This document describes the design and construction of a concentric cylinder viscometer that allows for highly accurate viscosity measurements at extremely low shear stresses. The viscometer uses a single rotating cylinder (rotor) inside a fixed outer cylinder (stator) and can measure viscosities with shear stresses as low as 0.003-0.0008 dynes/cm2. Experimental results show the viscometer was able to detect a phase transition in solutions of poly-(butylisocyanate) in carbon tetrachloride as temperature was varied.

1. Instrumentation Journal of Physics 35 No. 2 (1989) 274-281
Concentric Cylinder Viscometer Extremely
Low Shear Stress.
R. T. Rodriguez, Raul Montiel C. and A. Romo U.
Department of Physics, University Autonomy Metropolitan - Iztapalapa,
PO Box 55-534, 09340 Mexico, DF
(Received August 2, 1988; accepted January 13, 1989)
Summary.
This paper describes the design and construction of a viscometer of Zimm-
Crothers type, which allows very accurate viscosity measurements at various values
of shear stressesusing only an extremely small rotor.
Abstract
We describe the design and construction of a Zimm Crothers type viscosimeter which
permits us to get very accurate neasurements of viscosity at several values of the
extremely low shear stress, using only one rotor.
1. Introduction directly proportional to viscosity.
One of the oldest techniques and used It may happen, however, that the
in the characterization of materials in viscosity of the polymer solution is
solution is plyometrics viscometry. This dependent on the flow conditions of the
is based on the fact that the presence instrument used: in these cases it is
of large particles dissolved or said that the non-Newtonian
suspended in a liquid produced a viscosity. This type of behavior is found
radical change in the flow property mainly in solutions of highly asymmetric
of the system. molecules rigid or flexible molecules in
solutions of very high molecular
A very important advantage of this weight.
technique is that the amount is
determined experimentally, either The capillary viscometer has proven to
viscous or the torque flow time is be a versatile and inexpensive,

2. however, due to progress in the study
of biological macromolecules, has been
found that many of these molecules are
degraded under the action of even
small shear forces found in the FIGURE 1. The diagram shows the
viscometers capillaries. Furthermore, position of the rotor in the
some biological and synthetic stator.
molecules have non-Newtonian
behavior when subjected to shear 2. Design and construction
stresses experienced in regular sized
capillaries. The viscometer of Zimm-Crothers
type [1], is a concentric cylinder
viscometer, which is made entirely
In view of this, there is need for a of glass, this feature provides the
viscosity comparable to convenience facility to work with almost any
and availability of a capillary solvent.
viscometer, but operating at high shear The outer cylinder (called the stator)
rates of several orders of magnitude remains fixed, while the inner
lower than the capillary. cylinder (called the rotor) is rotating
(Fig.1).
The instrument described herein is
cheap, puts the solution in contact with At the bottom of the stator was
only glass, runs at different shear placed a tube for introducing the
stresses and has been used in cutting sample is from the bottom of the
forces from 0.003 to 0.0008 dynes/cm2, viscometer. This device also
which are several orders of magnitude facilitate filling, very accurately
less than commonly, used capillary adjusts the height of the rotor on the
viscometers. stator core to be reproducible in the
viscosity measurements, in general,
the relative viscosity measurements
have an accuracy of no more than
0.2% .
All the viscometer is introduced into
a heating jacket (Fig. 2) which
allows the device to operate at
different temperatures. As
temperature control was used brand
Haake recirculating bath with
platinum resistance control, which

3. controls with accuracy of
±0.05°C.
The viscometer should be mounted
rigidly to preserve the geometry of
the system. For this is supported
with a nylon ring which is mounted
on a bracket that allows five
movements: first, the position of the
viscosity on the external magnetic
field is carried out through three
platforms that move in the x - y -
z; second, the orientation thereof
with respect to the magnet takes
place by three screws placed in the
nylon ring which allow movement
zenithal and azimuthal (θ, φ) (Fig. FIGURE 2. The figure shows a
2). It is important to note that the cross section of the concentric
alignment of the viscometer with cylinder viscometer and the
respect to the external magnetic description of its components.
field is vital to prevent movement of
precession of the rotor.
where P is the period of revolution
for the solution to the solvent P0 and
By determining the viscosity is Pm to the external magnetic field. In
directly proportional to the time of our case having us that Pm = 0.1
revolution of the rotor as shown in second, thus a negligible amount is
the following expression: about P which is on the order of 300
seconds and P0 is the order of 90
− seconds.
=
−
To determine this period of
revolution is made a small mark on
the aluminum which is observed
using a cathetometer, which is fixed
to the worktable. Was used
additionally an electronic counting,
which operates in the following
manner: a disk mounted with
regularly spaced perforations on the

4. synchronous motor, and through an supported solely by flotation, can be
optocoupler mounted on the base of used
the viscometer (Fig. 2), the
frequency was measured angle of only a single rotor with liquids
rotation of the disc which resulted to whose densities vary in a range of
be of 16.4-Hz, the signal obtained less than five percent. Fig 5 shows
by rotating the disc is sent to an a schematic diagram of the
electronic counter, the reading of experimental equipment and Figs. 6
this is proportional to the viscosity of and 7 show graphs of the calibration
the solution in the viscometer. In Fig curves of viscosity for toluene and
3 shows a photograph of the carbon tetrachloride, respectively. In
instrument, and in Figs. 4a and 4b Tables I, II, III summarizes some of
show schematic diagrams of the physical characteristics of the
electronics involved in this device. instrument.
It is very important to keep a careful There have been several attempts
cleaning of the rotor in operation, it by other authors [2, 3], in order to
should not be touched with fingers automate this instrument by adding
while the viscometer is placed in, as optical devices, which allow more
this will cause problems in flotation precise measurements.
and centered.
Figure 3. The photograph shows the
viscometer mounted on its base.
It should be noted that the density of
the liquid is very important in the use of
this viscometer, because the rotor is

5. 3. Experimental results. tetrachloride (CCl4 PBIC on.
Molecules of poly-(butylisocyanate)
As mentioned above, some of the for not too high molecular weights
systems suitable for use in this type (less than 105) have the form rigid
viscometers are those in which the rod.
molecules are asymmetrical, or
polymer molecules which have the Due to the asymmetrical shape of
form of rigid rods, this is because the molecules, they have a phase
the analysis of viscometer these transition, which was predicted by
solutions must be made extremely Flory [4] of an isotropic state in
low cutting speed. which all the molecules have
random orientations to a nematic
Because of this, we used this type state in which there is a
viscometer on solutions of poly- direction privileged along which the
(butylisocyanate) in carbon polymer chains tend to align.
This phase transition modifies the viscosity of the solution, and is intended to detect
this by viscometric measurements. However, the viscosity must
Perforated disc
output
FIGURE 4a. The photo detector output signal is
a square type of 0-5V.
FIGURE 4b. Electronics concentric cylinder
viscometer.

6. Have very low shear for the velocity field does not induce the phase transition.
Two solutions were prepared in CCl4 PBIC. Was analyzed each of these solutions
at different temperatures in the range of 18°C to 42°C.
In Figure 8a shows a graph of experimental results obtained for the system in CCI4
PBIC. Clearly shows that there is a discontinuity in the viscosity when the
temperature changes. This graph was made at a concentration of 8.6 x 10-4g / g. In
Figure 8b shows the detail of the transition for the same system at a concentration
of 9x10-4g/g.
FIGURE 5. The figure shows the
experimental setup used.
FIGURE 6. Calibration curve of toluene.
FIGURE 7. Calibration curve for carbon tetrachloride.
FIGURE 8A. Log graph of viscosity vs. reciprocal
temperature for the solution-CCI4 PBIC the
concentration of 8.6x10-4g/g.

7. FIGURE 8. Log graph of viscosity
vs. reciprocal temperature for the
solution-CCI4 PBlC the
concentration 9.0x10-4g/g.
TABLE 1. Physical data of the stator and TABLE 2. Details of the aluminum
rotor comprising the concentric cylinder core of the rotor.
viscometer.
TABLE 3. Comparative data between the concentric cylinder viscometer and a
capillary viscometer typical.
4. Conclusions
The concentric cylinder viscometer presented here, despite being a little more difficult
than using a capillary viscometer, practically does not disturb the system under study,
the shear so small that they can be obtained with this instrument at all, in some cases ,
the only means which can measure the viscosity of solutions or suspensions of large
particles.

8. 5. References:
1. H. H. Zimm & C.M.Crothers, Proc. Nat. Acad. Sci. 48 (1962) 905.
2. W. H. J. Stork & H. Vroome, J. Phys. E: Sci lnst 5 (1972) 314.
3. H. J. Seherr, H. C. Vautine & L.P. Witnaver, J. Phys E: Sci Inst 3
(1970) 322.
4. P. J. Flory, Proc. Roy. Soc. London A234 (1956) 73.