Cone-Plate Viscometer Comparison with Coaxial Cylinder Viscometer RAYMOND M c K E N N E L L Ferranti Ltd., Manchester, England
The cone-plate tiscometer provides a rapid means of obtaining reproducible flow measurements on nonSew tonian fluids by suhjecting the sample to definite uniform shear rates. The conrentional coaxial c?linder tisccirneter suffers the disadtantages of shear rate variation across the measuring annulus, end effects, limited range of operation, and filling, cleaning, and centering difficulties. The cone-plate configuration provides constant shear conditions without introducing constructional complexity. In practice, filling, cleaning, and temperature stabilization can be completed in about 30 seconds. The flow- curve recorder is capable of plotting a curie in 15 seconds with uniform shear acceleration.
T(4)
HE cone-plate viscometer !vas designed in its original form
for starch pastes and gums used in t,he textile industry. The scope and acciiracy have since been increased to embrace a mrich wider range of mat'erials with either Newtonian or anomalous flow properties. The instrument which evolved from this development has been described in detail elsewhere (6). The chief design consideration3 were as follows: The operating shear rate and shear stress should he conshnt throughout the fluid sample. The layer of liquid sheared in the measuring gap should be as thin as possible in order to minimize the temperature rise in the Ailid at high shear rates, and also to allow rapid initial temperatiire stabilization. The vipcornet.er should be simple to set up, fill, and clean. This means that t,he foregoing tn.0 requirements must not introduce complexity into the construction of the measuring elements. The rate of shmr shoiild lie continuously variable over a m-ide rxnge. The viscometer should be recidily adaptable for automatic flow ciirve recording. The cone and plate measuring system provides a satisfactory solution t o all these requirements. Essentially, the viscometer consists of a flat plate and a rotating cone \vith a very obtuse angle. The apex of the cone just touches the plate surface and the fluid sample fills the n:irrow gap formed tiy the cone and plate. Both the gap n-idth (c, Figure 1) a,nd the linear velocity of a point, T , on the cone are proportional to the radial distance; hence, the rate of shear, which is given I)? the ratio of velocit,y, Rr, and gap width, c, remains ronstant throughout,, because each concentric annular element of fluid (width d ~ is) sheared at the same rate as the adjttcent elements. Theoretically a cone half-angle of +b = 6' gives rise to a departure of only 0.35% from shear rate uniformity. However, if is greater than about 4 O , errors may arise due to edge effect and, at higher shear rates, due to temperature rise n-ithin the fluid (Equation 1). I n practice, an angle of only 0.3" is used, with an average gap width of about 0.05 mm., requiring a sample of about 0.1 cc. Cone angles of this order simplify the mathematical analysis of non-Nextonian flow data because the whole of the measured sample attains a uniform shear rate and, hence, i: constant apparent viscosity.
Figure 2 shows the frindnmental simplic,it>. of the cone and plate measuring system compared with t1i:it of the consial cylinder viscometer. I n the expression for viscosity, the shear 12
,
stress term, __ 3G in dyne/cm.*, and the shear rate t'erm. 2aR3' IC' I n sec.-l, appesr definitely as a ratio. I n the case of the coaxial cylinder viscomet,er the rate of shear varies from minimum at the outer cylinder (R,) to maximum a t the inner cylinder ( R t ) . I t is not possible to att,ain a constant shear rate because the cylinders must have a finite radius. I n practice, if the ratio of t,lie outer and inner cylinder radii is 1.1 to 1, the shear rate varies by 20% for a Sewtonian fluid. I n the case of a non-Xewtonian fluid the varitttion could be much greater (loj. This is about the smallest gap width xvhich may be used m-ith convenience, so that it is usually necessary t o use an average value for the shear rate. It is, of course, necessary to eliminate the end effect due to the viscous traction on the ends of the inner cylinders by guard rings or by other means.
I
I
I
I
CMAX
-1 Figure 1.
1
Method of achieving constant shear rate throughont measured sample
Shear rate
=
D
=
linear velocity gap width =
J.
at
cm./sec.
7( 7 )
eec.-I
These measures are not necessary in the cone and plate viscometer because the edge effect, or torque on the cone due to excess fluid round the periphery, is negligible for small cone angles. This can be shown experimentally (Figure 3) by plotting the torque on cone G against R3 for four cones of different radius R. The cone angle, $, rotational velocity, R, and viscosity 7 are all constant. The data shown were obtained with a Sewtonian sample fluid (silicone, q=9.1 poises). A highly thixotropic or plastic material might conceivably give rise to a slight edge effect. However, such a substance possesses sufficient rigidity at rest to enable the excess material to be cut off flush with the cone periphery before commencing the measurement. With a measuring gap of this kind, cooling is ensured by the large mass of the plate and cone compared n i t h the small volume of fluid present (approximately 0.1 cc.). The dissipation of stress-induced heat can be further assisted by efficient water cooling. The practical advantages of the cone-plate measuring system are substantial. The initial filling is rapid and temperatiire
1710
V O L U M E 28, N O . 1 1 , N O V E M B E R 1 9 5 6
1111
CONE
- PLATE
SCHEMATIC
2n RATE OF SHEAR, D DMAX. = Rl2 (&- & )I SEC.-I
DMIN.
=
2n
RO'
ck -
R1,2
)
*
D= JL
ILASTIC VISCOSITY
-
J= (G -G2)5 POISE a
=(ki2-k o 2 ) 4rrh
HERE IS THE EXTRAPOLATEC LLUEOVIORQU& F O R n + O
YIELD VALUE
Figure 2. Comparison of coaxial cylinder and cone-plate viscometers
-
Figure 4. Coneplate viscometer
Figure 3. Proportionality of and Ra, indioating negligible edge effect
G
50
CONE TORQUE G = R?
4Q
4
6
CONE TORQUE,G,
8
IO
DYNE-CM.
x~05
)
s =3p
ZTI R3
ANALYTICAL CHEMISTRY
1712 equilibrium in t.he test sample is normally attained in a f e n seconds. Wit'h conventional rotation viscometers cleaning is generally a time-consuming operation. This present instrumelit, however, is cleaned by simply wiping off the flat plate : ~ i i dthe almost flat surface of the cone. CONSTRUCTION
The general form of the viscometer is shown in Figiur 1. Thc measuring unit is on the left, the indicator unit in the center, anti the electronic speed control amplifier for the drive motor :it the right. The indicator unit houses a 10-turn potentiometer, cn3bling the cone speed to be set with an accuracy of better than 156, and a five-range sensitivity switch for the measurement, of cone torque. A further switch position provides precise electrical indication of contact between the cone apex and the plate in conjunction with a micrometer screw. This device f;rcilit:ites the preliminary setting of the measuring gap. Figure 6 is a simplified diagram of the measuring unit, showing the cone drive and the electro-mechanical torque measuring system (6). The operating height of the plate is preset by the micrometer screw, but subsequently the plate is raised m d lowered by a lead screw and nut device, operated by rotating cylinder 13. It is important to have a means of reproducing automatically the upper position of the plate with a high degree of accuracy ( 7 ) . This is achieved by spring loading a hardened flange on the plate support column against three matched steel balls. This system has been found to reproduce the plate height to within 0,0001 inch. Thermocouples in the plate surface, in direct cont:ict with the fluid, measnre the temperature rise a t the boundai 1- at high shear rates. INFLUEYCE OF STRESS-INDUCED H E 4 T
According to Carslaw and Jaeger (3) the rise in t e i n p < ~ i L ~ t t u t ~ ,
Figure 5.
(I' where I' is the t1ist:iiicXe from t'he axis of rotation, t is tile time in seconds, H is the heat generat'ed per second per unit vohune of liquid, and K a n d K are the conductivity and diffnsivity of t h r cone and plate, respectively.
=+ -
1. 2.
Schematic diagram of measuring unit
Cone spindle Cone (included angle decreased for clarity)
3: 8 : : ~ ~ ~ ~ $ ~ ~ A: Torque dynamomete: ~
7.
8,9.
,
O
~
Wiper for Slip rings
~
~
?
~
~
~
&
potentiometer
N O COOLING
0'
6.
w= 5. Q u=4
L"
a W
3-
a
2
2
2-
a W n u I 1.
P
