrument in ivhich it was possible t o prevent t h e settling of t h e >olids in suspension bjproviding paddles a t t h e bottom of the rotating inner cylinder and baffles on t h e wall of the stationary container, They determined the flon- properties of roncentrated suspensions of cement rock ant1 Filter-cel in w-ater in the visrous as well as turbulent range. In viscometers with stationary cup and rotating spindle. the inner cylinder is driven by a predetermined torque delivered
kpi\-
(2)
This difficulty can be overcome by using the method developed by Squires and Dockendorff (6)for t h e evaluation of viscosity in rotational viscometers when t h e motion of the fluid is turbulent. I n this procedure, a calibration curve is made for a specific instrument in terms of friction factor us. Reynolds nnniber where the friction factor is defined as 18)
By analogy n-ith flow of fluids in pipes. .f is a function of Reynolds number, Re. \vhich can be defined as
This meansf =
‘p
(Re)
(5)
where q represents the functional relationship. I n the viscous region t h e slope of t h e curve, obtained by logarithmic plot of torque against speed, is unity and therefore t h e relation becomes simple and reduces to
I n the turbulent range, for a given fluid, hon.ever, there wil be only one value of viscositj- corresponding to m y given value of .f and Re-that is. to any given value of S. I n instruments \\-here there are baffles, paddles, otc., a new friction factor term 7’
and a nen- Reynolds criterion
have been defined. T h e terms f ’ and R e ’ are proportional t o friction factor and Reynolds number, respectively, and the constants of proportionality are dependent on the design of t h e instrument. T h e quantities f ‘ and R e ’ are determined for fluids of known viscosity in the turbulent region and a plot correlating these is used as the calibration curve for the particular instrument, S o x , from t h e measurement of torque a t a particu1:ir speed, f ’ for a given fluid can easily he calculated. The turbulent viscosity is then evaluated from Re’, ohtainrtl from thc c~alibration curve. corresponding t o this value off’. 1287
ANALYTICAL CHEMISTRY
1288 I n the present paper are described the design and calibration of a rotational viscometer of the rotating spindle tvpe in R hich the outer cylinder is also free t o move. The torque exerted on the outer cylinder sets it in motion, which, however, is simultaneously counteracted by a calibrated watch spring This brings the cylinder to rest. From the degree of tn ist of the spring the viscosity values are calculated. -4fevi typical data on the apparent viscosities of some quickly settling suspensions are also presented. DESCRIPTION OF VISCOMETER
T h e viscometer is shown in detail in Figure 1. T h e instrument essentially consists of two brass cylinders, and B . The outer cylinder, B , of internal diameter of 2 inches and internal height of 49/16 inches serves as the container. It has a working capacity of about 100 cc. and is provided i-iith a hollow stem, C, to drain out the contents. The opening is closed by a small plug, D. This cylinder is supported by two extra light ball bearings (E.L. 9 A),E, F , lodged in two steel housings, G, H . These housings are fitted in circular spigots and held together b y three screws. T h e supporting casing, I , is fixed t o the bottom plate, J , along with G and H by three screws. T h e drive shaft of the inner cylinder is fitted in the ball bearing, K , cased in the steel housing, L, which rests on I . The purpose of the supporting case, I , is t o hold in position the bearing housings, fitted to the inner cylinder shaft on the top and the outer cvlinder a t the bottom, in specially made circular spigots to secure the concentricity of the cylinders. Six symmetrical holes are provided in L , which permit introduction of the test fluid and allow inspection during operation. The inner bob, A , of diameter of 1.5 inches and height of 3 inches is hollow b u t closed a t both Mt, are fitted a t the bottom to keep ends; two small paddles, JI~, the solids in suqpension b y stirring action. The inner cjlinder is directly coupled to a '/?a-hp. Iiestner alternating-direct current motor, which is fixed on the top
triangular plate, 2'. The instrument is provided with three supporting legs, P I , P?, PA, whirh are extended by mild steel rods to hold the triangular plates, J and S, in position. The legs are rigidly fixed to the working table to prevent any vibration during operation. The motor is connected to a constant 110-volt alternating current supply through a 230-volt stepdown transformer with a voltage regulator from the mains. T h e speed of the motor, controlled by an external Variac, is measured by a tachometer having a range of 0 to 1000 r.p.m. T h e tachometer is carefully mounted on the top of the motor with the help of a specially made fixture provided with springs t o absorb any sudden shock during the speed measurement. The revolutions per minute of the motor can be noted whenever required b .v pressing the release key of the tachometer. The motor rvith the top plate and the inner cylinder is removable. This permits ready access to the outer cylinder for cleaning and refilling.
0
5
iD
15
2 0 2 3
3 0 3 5
TORQUE Figure 2.
Spring calibration diagram deflection Deflection.
1 u n i t = 4'
The light pointer, Q, attached to the stem, C, can move over a circular graduated disk, R. T h e scale is divided into 180 equal divisions, each representing 2". A spiral spring, S , Roscoe watch spring S o . 13, is housed in a suitable rasing, T . The outer end of the spring is fixed to the inner wall of T while the inner end is attached to a hook on a small collar fitted t o the stem, C, b y a small screw. T h e spring housing is held in position by means of a brass rod fastened to one of t h e legs. C4LIBR4TION OF SPRING
b
Ir'
i Figure 1.
Sectional view of viscometer
T h e method of calibration is simple and direct. The torque required to turn the spring through a number of degrees is measured as on an analytical balance. This is done by attaching a string to the stem of the outer cylinder and running i t over a small pulley fixed to a stand, C. The string carries a sniall pan, 8,similar to a balance pan, a t its lower end. Known n-eights, placed on the pan, cause the spring to twist through a certain number of degrees. T h e torque produced is the product of the radius of the stem, C, and the m i g h t . A plot of torque against spring deflection is approximately linear up to a certain range and beyond that there is sharp deviation (Figure 2). The n-orking range for a particular spring should be limited to the linear portion of the plot. T o extend the working range of the instrument n-atch springs of different stiffness may be used. PROCEDURE 4 Y D RESULTS
The instrument was initially calibrated with liquids of known viscosity. A definite volume of liquid was introduced in the outer cylinder after plugging the drain hole. The motor was brought t o several speeds by means of the external Variac and the revolutions per minute were noted by means of the tachometer. The degree of rotation of the outer cylinder corresponding to a particular .peed of the inner spindle n-as recorded from
V O L U M E 27, NO. 8, A U G U S T 1 9 5 5 the deflection of the pointer on the graduated scale. Experiments were performed in the speed range of 400 to 1000 r.p.m. T h e scale readings were reproducible within 5 1 ' C. Most of the measurements were carried out a t a temperature of 30" z!c 0.2" C. T h e liquids employed for calibration were water and three water-glycerol solutions which covered the required range of 1 to 5 centipoises. I n order t o determine the viscosity of the glycerol water solutions, Ostn-ald-Fenske viscometers S o s . 50 and 100 were used. The Ostwald readings were checked n i t h water a t 30" z!c 0.1' C.
1289 vided powders of commercial kieselguhr in water, and iron catalj-sta in kerosine were determined. Some typical data are presented in Table I. On comparing the data for kerosine measured in the Ostwald viscometer and the present instrument, it will be observed t h a t a deviation less than 2% was obtained. T h e present instrument can be employed for the measurement of viscosity of a wide variety of materials such as muds, sand slurries, and fine coal suspensions in 11-ater. The working range of the apparatus can be extended t o suit a particular fluid by use of a watch spring of proper stiffness. From the data given in Table I, it n-ill be seen t h a t there is a trend for the viscosity to increase with the Re'. Further u-ork is needed to determine the causes for this behavior. -4number of secondary effects such as centrifugal and end effects, however, may be expected to occur in a n instrument of this type. Kilhelm et al. ( 6 ) observed t h a t before the installation of the baffles in their viscometer, operation was unstable in the turbulent range with liquids of about 60 centipoises or less. Also, they obtained different torque us.
Table I. R.P.11.
-I
Density
=
5d0 590 6,x 710 780 820 850 913
Typical Experiniental Data
Deflection, Torque, Degrees Gram Cni.
j'
X 105
Re
Tiscosity, CP.
Kerosine 0.795 grani/cc. a t 30.2O C. Viscosity by Ostwald pipet = 1.242 cp. 12 16 22 28 3i j 10
6.25 7.25 8.25 9.50 11.25
44
12.75 11.25
5.)
12.00
2.60 2.62 2 1ii 2 37 2.33 2.24 2.22 2.14
380 375 422 4.52 470 3 03 510 552
1,150 1 251
1.220 1.249 1.319 1.291 1.310 1.318
1 263
Average Deviation
+ I 7%
Water-Kieselguhr Slurry IIaterial. Commercial kieselguhr powder (infusorial earth) unsieved. Concentration. 5 grams/100 cc. of slurry. Density, 1.021 grams/cc. a t 30.0' C. a
460 500 5.50
N Figure 3. Torque-r.p.m. relations for gl?-cerol-water solutions a t 30" C.
A R
c
I)
Density, Grams/Cc.
Vibcosity, Centipoise3
1.125 1.090 1.046 0.996
4.315 2.650 1.360 0.800 ( w a t e r )
A logarithmic plot of torque readings against revolutions per minute n-as made as shown in Figure 3. It n-ill be seen t h a t these curves have slopes greater than unity. It was, therefore, evident t,hat the determinations were carried out in the turbulent range. Hence, the values off' and Re'were calculated for several values of S from the knoxledge of density and viscosity data using Eqiiat,ions i and 8. On plotting j ' against Re' a straight line was obtained correlating viscometer data for glycerol-water solutions and ivater. This represented the calibration curve for the instrument (Figure 4 ) . The above linear relation was possible to obtain because of the narrow experimental range with specific Reynolds number varying from 100 to 1000. T o determine the viscosity of unknown liquids and suspensions, a measured volume Tvas introduced and the inner cylinder was rotated a t several speeds and the pointer readings on the dial were noted. From the spring calibration chart, the corresponding values of torque 17-ere found. The values of ,f' were calculated for each r.p.ni. and corresponding Re' n-as obtained from the calibration curve. From the knowledge of Re' values the apparent viscosity of the fluid was calculated. Following this procedure, viscosities of kerosine, several dilute siisprnsions of finely di-
8 12 1li
Boo txn
22 28 34
730 810 870 925
An
inn
.Is 31,
64
5.30 6.23 7.25 8 2.5 9.50 10.75 12.00 1 3 ,50 15.00 16.50
2 66 2 43 2.36 2.24
3ii.i
2 20 2 . 10 2 09
52.; .5 0 072 624 600 690
1 ,259 1 201 1 221 1.213 1.204 1.299 1 389 1 323 1.340 1.330
Arerage
1 282
2.01
1.94 1.89
423 460 505
Kerosine-Catalvst Slurrv ~ ~ _ _ _ b IIaterial. Iron C l O f i copper (3), calciiini oxide (IO), kieselguhr (30). Concentration. 10 grams solid/100 c c . of sliirry. Density. 0.801 grarnlcc. a t 30.2' C. Period of aging. 1 month ~~~~~
600 666 700 760
24 32 36 44
son
.5 0
845 873
.5 6 60
900
64
m
72
8.73 10,50 11.2.5 12.75 13.73 15 on 1.5 7 5 ifi.50 18.00
2 87 2.76 2 07 2 36 2 50 2.44 2.38
2.37 2.32
327 340 360 390
1,580
1.684 1 674 I 078 1 680 l.iiS1 1 .674 1 714 1.733
410
430 4.50 452 472
_
_
.
_
~
llateriol. Iron (loo), mpper (8). calciiini oxide (31, kieselguhr (15). Concentration, 20 grams solidI100 cc. of slurry. Density, 0.943 grarn/cc. a t 30.0' C. Period of aging. 1 month R3,j 620 07.5 730 780 830 880 925
8 75 io.5n 12.00 13.50 1.3 00 i6.a 18.00
19.50
3 01 2 89
2 79 2 09
2 61 2 54
28i 310 339 3.53 377 301;
2.46
'420
2 42
1 83i 1 .88ii 1.917 1.939 1.951 1 .97fi 1 ,976 1.991
438 Average 1 934 Particle size, 40 microns. average
a Displacement specific gravity, 2.280. microscopic. b Displacement -gecific g r a r i t y , 2.310. Particle size. 80 niicrons. hindered sedimentation. Particle size. 51 microns, hindered c Displacement specific grarity. 2.82. sedimentation.
~
1290
ANALYTICAL CHEMISTRY Replacement of the present niechanical arrangement by a n electromagnetic Pystem, in which the small torque on the cup would be measured b y balancing i t against the action of a coil carrying an electric current in a magnetic field, as in a large moving coil galvanometer ( 4 ) . A jacket around the outer casing with necessary fittings to serve as a constant tempernture bath. This tvould enable viscosity determination at different temperatures. ACK\-OF-LEDG3IENT
The authors nish t o express their sincere thanks to S. R. Sen Gupta and G. H. von Hoessle for their kind interest and encouragement during the course of this investigation. They also wish t o acknowledge the kind assistance received from A. K. Basu and the n-orlishop staff of this institute in fabricating the instrument. 3 0 3 1ENCLATURE
f'
= friction factor, dimensionless = specific friction factor
h .\r1 r2
= = = =
f
R Re
=
'7
= = =
7
= = =
Re' Figure 4.
Calibration curve for viscometer
r.p.m. readiiigs h y changing the method of acreleratiilg the rotor from rest t o a high speed. It is important. therefore. to restrict the measurements within the range of S in v-hich such effects are maintained constant and the operation of the instrument is stable. In the present work, the speed of the rotor in the range of 500 to '300 r.p.m. has been found to give mtisfactory results. PROP0 S ED REFINEMENTS
Khile working n-ith this instrument it n-as found t h a t certain modifications are possible n-hich would make it more sensitive and easier t o opwate. Replacement of the ordinary niotor by a aynchronou- one. For the variation of the speed of the rotor, a n r.p.m. regulator of the continuously variable speed transmission type may be used.
JV w 'p
=
I.(
=
T
=
p
=
S!
=
height of inner cylinder, mi. number of revolutions per minute radius of inner rylintler, m i . radius of outer cylinder, cm. radius cf pulley, rm. Reynolds number, dimensionless 3pecific Reynol torque, arbitrs applied load, g equivalent of friction i n rotating system, grains viscosity, poiPe9 function viscosity, centipoiw constant density, grams per rc. angular velocitj-, rndianr per second LITER4TURE CITED
(1) Barr, Guy, "lloiiograpli of Viscometry," Osford University Press, Loiidoii. 1931. (2) Bhattacharya, .I.,and Roy, A. S . , Ind. Eng. Chem., 47, 268 (1955). (3) lIukher,iee. J. S . , and Sen Giipta, h'. C., Indirirz .J. P h y s . , 16, 06-70 (1942). (4) Pearce. C..I.ll.. J . S c i . I m t r . . 30, 232-6 (1953). ( 5 ) Squires, L.,and Doi,kendorff, It. L.. 1x0. Esi;. CHEM., . \ N \ L . ED..8, 295-7 (1836). (6) TVilhelni, 11. H . , and TYroughton, D. >I,, I n d . E n g . C'hem., 31, 452-6 (1 0:39).
RECEIVED for revie!\- Octoher
11, 1954.
Accepted rrhl?iar?- 23, l%jL5,
Use of 1,2-Naphthoquinone-4-sulfonate for the Estimation of Ethylenimine and Primary Amines DAVID H. ROSENBLATT, PETER HLINKA', and JOSEPH EPSTEIN Chemical Corps M e d i c a l Laboratories, Army Chemical Center,
Dilute aqueous solutions of ethyleninline or of n-but>-lamine react w-ith 1,2-naphthoquinone-4-sulfonatea t pl3 10.3 to give reddish d>es w-hich are extracted with chloroform. .QuantitatiF-e estimations of the amines can be made b?; measuring absorbance at 420 and 450 mp, respectively. Ethanolamine also forms a reddish product is not extracted from an dye, but solutiou with chloroform; extraction can be effected with isoam?l a"oho1 and quantitati'e deternllinationl carried out by measuring absorbance at 120 rrlp.
I
Md. S COSSECTIOS \\-it,h the study of certain compounds
related to ethyleniniilic, the authors divovered that, dilute solutions of this imine give a rapid color resction with potassium 1,2-naphthoquinonr-4-sulfonate,a reagent used in Folin's teFt for amino ( d > 7 1 , sirlce the literiiture, f a r as could he ascertained, cont,ains no reference to any specific a n a l y t i d niethod for ethyknimine, it seemed desirable to esploit the re:w tion as a means for e+tim:iting this increasingly important pubstance' Khereas others, in the determination of amino acids, h a r e used 1 Present address, Central Laboratory, Great Atlantic and Paclfio Tea Co., 10 East 40th St., New T o r k , S . Y.
