Theory and Praxis
of
Capillary Viscometry
- An Introduction –
Authors:
Prof. Dr.-Ing. habil. Jürgen Wilke
Hochschule Anhalt
Food and biotechnology
(Process and environmental Technology Faculty)
Dr.-Ing. Holger Kryk
Magdeburg
Dr.-Ing. Jutta Hartmann
Rheinfelden
Dieter Wagner
SCHOTT-GERÄTE GmbH
Viscometry development dept.
Table of contents
Page
1 Viscosity – Rheology ................................................... 2
2 Basics of capillary viscometry ................................. 5
2.1
2.2
Measurement principle ................................................. 5
Designs of glass capillary viscometers ......................... 5
3 Measurement of flow time .......................................... 7
3.1
3.2
3.2.1
3.2.2
Manual time measurement ...........................................
Automatic time measurement .......................................
Tasks and particularities ...............................................
Detection of the meniscus passage .............................
7
7
7
7
4 Working equation of
glass capillary viscometers ...................................... 9
4.1 Procedure for viscosity determination .......................... 9
4.1.1 Neglect of HC correction .............................................. 9
4.1.2 Calculation of HC correction resp.
use of given table values ............................................ 10
4.1.3 Experimental determination of the
individual HC correction ............................................. 12
5 Calibration ....................................................................... 14
6 Handling of capillary viscometers ........................ 15
6.1
6.2
6.3
6.4
General guidelines for the
selection of the measurement system ........................ 15
Cleaning of capillary viscometers ............................... 16
Preparation of the measurement ................................ 17
Performing the measurement ..................................... 19
7 Causes of errors and special corrections ......... 23
7.1
7.2
7.3
Correctable errors and corrections ............................. 23
Uncorrectable errors .................................................. 24
Frequently occurring error symptoms,
possible causes of errors, and
ways of elimination ..................................................... 26
8 Special applications .................................................... 28
8.1
8.2
8.3
Testing of plastics ....................................................... 28
Determination of the viscosity of oils and additives .... 30
Testing of food ........................................................... 31
9 Formula signs and units used ................................ 33
10 Bibliography ................................................................... 35
11 Standards used in capillary viscometry ............. 37
1
1
Viscosity - Rheology
Viscosity characterises the flow properties, the inherent friction of liquids and gases.
The relationship between dynamic viscosity h and
density r is referred to as kinematic viscosity n:
If a fluid is trapped between two plane-parallel plates,
it will require some amount of force to displace the
upper plate.
n =
The fluid particles which are directly adjacent to the
plates are firmly bonded to the surface by adhesion
forces. In this process the fluid layer neighbouring the
plate being displaced adopts the velocity of the plate.
All neighbouring layers stay more and more behind
with the increasing distance to the plate being
moved. The cause for this phenomenon can be
found in cohesion forces which counter-act the reciprocal dislocation of the individual layers.
y
F
h
= [m2 / s]
r
(1.5)
For reasons of convenience, the unit of mm2/s is
used which then numerically corresponds to the former cSt (Centistoke) unit.
In case of Newtonian liquids h will remain invariant
if the shear rate changes with all other test conditions
remaining unchanged.
Moving a liquid molecule requires a potential hill to
be surmounted which will lead to the following relationship if Maxwellian Boltzmann velocity distribution
is being applied:
v
D = k
x
Figure 1 Basic model of the shearing operation in
the case of laminar, stationary layer flow
The fluid starts to flow inside the gap. A layered flow
builds up (please ref. to Figure 1).
The shear strain t (also referred to as s1,2) refers
the quotient of force F and the boundary surface A of
the liquid:
J =
F
A
dv
dy
(1.2)
According to Newton's Viscosity Law there is proportionality between the shear strain t and the shear
rate D.
t=h•D
(1.3)
The proportionality factor h is referred to as dynamic
viscosity coefficient or, in short, as dynamic viscosity.
The unit of measurement is Pa • s, with the indication
being made in mPa • s i.e. in numerical conformity
with the former unit cP (Centipoise):
D =
2
J
= [Ns / m2 ]
D
e
E visk
RT
(1.6)
k
Potentiality factor
Evisk Measure of the height of the energy maximum
(activation energy of viscous flow)
R
Gas constant
T
absolute temperature
As a consequence of the differences in size, shape,
and interaction between the molecules, h may
change within very wide limits in the case of pure liquids.
(1.1)
The speed drop, i.e. the shear rate D, is the differential quotient:
D =
×
= [Pa • s]
(1.4)
Examples:
n-pentane
0.230
Water
1.002
Propane triol 1480
(Glycerine)
mPa • s (20 °C)
mPa • s (20 °C)
mPa • s (20 °C)
In the case of liquids, and in contrast to gases, h will
decrease in a strongly exponential manner with
rising temperatures. As a rule, the decrease will be
the higher, the higher the absolute values of viscosity
are and the lower the temperature is, since the intermolecular interactions are decreasing with the magnifying thermal movement of the molecules.
This effect indicates the major practical significance
of viscosity, for instance, with regard to lubrication
technology, as will be shown below.
In the case of liquids a complex molecule structure
and an increasing pressure lead to an increase in
viscosity.
As regards water, an anomaly occurs owing to the
particular structure. If pressure increases, viscosity
will pass through a minimum, since molecule aggregates are being formed the reciprocal friction of
which is lower.
Shear-rate dependent flow behaviour:
Dilatancy
The shear viscosity increases with rising shear rate (for
work hardening, please refer to Figure 2, curve b).
D
b
In the case of liquid miscible phases h is in general
not made up by the addition of h-values of the
pure components.
a
c
The viscosity of the miscible phase may be greater or
smaller than h of the isolated components, or may be
in between.
D
Figure 2
The viscosity of the solutions of solid matters is
frequently greater than the one of the pure solvent.
The indication is mostly given in terms of relative or
specific viscosity (please refer to chapter 8).
A particular behaviour can be observed with the concentration-dependability of viscosity of electrolyte solutions.
If the liquid layers are moving at different velocities,
the deformation of the ion cloud will cause the occurrence of additional inter-ionic interacting forces which
will affect friction between the individual layers.
H. Falkenhagen used the theory of inter-ionic interactions, applicable to highly diluted electrolyte, solutions
to derive the Limit Law of Viscosity:
D C = D0 + K
c
(1.7)
D c Viscosity at ion concentration c
Viscosity curves of fluids
a - Newtonian fluid
b - Fluid with dilatant flow behaviour
c - Intrinsic viscous fluid
Plasticity
The flow of the liquids begins only from a minimum
shear strain. Below this yielding point the substance
behaves like a solid matter.
Examples:
- Paints, varnish/lacquer
- Food (mayonnaise)
- Toothpaste
- Vaseline
BINGHAM substances:
t = f (D) is linear above the yielding point.
CASSON substances:
t = f (D) is non-linear above the yielding point.
D 0 Viscosity of the pure solvent
at same temperature
K
Constant depending on
the following influencing variables:
- Temperature
- Relative permittivity
Pseudo-plasticity (intrinsic viscosity)
These substances are characterised by Newtonian
behaviour at low shear rates.
At high shear rates h will increase with the shear rate
(please refer to Figure 2, curve c).
- Ionic valence
- Ionic mobility
Non-Newtonian flow behaviour
Disperse systems, concentrated polymer solutions,
and melts of macro molecules show a marked nonNewtonian behaviour with increasing shear rates.
In their case there is a non-linear dependency between shear strain and shear rate.
Examples:
- Lacquer/varnish
- Thermoplastics
- Lubricating oils (multigrade oils)
- Glues
- Additives
3
In addition to these effects a shear-time dependent
flow behaviour can be observed with some nonNewtonian matters:
t = f (D, t)
h = f (D, t)
This means that shear viscosity is influenced by the
duration of the shearing action (please refer to Figure
3).
h
b
a
Rheometry deals with the specific methods and procedures of determining rheological characteristics.
Within this nomenclature viscometry is a partial discipline of rheometry.
Principles of viscosity measurement
Rheological measurement procedures are mainly
based on mechanical methods, since tension and
elongation are mechanical values which are determined on the basis of a defined deformation of the
sample.
The simultaneous measurement of the electrical,
magnetic, and optical properties which may change
during the deformation or flow process of the fluids is
becoming more and more interesting.
c
ts
Figure 3
The complex nature of this field of work has lead to
the crystallisation of an original term, i.e. rheology
(science of flow behaviour).
Dependency of shear viscosity
on the shear time
Figure 4 shows the major manners of realising the
deformation of the sample.
a = shear-time independent flow behaviour
b = Rheopexy
c = Thixotropy
2
4
M1
2
5
3
The following distinction is made:
1
M2
Shear viscosity decreases at constant shear rate with
increasing shear time (typical for sol/gel transformation).
v
v
a
Rheopexy
Shear viscosity increases at constant shear rate with
increasing shear time.
Rheopexy can, for instance, be seen with PVC plastisols. They are used for corrosion protection on metals. If the coating rate is increased the material becomes more thick-flowing. Rheopex liquids are characterised by a gradual structure formation under
shearing strain.
In addition to these viscous properties one can observe the occurrence of elasticities (1st and 2nd
normal-stress difference) acting perpendicularly to
the flow direction.
The combination of viscous and elastic behaviour
leads to the description of viscoelastic fluids. Polymer solutions, and recently also biopolymers exhibiting molecular-structure dependent viscoelastic properties of this kind meet with more and more technological interest, e.g. in the production of paints and
coatings, food, cosmetics, and pharmaceutics.
4
6
2
Thixotropy
b
c
Figure 4 Measurement principles of viscometers
a = Capillary viscometer
b = Rotational viscometer
c = Falling-ball viscometer
1 = Capillary
2 = Sample
3 = Coaxial cylinder
4 = Torque sensor
5 = Measurement ball
6 = Glass cylinder
M1, M2 = Measurement marks
The present brochure covers the methodological and
metrological particularities of low-pressure capillary
viscometers, the most important of which, in turn,
are the glass capillary viscometers.
They are in particular suited for viscosity measurements with Newtonian liquids with a kinematic viscosity of more than 0.3 mm2/s.
Perfection in the manufacture and the sophisticated
quality-assurance methods form the basis of standardised measurement systems which are meeting
today highest accuracy requirements as to reproduction incertainties and absolute measurement incertainty.
2
Basics of capillary viscometry
2.1 Measurement principle
Inside the capillary viscometers, the velocity drop required for viscosity measurement is built up in the
form of a laminar tube flow within a measurement
capillary.
Under idealised conditions
This issue is approached in a satisfactory manner the
design of device in the form of comparison measurement methods.
Ÿ laminar, isothermal flow
Ÿ stationary flow condition
Ÿ Newtonian flow behaviour of the liquid
Ÿ pressure-independence of viscosity
Ÿ incompressibility of the liquid
Ÿ wall adherence of the liquid
Ÿ neglect of the flow influences at the entry and
exit of capillary of sufficient length
An application of this can be found in solution viscometry where the viscosity of the pure solvent is
used as a reference liquid. The measurement itself is
made, inter alia, on the basis of a ”pneumatic Wheatstone bridge”.
the liquid flows in coaxial layers towards the pressure
drop through the capillary. A parabolic velocity flow
occurs (please refer to Figure 5).
R
vmax
r
The first measurement principle can be used for the
design of continuos viscometers the measurement
accuracy of which is depending on the achievable
measurement incertainty in differential-pressure
measurement and the stabilisation of a defined volume flow.
Another application of the first measurement principle
is viscosity measurement on plastics melts. This
process involves short capillaries, frequently gaps of
a predefined geometry (high-pressure capillary
viscometry).
v
2.2 Designs of capillary viscometers
In the case of low-pressure capillary viscometers
the imaging signal used for viscosity is the time required by a defined liquid volume to flow through a
measurement capillary.
v=0
Figure 5
Velocity profile with laminar tube flow
The Hagen-Poiseuille Law is the physical basis of
viscometers working according to the capillary principle /1, 2, 3, 4/:
4
FR ,p
V
=
8LD
t
(2.1)
With regard to viscosity measurement, this results in
two different fundamental measurement principles:
Ÿ Measurement of the differential pressure at a constant volume flow of the sample through the capillary
Ÿ Measurement of the volume flow through the capillary at a given differential pressure.
The driving force is the hydrostatic pressure of the
liquid column. To achieve higher shear rates, it is
possible to use over-pressure.
Irrespective of the specific design, the mostly
U-shaped glass bodies have ball-shaped extensions
the volume of which determines the quantity of the
sample.
Measurement marks on the glass body, or accurately
defined fixed sensors, allow the measurement of the
passage time of the boundary layer between the
sample and the air (meniscus), a process which enables the passage time of a product volume restricted in such a manner to be measured with
measurement incertainties < 1/10 s.
5
Figure 6 shows the two fundamentally different viscometer types after OSTWALD and UBBELOHDE.
2
In this way the hydrostatic pressure of the liquid column is independent of the sample quantity being
filled in.
3
In addition, owing to the geometrical shaping of the
levelling bulb (6), the influence of surface tension on
the measurement result is almost eliminated.
M1
8
M2
7
L
hm
6
10
L
In the case of the UBBELOHDE Viscometer, too, the
measurement is aimed at the time required by the
liquid meniscus to sink from the annular measurement mark M1 down to the annular measurement
mark M2.
In the case of very strongly tinted, opaque liquids, it
can be possible that a visual detection of the meniscus passage through the measurement marks is impossible owing to the wetting of the tube. For manual
operation, the Reverse-Flow Viscometer (please refer to Figure 7) is used in such cases.
7
a)
Figure 6
b)
4
Glass capillary viscometers after
a) UBBELOHDE and b) OSTWALD
With both viscometers the liquid being examined is
filled through the filling tube (3) into the storage container (4).
Considering that the mean pressure height in the
case of the OSTWALD Viscometers depends on the
filling height, the prescribed measurement volumes
have to be observed under any circumstances. For
this reason filling is done using a pipette. To perform
the measurement, the sample is sucked into the tube
(2). The measurement aims at the time the meniscus
requires to sink from measurement mark M1 to
measurement mark M2 (annular measurement
marks).
In the case of the UBBELOHDE viscometers the
transition point from the capillary (7) to the levelling
bulb (6) has the shape of a ball joint being the end
point of an additional venting tube (1) /32, 33/. After
filling the sample through the tube (3) into the container (4), the venting tube is closed.
Depending on the operational mode, i.e. pressing or
sucking action, the sample is filled by over-pressure
applied to tube (3) or by suction via the tube (2) into
the reference level vessel (6), the capillaries (6), the
measuring sphere (8), and at least up to half of the
pre-run sphere (9).
3 = M1
5 = M2
7 = M3
hm 2
hm1
L
Figure 7 CANNON-FENSKE
Reverse-Flow Viscometer
The sample is filled into the spherical extension of
the capillary tube (2). The tube (1) is closed during
thermostatisation and opened at the beginning of the
measurement. The imaging signal used for viscosity
is the time required by the meniscus to flow through
the measurement marks M1, M2 and M3 at the reverse-flow (1).
The standard viscometer introduced was the
CANNON-Master instrument with a capillary diameter of 0.45 mm and a capillary length of 400 mm.
After venting tube (1), the liquid column in the levelling bulb breaks off. At the exit of the capillary the socalled suspended level develops (also refer to Figure 22). For this reason only a limited sample quantity
- max., min. filling marks (10) - may be filled in. After
ventilating tube (2) the sample flowing out of the capillary will flow off along the inner wall of the levelling
bulb (6) in the form of a film.
With the determination of the viscosity of water
h = 1.0019 [cP] ± 0.0003 [cP] 1) (20 °C),
it was possible to define a viscosity scale.
6
__________________________________________
The capillaries of viscometers used for industrial applications are usually shorter (70 - 250 mm).
1)
National Bureau of Standards, USA, 1953
3
Measurement of the flow time
3.1 Manual timing
In the most simple case the flow time is taken by an
operator using a stop watch. Glass viscometers
manufactured for this purpose have annular measurement marks burnt in above and below the measurement sphere (please refer to Figures 6, 7).
The disadvantages of this method are obvious:
Ÿ Subjective observation errors or differences in the
reaction time of the operator at the beginning and
end of the timing lead to increasing reproducibility
incertainties and, under certain circumstances, to
systematic errors.
Ÿ In the case of opaque substances the meniscus
cannot be seen. One has resort to Reverse-Flow
Viscometers with their more awkward handling and
reduced accuracy.
3.2 Automatic timing
3.2.1 Tasks and particularities
In the case of automatic capillary viscometers an
electric signal has to be generated during the passage of the air/sample or sample/air boundary layer,
respectively, through the measurement marks. This
electrical signal is required as
Ÿ a start and stop signal for the timing process
and as
Ÿ a status signal for the automatic operation
(filling, emptying of the capillaries).
The detection and transformation of a time signal
does not pose any metrological problems. In practical
viscosity measurement the measurement incertainties are determined by the fluid-dynamic circumstances and the detection of the meniscus passage
through the measurement marks.
The manufacturer of the measurement device has to
ensure by design and production measures that the
viscometer constant will not change even if the
measurement conditions should deviate from the
calibration conditions (e.g. measurement and calibration temperature).
3.2.2 Detection of the meniscus passage
This task requires the use of sensors responding to
the difference between the material properties of the
air and the product being analysed during the passage of the meniscus through the measurement
marks.
Optical sensors
During the meniscus passage the optical conditions
such as refraction and reflection within the detection
plane are changing. This leads to a change n the radiation intensity of the light arriving from the transmitter at the receiver (please refer to Figure 8). For the
measurement of time, for instance, the analogous
signal provided by a photo diode is transformed into
a pulse used for the start and stop of the time measurement. Specific threshold values of the analogous
signal may be defined for the "filled" or "empty"
status.
Advantage:
Versatile application, simple set-up
Disadvantage: Highly tinted or opaque liquids, especially those which adhere strongly to
the wall, cannot me measured.
On the viscometers from SCHOTT-GERÄTE all optical sensors are accommodated in a measurement
tripod made of metal or plastic. Within the tripod the
fixation rack and the glass viscometer are fastened
using a clamping mechanism. Figure 8 shows the arrangement of the optical sensors within the measurement tripod on the viscometer.
The light is guided out of the tripod head through fibre optics into the tripod legs up to the upper and
lower measurement plane. The watertight sealing
enables the measurement tripods to be placed in liquid thermostats.
Owing to high precision in the glass-technological
and mechanical production as well as through measures of quality assurance it is ensured that the glass
bodies and tripods are freely interchangeable, with
the certified viscometer constants remaining valid.
As a result, there would be incidental errors which
would have to be determined and identified for each
device separately. Otherwise the user himself would
have to perform calibration. And this is the point
where low-pressure capillary viscometry has a decisive advantage over other viscosity measurement
procedures.
The well-adapted selection of materials, the engineering-technological mastery of the production
processes, and the sophisticated methods of quality
assurance enable a calibration of the viscometers to
be made.
1
Figure 8
2
Arrangement of the optical sensors
on the viscometer
1 = Optical fibre input
2 = Optical fibre output
__________________________________________
1)
National Bureau of Standards, USA, 1953
7
Conductivity sensors
Electrolytically conductive measurement liquids (solutions of salts, acids, bases) can be detected using
small-sized electrodes melted into the measurement
plane in the glass wall. For signal generation the
electrical resistance is measured.
Advantage:
Simple set-up; detection of tinted
and opaque liquids
Disadvantage: The sample must be electroconductive; the supply lines to the sensors are to be protected against water penetration if liquid thermostats
are being used.
Thermal-conductivity sensors
Small-sized thermistors (NTC resistors), melted in on
the level of the measurement plane, are heated up.
As a result to the improved thermal conductivity of
the liquid the thermistor will cool down at the
air/sample transition, and its electrical resistance will
diminish.
Advantage: Measurement-signal generation is independent of the tint, transparency, and conductivity of
the product being analysed.
Disadvantage: More demanding production owing
to the required melting-in of the sensors; incrustation
and contamination hazard in the case of thermally
decomposable samples.
Figure 9 shows a TC Viscometer from SCHOTTGERÄTE. In the tube axis the thermistors with a diameter of < 1 mm in the sealed-in head portion are
clearly visible.
U [V ]
14
b
12
10
8
6
4
a
2
0
1
2
s
Figure 10
3
4
t [s ]
TC sensor signal
a during filling and b during emptying
S - switch point of the timer device
Ultrasonic sensors
The propagation of sound waves in the frequency
range > 20 kHz is different in gases and liquids, and
owing to the changing sound impedance (product of
sonic speed and specific weight) the waves are reflected from boundary layers.
In the case of the echo process (reflection) a sound
head, attached to one side of the measurement mark
and acting both as emitter and receiver, detects
whether gas or liquid is present in the measurement
plane.
The radiation process uses separate emitting and receiving modulators located at opposite tube positions.
Advantage:
upper NTC sensor
lower NTC sensor
Figure 9
TC Viscometer from SCHOTT-GERÄTE
The essential factor for safe operation is a good dynamic behaviour. Figure 10 shows the signal course
resulting developing during filling and run-off (measurement process) through the changing thermal conductivity in the surrounding of the sensor.
To compensate the influence of the sample on dynamics, the SCHOTT-GERÄTE viscosity measurement devices perform an automatic calibration. The
working point of the start/stop timing is adaptively set
by the device software during the filling process of
the capillaries on the basis of a respectively determined dynamic ID value.
8
The signal formation is independent
of other sample properties, i.e. the
application of the process is versatile; no sealing in the glass required
Disadvantage: Coupling of the sound heads bears
production-technological difficulties,
especially in the case of an application in liquid thermostats; greater
signal-processing efforts required;
higher price
Gas-ionisation spark-discharge detection
The electrodes melted in on the level of the detection
planes are connected to a high-voltage generator. If
the liquid, acting as an electrical insulator, uncovers
the electrodes a spark discharge will occur in the gas
chamber if a sufficiently high breakdown voltage is
selected. The electrical pulse is used as a control
signal.
Advantage:
Detection is possible in dull, opaque
liquids
Disadvantage: The process cannot be used in the
presence of least traces of water in
the product being analysed (water
contents > 0.5 %); high-voltage requires extensive insulation.
4
Working equation of glass capillary viscometers
In the metrological sense, the working equation
represents the statistical characteristic of capillary
viscometers. The user uses them for the determination of viscosity on the basis of the flow time.
The starting point is formed by the flow model in the
form of the Hagen-Poiseuille Law (equation 2.1). The
driving force is the hydrostatic pressure of the liquid
column in the form of the mean pressure height hm
(please refer to Figures 6, 7).
Considering that the volume flow V is recorded via
the measurement of the flow time t, the following
equation results for kinematic viscosity n:
n =
p R 4 g hm
h
=
t
r
8LV
(4.1)
In addition to the flow time, equation (4.1) contains
only constants and geometric details.
For a given viscometer they can be summarised into
one characteristic magnitude, the so-called viscometer constant K:
n=K•t
(4.2)
In order to take into account the tolerances which are
inevitable in the manufacture of the devices, K is determined for each individual viscometer by way of a
calibration (please refer to Chapter 5).
According to equation (4.2) there is a linear correlation between kinematic viscosity and flow time. Figure 11 shows this correlation in the form of a characteristic (curve a).
n
The basic hydrodynamic process was first examined
by Hagenbach /5/ and Couette /6/.
The difference between the measured and theoretical flow time tH is therefore referred to as Hagenbach-Couette Correction Time (or, in short, HC
correction or Hagenbach correction):
tH = tg - t
(4.3)
This results in the following corrected working equation for glass capillary viscometers:
n = K • (tg - tH)
(4.4)
The smaller the flow time is, the greater becomes the
Hagenbach-Couette Correction Time. Curve b in
Figure 11 shows the real course of the characteristic.
In practical viscosity
ciple three ways
Hagenbach-Couette
mine the kinematic
analysed.
measurement there are in printo take into account the
Correction and thus to deterviscosity of the product being
4.1 Methods of viscosity determination
4.1.1. Neglect of HC correction
The selection of a capillary with a small diameter,
adapted to the viscosity of the product being analysed, involves long flow times. In this case HC correction takes such a small value that a correction
may be omitted within the framework of the required
accuracy.
The flow times to be observed if HC correction is neglected in order not to exceed a relative error e can
be calculated according to equation (4.5) or equation
(4.6), respectively:
a
1
b
n
t tg
Figure 11
æ mV ö2
tg ³ 19.95 ç
÷
è Î L Kø
t
a ideal and
b real viscometer characteristic
When applying the flow model in the form of the
Hagen-Poiseuille Law, additional pressure losses occurring at the capillary ends are not taken into
account. Owing to the finite capillary length, however,
the pressure losses occurring at the in- and outflow
affect measurement accuracy. As a consequence of
these additional pressure losses the measured flow
time tg is greater than the time t resulting from
Hagen-Poiseuille Law.
1
æ Vö 2
tg ³ 4.9 ç ÷ (e L)
è Kø
(4.5)
1
2
R
-
1
3
(4.6)
m = empirical coefficient of HC correction
m = 1.12 (Re > 100) /N10/
Equation (4.5) is applicable to viscometers with
sharp-edged capillary ends. When using viscometers
with funnel-shaped capillary ends, equation (4.6)
should be used /N10/.
9
4.1.2. Calculation of HC correction resp.
use of given table values
L
le
The manufacturer calculates HC correction times on
the basis of the geometrical dimensions as a function
of the flow time and states them in the device descriptions.
Understanding the calculation algorithm requires first
an explanation of the theoretical basics of Hagenbach-Couette Correction.
,p
Figure 12 shows the true march of pressure in the
capillary /7/.
The deviations from the ideal march result from hydrodynamic processes in the in- and outflow zone of
the capillary. They are taken into account in the flow
model (please refer to Figure 13) in the form of additional terms.
l
Figure 12
Axial march of pressure in the capillary
Dr
Hagen-Poiseuille Law
Viscous portion
Dp=
Figure 13
8 D V L
FR
4
Hagenbach-Couette Correction
Pressure loss owing to the
increase in the kinematic
energy of the liquid when
flowing into the capillary
+
r
2
V Pressure loss owing to
the formation of the parabolic velocity profile in the
flow path Ie
+
V
R2 F
(4.8)
, pc F R4
H V
, p F R4
8F L
8 V L
8 V L
(4.9)
Couette did already take into account the pressure
loss Dpc by way of adding a fictitious length n · R to
the capillary length L in equation (4.10).
10
D pC
(4.7)
This correlation was confirmed by Kerstin, Solokov,
and Wakeham /8/ by a numerical solution of the Navier Stokes' equations.
D =
In this way the following corrected Hagen-Poiseuille
Law for the determination of viscosity results from
equation (4.7), Figure 13:
D =
+
Flow model with correction terms
The mean flow rate v in the capillary results from:
v =
H
2
2
Pressure loss owing
to the increased wall
friction inside the
flow-in path Ie
m H V
, p F R4
8 F (L + n R)
8 V (L + n R)
(4.10)
An explicit determination of the Couette correction
poses problems in terms of metrology. However,
since the viscometer constant K is determined by
way of calibration, Couette correction is implicitly
taken into account in the form of a mean value. Couette correction within the Hagenbach correction term
of equation (4.10) is considered concurrently in the
form of the empirically determined parameter m.
Therefore this correction is often briefly referred to as
Hagenbach correction in literature /12, N6 ... N10/.
For a given glass capillary viscometer
D p = r g hm
(4.11)
and
V
V =
,
tg
(4.12)
with equation (4.13) being derived as working equation.
n =
p R 4 g hm
mV
tg 8VL
8 p L tg
(4.13)
For Re > 100 the value as calculated was confirmed
in experiments. In the case of Re numbers below 100
m will drop sharply and retain only approx. 30 - 40 %
of its initial value at Re = 25/12/. With Re < 10, m is
so small that it can be neglected /13/.
If the capillary ends are funnel-shaped, m will be a
function of the Reynolds number all across the metrologically utilised flow-time range.
Cannon, Manning, and Bell /14/ arrived at the following functional correlation:
m = 0.037 Re
(4.15)
Parameter m mainly depends on the shape of the
capillary ends and the Reynolds number (Re).
Equation (4.15) forms the basis of the calculation of
HC correction according to the applicable standards
/N6, N8, N10/.
The Reynolds number is an important nondimensional similitude characteristic for fluidic description of incompressible fluids:
In this way the following working equations result for
viscometers with sharp-edged or funnel-shaped capillary ends:
Re =
V v r
2V
=
h
p R n tg
(4.14)
It characterises the flow shape, i.e. laminar or turbulent, conditioned by inertia and friction (viscosity).
Depending on the production technology the capillary
ends of viscometers may be sharp-edged or funnelshaped (please refer to Figure 14).
sharp-edged capillary ends
B
tg
n = K × t -
(4.16)
B =
1.12 V
8 FL
UBBELOHDE Viscometer:
B
K tg
tH =
B = 2.5 /N6/
(4.17)
funnel-shaped capillary ends
If Hagenbach-Couette correction in the form of a time
correction according to equation (4.4) is used, the
HC correction time is calculated as follows:
n = K×t-
a
Figure 14
b
Capillary ends of viscometers
a - sharp-edged
b - funnel-shaped
With regard to sharp-edged capillary ends a constant
value of m = 1.12 was calculated on a theoretical basis /9, 10, 11/. This value is also contained as a
maximum guidance value in /N10/. For reasons of
production technology, however, ideally sharply cut
capillary ends are not realisable.
E
tg
2
1.66 V
E =
3
2
(4.18)
1
L (2 K R) 2
tH =
E
(4.19)
K t g2
11
The E / K correction terms for UBBELOHDE and
Micro UBBELOHDE Viscometers can also be taken
from the relevant DIN standards /N6, N7/.
For reasons of production technology, capillary viscometers from SCHOTT-GERÄTE have funnelshaped capillary ends. The correction times tH are
given in the operation instructions.
2. Determination of the Hagenbach correction tH
for the flow time tg by way of linear interpolation
between the values t H1 und t H 2 :
æ 1
1
t H 2 = t H 1 - K 12 ç
ç tg tg
è 2
1
K 12 =
4.1.3. Experimental determination of the
individual HC correction
In the case of small flow times HC correction will
have a increased influence on the measurement result. In addition, owing to after-flow effects of the liquid and the beginning of the deformation of the suspended level, the viscometer characteristic of
UBBELOHDE Viscometers is affected.
If falling short of the measurement range as recommended in the operating instructions is inevitable, an
individual HC correction for the respective viscometer
has to be determined in experiments.
To do so, two standard liquids of a known viscosity
are to be used, with the viscosity of the product being
analysed lying between the viscosities of the standard liquids. The smaller the difference between the
viscosities, the more accurate the result of the correction procedure.
ö
÷
÷
ø
(4.21)
tH 1 - tH 2
1
1
tg 1 tg 2
(4.22)
Figure 15 illustrates the correction procedure:
t H
c
t H
2
t H
tH
1
a
b
Realisation of the correction procedure:
1. Determination of individual values for the
Hagenbach correction with the standard liquids:
1 /t
Figure 15 individual Hagenbach correction /N9/
tH i = t g i -
12
ni
K
i = {1;2}
(4.20)
a Hagenbach curve according to equation (4.19)
b real course of the individual Hagenbachcorrection
c interpolation straight line
Examples of viscosity determination
Viscosity measurement of n-decane at J = 23 °C (n » 1.21 mm2/s) with UBBELOHDE Viscometers
1. Case
3. Case
Selection of a viscometer with capillary 0
K =
0.00098 mm2/s2
L = 90
mm
V = 5.7
ml
mm
D = 0.36 mm
hm = 130
Selection of a viscometer with capillary Ic
K =
0.0303 mm2/s2
L = 90
mm
V = 5.7
ml
mm
D = 0.84 mm
hm = 130
Measurement range according to
operating instructions:
0.2 ... 1.2 mm2/s
Measurement range according to
operating instructions:
3 ... 30 mm2/s
mean measured flow time: tg = 1234.57 s
mean measured flow time: tg = 39.95 s
HC correction time is approx. 0.3 s. This corresponds Calculated HC correction
to approx. 0.024% of the flow time. This means that according to equation (4.19):
neglecting the HC correction time would not cause tH = 1.03 s
any significant change of the measurement result.
The measurement range of the viscometer was fallen
short of. Furthermore, the HC correction time is
Calculation of viscosity:
above the max. correction time of tH = 0.66 s as indin = K · tg
cated in /16/ for precision measurements.
2
2
n = 0.00098
mm /s × 1234.57 s
= 1.21
mm2/s
2. Case
Selection of a viscometer with capillary I
K =
0.0105 mm2/s2
L = 90
mm
V = 5.7
ml
mm
D = 0.84 mm
hm = 130
In this case a viscometer with a smaller capillary diameter should be resorted to. If this is impossible,
the individual HC correction time for precision measurements has to be determined in an experimental
manner.
Measurement range according to
operating instructions:
1.2 ... 10 mm2/s
mean measured flow time: tg = 116.05 s
Calculated HC correction time
according to equation (4.19):
tH = 0.69 s
Calculation of viscosity:
n = K · (tg - tH)
n = 0.0105
= 1.211
mm2/s2 × (116.05 - 0.69) s
mm2/s
13
5
Calibration
The viscometer constant K is determined individually
for each glass capillary viscometer by way of calibration.
The constants of the test specimens are determined
on the basis of kinematic viscosity of the test liquid
and the flow time (please refer to Figure 16).
By careful calibration in combination with the use of
high-quality measurement and testing means and
close-tolerance reference standard sources the
manufacturer guarantees a reproducible calibration
of highest precision. Measurement and reproducibility incertainties of calibration have a direct influence
on the measurement incertainty of the viscometers.
To ensure a high statistical certainty, two measurement cycles involving seven flow-time measurements
each are run, with the first measurement of the respective measurement cycle being considered as
preliminary test.
Measurement principle
The determination of the constants is done by a simultaneous flow-time measurement in the viscometers to be calibrated (test specimens) and in the reference standard sources the constants of which were
determined by the "Physikalisch-Technische Bundesanstalt (PTB)" (Federal Physico-Technical Institute)
in Brunswick.
Realisation
In a thermostat bath with a constant temperature of
± 0.01 K the flow time of a test liquid through a multitude of glass capillary viscometers is measured.
Test liquids are no reference standard sources. Their
viscosity is only known within a tolerance range of
± 10 % around a guidance value. The test liquids
used are mono-substances or mineral-oil products
with narrow boiling profiles.
Two of the viscometers are reference standard
sources the flow times of which is used to calculate
the kinematic viscosity of the test liquid. Owing to the
use of two Reference Viscometers a functional test is
carried out automatically during calibration.
Test specimens
P1
P2
P3
The measurement temperature is 23 °C ± 0.01 K. It
is verified using at least two officially gauged mercury
capillary-column thermometers with a resolution of
0.01 K.
Each calibration can guarantee the metrological correctness of the viscometer constants only for a limited period of time. It is therefore recommended to
check the constants on a regular basis or to have
them checked by the manufacturer, respectively. The
check may be done either by comparison measurements using reference standard sources (please see
above) or with calibrating oils from the ”Deutsche Kalibrierdienst (DFD)” (German Calibration Service).
However, if regular oils are being used, the limitation
of the accuracy of the test procedure caused by the
incertainty of the regular-oil viscosity indication
should be noted. Considering that this incertainty is in
general above the measurement incertainties stated
for glass capillary viscometers, this calibration
method is not recommended for precision measurements.
Please refer also to DIN 51 561 - 4, Part 4: Viscometer calibration and determination of measurement incertainty, taking into account the user note /N9/.
Reference Viscometer
R1
R2
n 1 = K R 1 (t g R 1 - t H R 1 )
K P1
Figure 16
14
n
=
t gP1 - t HP1
Calibration of glass capillary viscometers
n 2 = K R2 (t gR2 - tHR2 )
n=
n1 + n 2
2
6
Handling of glass capillary viscometers
6.1 General guidelines on the selection
of the measurement system
Selection of the viscometer type
The following viscometers from SCHOTT-GERÄTE
can be used for viscosity measurement with transparent liquids:
Ÿ UBBELOHDE Viscometer
Ÿ OSTWALD Viscometer
Ÿ CANNON-FENSKE-Routine Viscometer
These include devices for both manual or automatic
measurements involving optoelectronic detection of
the meniscus passage. In addition it is possible to
use TC-UBBELOHDE Viscometers equipped with
thermistor sensors. Owing to the advantages referred to in chapter 2, UBBELOHDE Viscometers
should be preferred over the other types in most applications.
In the case of measurements involving low-foaming
or bubbling liquids one should use OSTWALD or TCUBBELOHDE Viscometers, since foam of bubbles
affect the functioning of the photoelectric barriers. In
the case of highly foaming liquids, however, TCUBBELOHDE Viscometers should not be used, since
the thermistors' function may be affected by adhering
foam particles. In addition, no clear detection of the
meniscus passage is possible in the presence of intense formation of foam.
For determining the viscosity of mixed substances
containing highly volatile components and matters
reacting with the ambient air, the use of OSTWALD
or CANNON-FENSKE Routine Viscometer is recommended.
If only sample or solvent small quantities are available, the use of Micro UBBELOHDE or Micro
OSTWALD Viscometers is favourable.
For reason of thermally caused volume changes of
the product being analysed, high- or low-temperature
measurements should always be performed using
UBBELOHDE Viscometers.
CANNON-FENSKE Reverse-Flow Viscometers for
manual measurement of the viscosity of opaque liquids, or BS/IP/RF U-Tube Reverse Flow Viscometers
(from approx. 6000 mm2/s) for highly viscous substances are available.
For automatic viscosity determination, to be used in
particular with opaque oils and emulsions,
TC-UBBELOHDE Viscometers are the choice. Owing to the fact that the thermistor sensors are glasssealed and melted hermetically tight in the viscometers, it is, for instance, also possible to measure conductive and highly aggressive liquids.
Capillary selection
The measurement range of the viscometers is determined by the capillary diameter (0.25 ... 10 mm).
Each capillary diameter has a capillary number and a
viscometer type number assigned which is indicated
on a test certificate.
To select a viscometer, the viscosity of the substance
to be analysed has to be estimated.
The selection as such is based on a rough calculation of the flow time exclusive of the HC correction
according to equation (4.2).
In accordance with the DIN standard, the min. flow
time to be sought after should be 200 s /N10/ for
most viscometers. However, trials have shown that it
is also possible to realise shorter flow times without
impairing the measurement accuracy.
When using micro viscometers the flow time can be
reduced to 30 s. According to the most recent research results, even flow times down to approx. 10 s
/15, 34, 35/ are possible if individual HagenbachCouette Correction with automatic flow-time measurement is applied.
In the operating instructions of the viscometers the
min. flow times are stated as a function of the capillaries.
Table 1 shows as an example the measurement
ranges as a function of the capillary diameter for
UBBELOHDE Viscometers.
15
Table 1
Measurement ranges of UBBELOHDE Viscometers /16/
Capillary Capillary diameter
no.
[mm]
0
0c
0a
I
Ic
Ia
II
IIc
IIa
III
IIIc
IIIa
IV
IVc
IVa
V
0.36
0.46
0.53
0.63
0.84
0.95
1.13
1.50
1.69
2.01
2.65
3.00
3.60
4.70
5.34
6.40
K (guidance value)
[mm2/s2]
0.001
0.003
0.005
0.01
0.03
0.05
0.1
0.3
0.5
1
3
5
10
30
50
100
Measurement range
[mm2/s]
0.2 ...
1.2
0.5 ...
3
0.8 ...
5
1.2 ...
10
3 ...
30
5 ...
50
10 ...
100
30 ...
300
50 ...
500
100 ... 1000
300 ... 3000
500 ... 5000
1000 ... 10000
3000 ... 30000
6000 ... 30000
> 10000
In addition, SCHOTT-GERÄTE
offers a KPG utility pipette for
determining the optimally suited
capillary number for the respective measurement task.
6.2 Cleaning of capillary viscometers
Careful cleaning of viscometers is an essential prerequisite for an exact and reproducible measurement
value. Practical experience has shown that increased
scattering of the flow times is in most cases caused
by contamination. In this context even smallest quantities of microscopically small particles of dust within
the viscometer may lead to standard deviations of up
to several per cent.
Particles which adhere firmly to the capillary wall and
are frequently almost invisible are often the cause of
systematic measurement errors. Errors of this type,
leading to an increase of the flow times, can hardly
be told from the individual values of a measurement
series. The larger the capillary diameter, the smaller
is the danger of contamination.
In addition to solid particles, oil or fat films adhering
to the internal wall of the viscometer may affect the
flow times. In particular when measuring substances
with a higher surface tension (e.g. aqueous media)
droplets, adhering to the wall and affecting the
measurement result, may occur during the start-up
process. This is why it is recommendable to measure
only substances with similar properties in one and
the same viscometer. If this is impossible, a particularly careful cleaning process has to be carried out.
As a principle, all cleaning agents should be filtered
prior to use using glass frits with a corresponding
pore width. Paper filters have a tendency of losing fibres and are thus not recommendable.
16
Initial cleaning
Especially as a result of transportation and storage,
severe contamination may occur so that a thorough
initial cleaning is inevitable.
The following cleaning agents have proven
to be suitable:
Ÿ concentrated sulphuric acid with an addition of potassium dichromate (chromic-sulphuric acid mixture); when working with chromic-sulphuric acid
mixture, extreme care has to be taken; chromium(VI) compounds are toxic
Ÿ a solution consisting of 15 % hydrochloric acid and
15 % hydrogen peroxide
Cleaning methods:
1. Fill the viscometer completely with one of the
above cleaning substances
2. Let the cleaning substance act for at least
12 hours
3. Rinse the viscometer using distilled water
4. Rinse with a filtered, miscible, highly volatile
solvent, e.g. with acetone
5. Dry by way of purging with dry, dust-free air or in a
drying cabinet
They use of highly alkaline solvents may lead to irreversible leaching in the glasses which may even
cause a change in the viscometer constant.
Initial cleaning
Automatic cleaning
Immediately after each measurement, the viscometer
has to be cleaned using suitable solvents. The use of
a vacuum pump has proven suitable for this purpose.
Especially for examinations of mineral oils in
UBBELOHDE or CANNON-FENSKE Routine Viscometers, SCHOTT-GERÄTE is offering the AVS 26
Viscometer Cleaner. Using this device it is possible
to clean viscometers without having to take them out
of the thermostat baths. This process requires special viscometers with an attached rinsing tube.
Cleaning method when using a vacuum pump:
1. Connect the vacuum pump via a liquid trap to the
capillary tube
2. Fill the cleaning liquid into the filling tube and the
venting tube
(in the case of UBBELOHDE Viscometer)
3. Periodically close the filling and the venting tube
while the liquid is being sucked off
A pulsating liquid column will occur, dissolving
even set-in contamination
4. Repeat the cleaning process two or three times
5. Rinse with a highly volatile solvent
6. Dry by way of sucking dry, dust-free air
through the assembly
Cleaning method without a vacuum pump:
1. Fill the cleaning liquid into the filling tube
2. Suck the liquid several times into
the measurements sphere
3. Clean the remaining viscometer parts
by shaking the viscometer
4. Empty the viscometer
5. Repeat the cleaning process two to three times
6. Rinse using a filtered, highly volatile solvent
7. Dry by purging with a dry, dust-free air
or in the drier
In particular when cleaning without a vacuum pump,
it is furthermore recommended to wait for an additional 20 to 30 minutes prior to the beginning of the
cleaning cycle. If measurements are not made immediately subsequent one to another, the cleaned
viscometers are to be stored in a dust-free environment. Immediately prior to the next measurements,
the glass body is to be rinsed and dried once again.
If the viscometer was not in use for several weeks,
cleaning should be done using one of the substances
suitable for initial cleaning after an action time of at
least one hour. The same cleaning process should
also be performed if scattering of the measurements
values above the repeatability limit specified for the
viscometer, or systematic measurement errors, occur
during operation, with such errors not being eliminated by cleaning using one of the correspondent
solvents.
In order to minimise the likelihood of the occurrence
of such errors from the onset, regular cleaning of the
viscometers using the liquid specified for initial cleaning is also recommended at larger timely intervals.
The AVS 26 Viscometer Cleaner works in combination with the automatic viscosity-measurement devices of the AVS series. Several rinsing programs
are available. During the rinsing process the viscometer cleaner pumps solvent alternately through
all tubes of the viscometer. The device is intended for
use with up to two solvents. The rinsing process may
be followed by a drying cycle. For automatic cleaning, the maximum viscosity limit of the product being
analysed is approx. 8000 mm2/s at 25 °C.
The use of an automatic rinser, however, does not
release the user from a periodical, careful manual
cleaning.
6.3 Preparation of the measurement
Preparation of the sample
Solid particles contained in the sample to be examined have a similar effect on the measurement result
as contamination in the viscometer
For this reason, you should immediately prior to performing the measurement:
Ÿ Carefully clean and dry all parts coming in contact
with the substance to be measured,
Ÿ filter the samples
- low-viscosity samples:
glass filter, porosity 2 to 4 (10 - 100 mm)
- highly viscous samples:
sieve, mesh width 0.3 mm.
Paraffin or resin-containing products as well as substances with a pour-point of less than 30°C below the
testing temperature are to be treated thermally prior
to performing the measurement. The measurement
temperature must be at least 20°C higher than the
pour-point.
17
Filling UBBELOHDE and OSTWALD
Viscometers
The substance to be examined is to be filled into the
liquid reservoir via the filling tube.
Considering that the average pressure height of the
OSTWALD Viscometer depends on the filling quantity, the sample volumes for OSTWALD and Micro
OSTWALD Viscometers indicated in table 2 are to be
adhered to in any case. For this reason, a pipette is
to be used for filling.
UBBELOHDE Viscometers have two division marks
on the reservoir vessel showing the minimum and
maximum filling quantity. In case of Micro
UBBELOHDE Viscometers there is only one mark
which is to be adhered to within a tolerance range of
about ± 1 mm. This means that more accurate dosing is not required. It should only be ensured that the
opening of the venting pipe on the reference level
vessel is above the liquid level.
Filling CANNON-FENSKE Routine Viscometers
CANNON-FENSKE Routine Viscometers (please refer to Figure 17) are held upside down for filling. The
capillary tube (1) immerses into the liquid to be
measured, while suction is upheld at the other tube
until the liquid has reached the annular mark M2. After filling, the viscometer is restored to normal measuring position.
Considering that filling a Reverse Flow Viscometer is
somewhat more complex, reference is made at this
point to the standards /N5, N28, N47/ as well as to
the operating instructions.
Considering that air bubbles occurring during the
measurement process may lead to scattering of the
measurements values, it has to be ensured that no
bubbles occur during the filling of the viscometers.
For this purpose, the viscometer is held in a slightly
inclined position, and the liquid is filled in such a
manner that it will float down into the reservoir vessel
along the filling tube without any bubbles occurring.
Best results when filling UBBELOHDE Viscometers
were achieved using throw-away syringes with an attached glass-tip filter. When using syringe filters, prior
filtration is not necessary.
Especially when filling in substances of a higher viscosity into OSTWALD Viscometers the pipette should
be immersed deeply into the filling tube in order to
prevent after-flow errors.
Figure 17 CANNON-FENSKE Routine Viscometer
Table 2 Filling quantities for
various viscometer types
Viscometer type
OSTWALD
Micro OSTWALD
UBBELOHDE
Micro UBBELOHDE
CANNON-FENSKE Routine
CANNON-FENSKE
Reverse Flow
BS/IP/RF U-Tube
Reverse Flow
18
Filling quantity
[ml]
3
2
15 - 22
3 - 4
5 - 12
approx. 12
approx. 20
1
2
3
4
5
6
7
8
9
tube with capillary
venting tube
reservoir
lower timing mark M2
upper timing mark M1
pre-run sphere
capillary
measuring sphere
tube extension
Suspending the viscometers in the racks
SCHOTT-GERÄTE offers for all viscometer types
fixation racks or holders, respectively, which ensure a
stable, vertical suspension of the viscometers in the
thermostat bath. In addition, they protect the viscometers from breaking.
Prior to the measurement, UBBELOHDE Viscometers are to be suspended in the racks provided for
this purpose, and fixed in position by pressing the
spring downwards.
The test temperature should be kept constant both
locally as well as timely in a range between + 15 °C
up to + 100 °C at an accuracy level of ± 0.01 K. Outside the indicated temperature range major fluctuation cannot be avoided in each case, but these fluctuations should still not exceed ± 0.05 K either. If, in
particular cases, extreme precision is required, it is
recommended to keep the test temperature timely
constant within a range of + 15 °C to + 100 °C at an
accuracy level of 0.01 K, and outside this range at
and a accuracy level of ± 0.03 K. The temperature
should be checked using gauged mercury glass
thermometers with a resolution of 0.01 K.
The liquid bath and in particular the thermometer are
to be protected from direct exposure to light sources.
There recommended bath liquids are.
below 0 °C:
antifreezers, e.g.
glycerine + water
0 ... 80 °C: distilled water + tap water
80 ... 105 °C: water + glycol
105 ... 200 °C: propylene glycol, silicone oil,
paraffin oil
The viewing thermostats of the CT series, developed
by a SCHOTT-GERÄTE especially for capillary viscometry, meet the requirements with regard to the
timely and local constancy of the temperature of the
bath liquid. They are equipped with openings or inserts, respectively, for two (CT 52/2, CT 1650/2) or
four capillary viscometers (CT 1650/4).
Once filled and placed in the fixation rack or the
holder, respectively, the capillary viscometers are
hung into the thermostat bath the temperature of
which was pre-adjusted. When using viewing thermostats of the CT series, special viscometer-rack inserts for manual measurement are available.
Subsequently, the sample is exposed to thermostat
treatment in the viscometer.
Figure 18
UBBELOHDE Viscometer
with fixation rack
6.4 Performing the measurement
Thermostat treatment
Viscosity is highly depending on the temperature
/24/. For this reason, the viscometers have to be
treated in a thermostat during each measurement.
The thermostats used are automatically controlled
liquid viewing thermostats. The viscometer has to be
immersed until the bath liquid is at least 2 cm higher
than the liquid meniscus in the viscometer in its highest position.
When
performing
measurements
using
UBBELOHDE, OSTWALD or CANNON-FENSKE
Routine Viscometers it is recommended to suck the
liquids at least three times into the measurement
sphere in order to speed up the heat transfer. This
procedure is not possible the case of Reverse-Flow
Viscometers. Their temperature adjustment should
therefore be correspondingly longer.
The following temperature-adjustment times are
recommended:
Ÿ 10 min:
Ÿ 20 min:
Ÿ 30 min:
low-viscosity substances;
high-viscosity substances,
low-viscosity substances in the case of
Reverse-Flow Viscometers;
high-viscosity substances in the case of
Reverse-Flow Viscometers.
19
Manual measurement
For the measurement of the flow times, the liquid is
sucked into the measurement sphere by applying a
vacuum to the capillary tube. When using viscometers with a feeder sphere, the latter should be filled at
least up to its half.
Viscometers without a pre-run sphere are filled until
the liquid meniscus is approximately 20 mm above
the upper annular mark. If UBBELOHDE Viscometers are used, the venting tube should be closed with
a finger tip prior to starting sucking in. Upon completion of the filling process the suction hose is removed
from the capillary tube and, in the case of the
UBBELOHDE Viscometer, the venting tube is released.
When measuring highly viscous samples it is recommendable to keep the capillary tube closed after
releasing the venting tube until the levelling bulb has
run empty and the suspended level has built up.
When examining highly volatile substances it is recommended to perform the filling of the measurement
sphere by applying an over-pressure to the filling
tube, if no bubbles occur in the liquid. Closing and
opening the venting tube in the case of
UBBELOHDE Viscometers should be done analogously.
The measurement involves the period of time over
which the lower for vertex of the meniscus sinks from
the upper edge of the upper annular mark down to
the upper edge of the lower annular mark. The stop
watch used for timing should have a dissolution of at
least 0.1 s. When the meniscus passage is detected,
it has to be made sure that the annual mark is at eye
level.
In order to make the measurement values available for
statistical evaluation the measurement process should
be repeated several times. Especially in the case of
UBBELOHDE Viscometers, on order to avoid any
formation of bubbles, it should be noted that a renewed sucking or pressing up of the measurement
substance must only begin when the drainage of the
liquid from the capillary is completed.
When using Reverse-Flow Viscometers, sucking the
liquid into the measurements sphere is not applicable. To perform the measurement, the tube which
was closed after filling, is opened on the side of the
measurement sphere, and subsequently one measures the time over which the liquid rises from the
lower to the upper annular mark. The CANNONFENSKE Reverse-Flow Viscometer is equipped with
two measurement spheres one on top of the other,
i.e. two measurement values are available after just
one liquid passage. To repeat a measurement when
using Reverse-Flow Viscometers, they have to be
emptied, cleaned, and refilled after each measurement.
If the repeatability limit of a measurement series
(2.8 times the standard deviation) exceeds the reproducibility limit indicated for the specific viscometer, one has to assume the presence of external influences. In this case the measurements have
to be repeated on a new part of the filtered sample
after the viscometer has been cleaned. If only a
”maverick” is present it may be deleted or, as a better
alternative, be replaced by an additional measurement value. If necessary, a check for runaway values
of this kind is to be performed /17/.
The calculation of viscosity is done on the basis of
the mean value of the flow times.
Automatic measurement
Figure 19 (c) shows the proper detection of
the meniscus passage.
For automatic viscosity measurement using
UBBELOHDE, OSTWALD, and CANNON-FENSKE
Routine Viscometers, SCHOTT-GERÄTE offers the
automatic viscosity measurement devices of the AVS
series.
Table 3 will give you an overview of the device program.
The selection of the AVS/S, AVS-SK, and AVS/S-CF
measurement tripods for automatic viscosity measurement with optical detection is determined by:
Figure 19
Detection of the meniscus passage
in the case if manual measurement
(a), (b) - wrong (c) – correct
20
Ÿ Viscometer type
Ÿ Bath liquid of the thermostats
(metal tripod for non-aqueous media,
PVDF measurement tripod as a corrosion-free
option)
For measurement using the TC-UBBELOHDE Viscometer no measurement tripod is required. The viscometer is clamped into a special fixation rack and
suspended in the thermostat bath. The connection
with the control unit is made using a cable which is
plugged into a socket on the viscometer head.
The AVSPro Automatic Viscosity Sampler is a fully
automatic viscosity measurement system for routine
measurements.
The maximum viscosity limit of the product being
analysed for use in the AVSPro Automatic Viscosity
Sampler is approx. 800 mm2/s at 25 °C.
This device performs measurements of kinematic
and relative viscosity up to calculation and documentation work in an independent manner.
The AVSPro Automatic Viscosity Sampler may be
operated with a maximum of eight Micro UBBELOHDE Viscometers equipped with TC Sensors in
two thermostat baths at two different measurement
temperatures simultaneously.
Filling, emptying, and rinsing of the viscometers are
integrated in the automatic course of the measurement.
Operating guidance is via menu-control using a
monitor, a mouse, and a computer keyboard.
Sample carriers for up to 16 sample bottles of 100 ml
each, or sample carriers for a 56 sample bottles of
20 ml each can be used.
Figure 21 shows a viscosity measurement station with the AVSPro Automatic Viscosity Sampler.
Figure 21
22
AVSPro Automatic Viscosity Sampler equipped with
8 Micro UBBELOHDE Viscometers with TC Sensors in 2 Viewing Thermostats CT 53
7
Causes of errors and special corrections
7.1 Correctable errors and corrections
Rising-height error
Thermal expansion of the capillaries
and the measurement vessel
Surface tension causes the liquid which is wetting the
tube wall to climb by a distance of Dh.
During high- and low-temperature measurements the
radius and the length of the capillaries, the volume of
the measurement sphere, and the average pressure
height of the viscometer will change owing to the
large difference between the measurement and the
calibration temperature. For this reason the viscometer constant has to be corrected in the case of precision measurements.
The size of the relative rising-height error e in terms
of % can be calculated on the basis of the following
formula:
A=
I
2
1
1 I
( - ) ( - 0 ) · 100 %
H0
g hm r1
r2 H
(7.1)
The corrected device constant according to the equation (7.2):
K´ = K (1 + a (J - J0))
hm - mean pressure height
g - acceleration due to gravity
r1 - radius of the upper reservoir vessel at
the liquid meniscus
r2 - radius of the lower reservoir vessel at
the liquid meniscus
s - surface tension of the measurement substance
s0 - surface tension of the calibration substance
r - density of the measurements substance
r0 - density of the calibration substance
In the case of precision measurements the influence
of the rising-height error is to be noted with the following viscometer types, if the relation between surface tension and density of the measurement liquid
deviates considerably from that of the substance
used for a calibration:
a) in the case of viscometers with a small
pressure height, where the liquid flows
from the upper vessel into another vessel
the diameter of which is considerably
different from the one of the upper vessel,
e. g. CANNON-FENSKE Viscometer,
OSTWALD Viscometer;
b) in the case of all of pipette viscometers.
In the case of UBBELOHDE Viscometers the correction will in general be no more than 0.1 to 0.2 % and
can thus be neglected in most cases.
(7.2)
Viscometers from SCHOTT-GERÄTE are calibrated
at a temperature of J0 = 23 °C. The coefficient a of
longitudinal expansion of the DURANâ-glass used
for production is 3.3 • 10-6 K-1.
2)
Thermal expansion of the
measurement substance
In the case of UBBELOHDE Viscometers no correction is required, since the measurement result is
largely independent of the substance quantity being
filled in. If, in the case of viscometers without suspended level, the substance temperature should deviate from the measurement temperature during the
process of filling the viscometer, a volume change of
the measurement substance leading to a change of
the viscometer constants will occur during the temperature adaptation.
In this case the constants are to be corrected according to equation (7.3) for OSTWALD and CANNONFENSKE Routine Viscometers, or according to equation (7.4) for Reverse-Flow Viscometers.
K ¢ = K (1 +
4 V (p 2 - p1 )
2
)
(7.3)
)
(7.4)
F Dm h m p2
K ¢ = K (1 -
4 V (p 2 - p1 )
F Dm
2
h m p2
Dm - mean diameter of the liquid meniscus
in the reservoir vessel
r1 - density of the measurement substance
at filling temperature
r2 - density of the measurement substance
at measurement temperature
2)
Registered trademark of
SCHOTT GLAS, Mainz, Germany
23
Inclination error
Viscometers have to be used in the position in which
they were calibrated. If the connection line between
the centre points of the reference level vessels deviates from normal position, the mean pressure height
of the viscometer will change. If, instead of the initial
angle f0 the connection line compared to perpendicular is at an angle of f the corrected device constant is to be calculated according to:
K¢ = K
cos f
cos f 0
(7.5)
The fixation racks or holders offered by SCHOTTGERÄTE ensure a perpendicular suspension of the
viscometer with a deviation < 1°. This corresponds to
a max. relative constant error of 0.02 %. This means
that the inclination error can be neglected if these
racks are being used.
Local independence of the acceleration
of the fall
A correction is required if the acceleration of the fall
at the calibration place g0 and the acceleration of the
fall at the measurement place g are significantly different.
Equation (7.6) is to be used to calculate the corrected
device constant.
K¢ = K
g
g0
(7.6)
Accuracy of the watches
If mechanical stop watches are being used, these
have to be adjusted in such a manner that their max.
accuracy error is less than 2 s per hour. In this case
the occurring error is less than 0.05 %. Prior to beginning the measurements the watch should be wound
up to exclude variations of the spring force. It is recommended to check the accurate march of the
watches regularly using a time standard.
If the time is measured electronically using a corresponding frequency standard, the frequency being
used has to be constant and to correspond at least to
10-4 of the set value.
Inaccurate adjustment and
measurement of temperature
Errors caused by inaccurate temperature adjustment or insufficiencies in the temperature stability or
temperature measurement are frequently very
large, since the viscosity of most of the liquids varies largely as a function of temperature /24/.
24
In the case of a temperature error of ½s½ £ 1K, the
relative error in the viscosity measurement is:
A = Un • s • 100 %
(7.7)
The temperature coefficient Un is determined according to the corresponding DIN standard /N4/.
The temperature measurement should only be made
fully in mass in gauged thermal metres with a resolution of 0.01 K. Their requirements imposed on the fair
most bats to be used are it described in Chapter 6.4.
7.2 Uncorrectable errors
Turbulence
Laminar flow is the basic requirement for viscosity
measurement according to the capillary principle.
Laminar flow is present if the Reynolds number Re is
< 2300. Owing to the sensitivity to disturbance of the
flow, it is useful to remain far below this value when
performing measurements.
For a given viscometer the Reynolds number can be
calculated according to the following numeric-value
equation:
Re = 63.7 ×
V
R × K × tg
V = [cm3]
(7.8)
2
R = [cm]
K = [mm2/s2]
tg = [s]
Considering that Hagenbach correction will increase
with an increase in the Reynolds number, one should
work with a Reynolds number below 200 if this is
possible in practice /N10/.
Disturbance of the suspending level
in the case of UBBELOHDE Viscometers
If viscosity measurements are performed with short
flow times, a deformation of the suspended level may
occur. This will lead to systematic measurement errors, since the average pressure height of the viscometer will change. In addition, one has to reckon
with an increased scattering of the measurement
values within the limit ranges between the disturbed
and the undisturbed suspended level, and the influence of surface tension on the measurement result
will increase.
Figure 22 shows various stages of level disturbance.
Drainage errors
Table 4 will give you an overview of the limit values
of the Reynolds numbers and the flow times up to
which in general no disturbances of the suspended
level will occur for UBBELOHDE Viscometers (normal design). Considering further that the limits are
also depending on the surface tension of the liquid
and the shape of the capillary outflow, disturbances
of this kind may even occur in the case of somewhat
longer flow times.
Drainage errors are caused by the fact that a small
liquid volume DV is adhering to the wall of the viscometer above the sinking liquid meniscus. DV will
increase with the viscosity and the sinking velocity of
the meniscus. The magnitude of the error is also influenced by the wettability of the wall, the surface
tension of the liquid, and the geometry of the viscometer. Depending on the constructional shape of
the device a shortening or extension of the flow times
may occur.
Table 4 Limit values of tg and Re
(UBBELOHDE Viscometer) /N9/
Capillary no.
Radiation heat
0c
0a
I
Ic
tg [s]
100
75
60
60
Re
500
500
300
100
To avoid an uncontrolled heating up of the liquid to
be tested by heat radiation, the liquid bath is to be
protected from direct exposure to the sun or light
sources. Cold lights or light sources with a premounted infra-red filter should be used for illumination preferably.
Start-up length
One of the preconditions are for capillary viscometry
is a parabolic velocity profile.
For this reason the flow time has to be selected in
such a manner that the start-length le for the formation of the profile is considerably smaller than the
capillary length. According to Schiller /10/ the start-up
length can be calculated as follows:
le = 0,115
Figure 22
V
p n tg
(7.9)
Stages of distribution of the suspended level in the case of UBBELOHDE Viscometers /N9/
(a)
no disturbance - measurement can be used
(b), (c), (d) disturbance - measurement cannot be used
25
7.3 Frequently occurring error symptoms, possible causes of errors and
ways of error elimination
Table 5 gives a summary of some of the major error occurrences occurring during viscosity measurements
using glass capillary viscometers, including their possible causes and ways of elimination. Errors which can be
attributed to device defects as well as improper use of the automatic viscosity measurement devices are not
listed in the table below.
Table 5
Frequently occurring errors when using glass capillary viscometers
Error symptom
Error causes
Possible error elimination
systematic measurement error:
flow time too large with
short flow times
after-flow error,
Hagenbach correction
too small
experimental determination of the Hagenbach
correction using substances having a similar
viscosity and a surface tension as the measurement product (please refer to Chapter 4)
systematic measurement error:
flow time too small with
short flow times
after-flow error,
Hagenbach correction
too large
as above, better: Viscometer with
a smaller capillary diameter
(please refer to Chapter 6.1)
systematic measurement error:
substance quantity filled in was empty, clean and refill viscometer
flow time too small with
too small
(please refer to Chapter 6.2 / 6.3)
(Ostwald, CANNON-FENSKE
or BS/IPRF U-Tube Reverse Flow
Viscometer)
systematic measurement error:
substance quantity filled in was as above
flow time too large
too great
(Ostwald, CANNON-FENSKE
or BS/IP/RF-U-Tube Reverse Flow
Viscometer)
systematic measurement error:
flow time too small with
short flow times
(UBBELOHDE Viscometer)
disturbance of the suspended
level
select viscometer with
a smaller capillary diameter,
(please refer to Chapter 6.1 / 7.2)
systematic measurement error:
flow time too small
temperature of the bath liquid
too high
check temperature;
if necessary, readjust thermostat
systematic measurement error:
flow time too large
contamination in the capillaries empty and clean viscometer
(please refer to Chapter 6.2),
repeat measurement
drift of the flow times
temperature of the bath liquid
too low
check temperature,
if necessary, readjust thermostat
drift of the bath temperature
protect the thermostat from direct radiation
exposure (please refer to Chapter 7.2),
if necessary, replace thermostat
temperature-adjustment of the continue temperature adjustment until
measurement substance not
the time values are stable
completed
(please refer to Chapter 6.4)
evaporation of a highly volatile apply pressing operating mode
component; reaction of the
product being analysed with the
air
26
Continuation of table 5
Error symptom
Error causes
Possible error elimination
increased stochastic scattering of
the measurement values
contamination in the
viscometer
empty and clean viscometer (please refer to Chapter 6.2); repeat measurement
contamination in the product
being analysed
empty and clean viscometer; repeat the measurement with a filtered sample; if necessary,
use a filter with a smaller pore width
(please refer to Chapter 6.2/6.3)
air bubbles in the viscometer
in the case calf pure matters with chemical and
physical heat resistance, drive out bubbles by a
shorter time increase of temperature
clean and empty viscometer (please refer to Chapter 6.2); during refilling, ensure absence of bubbles
(please refer to Chapter 6.3)
excessive stochastic scattering oc- contamination of the
curring during automatic measoptical sensors
urements using optoelectric
barriers
(Baron possibility of total
malfunction)
remove the viscometer tripod from the thermostat
bath; clean optical system using non-denatured alcohol on a soft cloth
errors triggered by the optouse a TC-UBBELOHDE, OSTWALD, or CANNONelectric barriers as a result of
FENSKE Routine Viscometer
the formation of bubbles, foam, (please refer to Chapter 6.1)
or liquid lamellae
excessive stochastic scattering oc- Incrustation of the sensors (in
curring during automatic measthe case of thermally instable
urements using TC Viscometers
media)
(possibility of total malfunction)
transparent media:
use optical flow-time measurement
opaque media:
use Reverse Flow Viscometer
wear and tear of the sensors
replace viscometer
increased stochastic scattering in
the case of short flow times
(UBBELOHDE Viscometers)
beginning deformation of the
suspended level
select a viscometer with a smaller
capillary diameter
(please refer to Chapter 6.1/7.2)
periodically fluctuating flow times
heating-up or cooling-down
phases of the thermostats
too long
set the heating and cooling of the thermostat
in such a manner that at least two complete
temperature cycles are completed during one
viscosity measurement cycle
no timely stability of the bathliquid temperature
(defective thermostat)
replace the thermostat
(please refer to Chapter 6.4)
malfunction caused by air bubbles substance quantity filled in was UBBELOHDE Viscometer:
during the sucking-in process of
too small
fill up the measurement substance;
the liquid into the delivery vessel
others: empty and clean viscometer;
repeat measurement
27
8
Special application
8.1 Testing of plastics
Measurement problem
Solution
One of the major quality features of synthetic materials is the mean molecular weight of the polymer
molecules. The molecular weight characterises the
chain length of the polymer molecules which has a
decisive influence on the processing properties of a
synthetic material.
That determination of the chain length, processing
properties, and quality of a synthetic material is done
in the form of viscosity measurements on solutions of
the plastic in suitable solvents using capillary viscometers (solution viscometry). Table 6 will inform
you about the solvents, viscometers, and the application of the relevant standards.
The strain exerted on the plastic by the processing
process may lead to changes in the polymer changes
(as a rule a decay of the chains). Under certain circumstances the properties of the finished part might
be changed to such an extent that it is no longer suitable for its intended purpose.
In the research and development of polymers new
polymers are being developed and produced. In this
process, too, the chain length of the polymer molecules is of essential importance as to the characterisation of the finished product.
This results in the following measurement tasks:
Polymer research and development
Ÿ Determination of the mean chain length of mean
polymerisation degree of the polymer molecules
Ÿ Objectives:
- Characterisation of the finished product
- Optimisation of its chemical and
physical properties
Rating of polymerisation installations
Determination of process parameters
Polymer chemistry (polymer production)
Ÿ Determination of the mean chain length or mean
degree of polymerisation of the finished product
(raw granules)
Ÿ Objectives:
- Characterisation of the finished product
- Quality assurance
- Optimisation of the process parameters
- Prevention of the production of spoiled batches
Polymer processing
Ÿ Characterisation of the properties and the capabilities of the starting material (raw granules)
Ÿ Objectives:
- Rating of plants for polymer processing
- Determination of optimum process parameters
Ÿ Determination of the chemical and physicalproperties of the finished part
Ÿ Objectives:
- Quality assurance
- Optimisation of the process parameters
28
The viscosity number (for a definition, please refer
to Table 7) gives information about the processibility
of plastic material. It plays a decisive role within the
framework of quality control of the granules. In addition, it is important to verify the viscosity number of
the finished plastic part.
In most cases the indication of the viscosity number
or of the relative viscosity (please refer to Table 7)
is sufficient as a quality criterion of established
plants. This requires the determination of the viscosity of the solvent and of the plastic solution (concentration is mostly 0.5 g/100 ml).
Instead of the viscosity number the determination
frequently involves the K value after Fikentscher
/N21/.
The determination of the mean molecular weight of
the polymer molecules is done via the limiting viscosity number (please refer to Table 7). It is of particular importance in the range of research and development of polymers and of procedures and installations for their production and processing. In addition, it is an important feature as regards quality assurance in the case of special applications, such as
plastic recycling and the processing of recycled plastics.
To determine the limiting viscosity number, polymer
solutions of different concentrations are produced
(so-called dilute series /36/). The limiting viscosity
number results from the extrapolation of the viscosity
numbers to a concentration = 0.
Table 6
Choice of applications for solution viscometry
(as a rule, concentrations of 0.5 g/100 ml are weighted in
and the measurements of viscosity are performed at 25 °C).
Polymer
Abbreviation
Solvent
Capillaries
DIN
Polyamide
PA
Formic acid (90%)
Sulphuric acid (96%)
m-cresol
I, Micro Ic
II, Micro IIc
II
53 727
53 727
53 727
Polycarbonat
PC
Dichloromethane
0c
7744, Part 2
Phenol / 1.2- dichlorobenzene
(1:1 parts by weight)
2- chlorophenol
m-cresol
Dichloroacetic acid
Ic
53 728, Part 3
Polyethyleneterephtalate PET
Polybutyleneterephthalate PBT
Ic
II
II, Micro IIc
Polyvinyl chloride
PVC
Cyclohexanone
Tetrahydrofurane
I
Ic
53 726
Polyethylene 1)
Polypropylene 1)
PE
PP
Decahydronaphthalene
(Decalin)
I
53 728,
Sheet 4
Polystyrol 2)
PS
Toluol
o-Xylol
1.2-Dichlorbenzol
I
I
I
7741, Part 2
Polymethycrylate 3)
PMMA
Chloroform
Acetophenone
0c
I
7745, Part 2
Cellulose acetate
CA
Dichloromethane / Methanol
(9:1 party vy volume)
0c
53 728,
Sheet 1
1)
For concentration, please refer to DIN 53 728, Sheet 4
Measurement temperature: 135 °C
3) c = 0,26 g/l
2)
Table 7
Definition of the terms used in dilute viscometry /18, N2/
Calculated value
Description
h
dynamic viscosity
n
= h/r
kinematic viscosity
hr = h / hS
relative viscosity, viscosity ratio
(h - hS) / hS = hr - 1
relative viscosity change, specific viscosity
Jv = 1 / c · (h - hS) / hS
Staudinger function, viscosity number
Ln (h / hS) / c
inherent viscosity
Jg = lim [1 / c × (h - hS) / hS]
Staudinger index, limiting viscosity number, intrinsic viscosity
c®0
29
8.2 Viscosity determination of oils and additives
Measurement problem
Petroleum is a mixture of hydrocarbons. By way of
vacuum distillation it is split up into different fractions
(fuels and lubricants, please refer to Table 8).
Table 8
Typical for fractions of the
distillation of crude oil /19/
Fraction
Boiling range [°C ]
Natural gas
below
20
Distillation of crude oil
30 ... 60
Ligroin or white spirit
60 ... 90
Gasoline
85 ... 200
Kerosene
200 ... 300
Fuel oils
300 ... 400
Lubricating oil and grease,
paraffin, wax, asphalt
above
400
Viscosity is a decisive characteristic for the flowing
and lubricating capabilities of an oil. The mixture of
various raffinates leads to basic oils, with different
viscosities. Their properties can be considerably improved by chemical additions or additives, such as
viscosity-index improvers (VI improvers), detergents,
dispersing agents, wear-and-tear reduction agents,
and oxidation or corrosion inhibitors.
So it is, for instance, that lubricating oils form a lubricating film between the rubbing parts inside the engine
which prevents a direct contact of the solid surfaces,
and thus wear and tear. The thickness of this lubricating film depends on the viscosity of the oil.
The viscosity of a mineral oil changes considerably
with temperature. At low temperatures (for instance,
in winter, during the cold start of the engine) the viscosity of the oil must still be low enough to enable the
oil being pumped to the rubbing parts inside the engine.
30
At high temperatures (for instance, in summer, when
driving at full throttle; under extreme loads, e.g. when
driving up a mountain) oil temperatures can raise up
above 100 °C. In this case, too, a still sufficient formation of lubricating film has to be ensured, so that
the lubricating film will not break as a result of the insufficient viscosity in the places being subjected to
friction.
The life of an engine oil is limited, since in operation
ageing and external matters are building up on the
one hand (e.g. caused by oxidation of the basic oil,
metal abrasion, formation of soot), and the additives
are pooring down on the other (e.g. caused by the
decay of the polymers owing to shearing action, oxidation, and thermal strain) /20, 21, 22/.
The determination of viscosity is playing a major role
in the production and development of doped oils (basic oil / additive mixtures). In the course of production, regular viscosity measurement ensures adequate quality control. As regards development on the
other side, the focus is on the examination of the viscosity-temperature behaviour of new oil/additive mixtures.
In the case of used engine oils the determination of
viscosity can be used to determine whether the formation of the lubricating film will still be sufficient
even at higher temperatures.
Solution
One of the frequently used characteristics of viscosity-temperature behaviour (VT behaviour) of a lubricating oil is the VI viscosity index. The VI of an oil
can be calculated on the basis of the viscosities at
40°C and 100°C by using tables /N11/. The magnitude of the viscosity drop occurring with increasing
temperature depends on the chemical composition of
the oil under concern. A minor temperaturedependence of the viscosity will lead to a higher viscosity index. Multigrade, engine, and gear oils are
characterised by a high VI /23/.
The classification of an engine lubricating oil in socalled SAE viscosity classes is based on dynamic
viscosity at -17.8 °C (0 °F) and kinematic viscosity at
98.9 °C (210 °F) /N12, N13/.
Table 9 contains a list of examples of viscometers and accessories from SCHOTT-GERÄTE.
Table 9 Measurement stations for viscosity measurements on oil and additives
automatic measurement
Viscometer
Ÿ UBBELOHDE
Ÿ CANNON-FENSKE Routine
Ÿ TC Viscometer (for dark oils)
Viscosity
Ÿ AVS 350, AVS 360, AVS 450
measurement Ÿ AVSPro
device
(up to n » 1200 mm2/at room
temperature)
Accessories
Ÿ Thermostat and cooler
Ÿ Viscometer Cleaner AVS 26 (optional)
manual measurement
Ÿ UBBELOHDE
Ÿ CANNON-FENSKE Routine
Ÿ CANNON-FENSKE Reverse Flow Viscometer
(for dark oils)
Ÿ BS/IP/RF U-Tube Reverse Flow Viscometer
(for viscid and / or dark oils)
Ÿ Stop watch
Ÿ Thermostat and cooler
8.3 Testing of food
Measurement problem
The raw materials, semi-finishings, and finished
products to be processed in food industry are characterised by very much different rheologic properties.
Provenience, temperature, water percentage, intensity of the mechanical processing, storage time, and
conditions of transportation are some of the factors
influencing the mainly non-Newtonian flowing behaviour of food masses.
But a number of fluids involved in food production
also presents Newtonian behaviour.
In food technology and machine engineering, knowledge of viscosity is of importance in multiple ways,
e.g. for:
Ÿ controlling technological processes
Ÿ evaluating the products’ quality
Ÿ designing food dispensers and
conveying apparatus
Ÿ selecting and operating packaging installations.
Objectives of viscosity measurement:
Ÿ optimisation of the mashing properties
Ÿ selection of filtration strategy
Ÿ quality evaluation of malt,
wort, and beer
b) Determination of viscosity of
fruit and vegetables juices
Raw-pressed juices with a high viscosity are hard to
clarify. Viscosity is mainly affected by the pectin percentage which, in the case of concentrated fruit
juices, may rise so high in the course of production
that there is a danger of jellying of the contents of the
tanks. Owing to the food-physiological importance, a
complete decay of the pectin is not desired.
By way of an aimed pectinological decaying process
in the course of the technological section of the fining
and clarification process of the juices one tries to adjust an optimum pectin percentage /27/.
Within the framework of food-technological research
and development the measured viscosities can be
used to draw valuable information about
Ÿ molecular structure
Ÿ chemical composition
Ÿ efficiency of enzymes
Ÿ percentage of viscosity-influencing
constituents and additives
Objectives of viscosity measurement:
Ÿ gathering of control parameters for the
pectinological process of optimising of
optimising clarification and fining
Ÿ quality surveillance
Ÿ characterisation of the jellying capabilities
of pectins, inter alia by the determination of the
limiting viscosity number /28/.
Examples of measurement tasks in
food industry
c) Viscosity determination in sugar industry
a) Determination of viscosity of
beer wort and beer /26/
Beers with a viscosity > 1.7 mPas are hard to filter,
and this leads to a reduction of the production output.
On the other hand a high viscosity has a positive effect on the full-bodiedness and the stability of the
foam.
In the extraction and technical processing of sacchararose solutions, information about viscosity is essential /29/. It increases in the form of an exponential
curve with rising concentration and has thus a substantial influence on the crystallisation readiness of
sugar solutions.
31
So it is that the crystallisation of sacchararose solutions is favoured with increasing concentration (state
of over-saturation), but will decrease with the rise in
the percentage of more than saccharide. Viscosity
increases with the rise in the molecular mass of the
solution components (mono- and disaccharides, glucose syrup /30/) and can be calculated as follows as
regards saccharide solutions:
h = wA log hA + wB log hB
(8.1)
w - Mass portions in the total mixture
A, B - Components
Glucose syrups are characterised by different saccharide fractions with one and the same saccharification degree, a fact which results in diverging viscous
behaviour patterns. Considering that they are used
as crystallisation inhibitors in the production of confectionery, viscosity is a major technological parameter.
Objectives of viscosity measurement:
Ÿ gathering of control parameters for
processing sugar solutions
Ÿ quality surveillance
Ÿ development of recipes
Ÿ provision of information for the rating of
appliances and apparatus for sugar industry
d) Viscosity determination in milk industry
Owing to the differences in the provenience and
composition of milk and dairy products, the rheologic
behaviour of dairy products differs greatly /31/.
The viscosity of milk, cream, condensed milk etc. is
influenced by the fat contents, the concentration of
the dry matters, and, to a high degree, by the processing conditions, e.g. by homogenisation.
32
On the other side it was possible to show that the
homogenisation effects can be improved through viscosity control.
An addition of hydrocolloids (thickening, binding, and
jellying agents) and stabilisers has a highly viscosityraising effect. Viscosity measurement provides valuable information required to reveal their chemical
structure and their effect in combination with components of the milk.
Objectives of viscosity measurement:
Ÿ Technology surveillance
Ÿ Quality evaluation
Ÿ Development of recipes
Solution
After examining the question of knowing whether the
food liquid to be analysed can be reasonably treated
as a Newtonian fluid, all types of capillary viscometers can be used in principle.
There may be some difficulties in the detection of the
liquid meniscus.
Owing to their low degree of transparency and the after-flow effects, an optical detection of dairy products
is problematic.
The use of TC Viscometers requires frequent, thorough cleaning, since the thermistors tend to soil as a
result of incrustation.
There are less problems in the viscosity measurement on beer, fruit juices and the like. Owing to the
fact that these fluids have a tendency of foam formation, OSTWALD Viscometers and even Micro
OSTWALD Viscometers have proven their suitability
for use. According to /26/ the standard deviation with
viscosity measurements performed on wort using
OSTWALD Viscometers was 0.004 mPas compared
to 0.02 in the case of measurements made using the
HÖPPLER Viscometer. Similarly good experience
was gathered on viscometer measurements made on
fruit juices.
9
Formula signs and units used
A
Surface being parallel with flow direction
m2
B
Constant of Hagenbach correction with
sharp-edged capillary ends
mm2 s
c
Concentration
g/cm3
D
Shear rate
1/s
E
Constant of Hagenbach correction with
funnel-shaped capillary ends
mm2 s
F
Force acting in flow direction
N
g
Acceleration of the fall at the place of the measurement
m/s2
g0
Acceleration of the fall at the place of determination of the constant
m/s2
hm
Mean hydrostatic pressure height
cm
Dh
Capillary rising height of the liquid
cm
Jg
Limiting viscosity number according to STAUDINGER
cm3/g
Jv
Viscosity number according to STAUDINGER
cm3/g
K
Viscometer device constant
mm2/s2
KP
Viscometer device constant (device being tested)
mm2/s2
KR
Viscometer device constant (reference viscometer)
mm2/s2
K´
Corrected viscometer device constant
mm2/s2
L
Length of the capillaries
cm
le
Inflow length
cm
m
Coefficient of Hagenbach correction
-
n
Coefficient of Couette correction
-
Dp
Acting pressure
mbar
DpC
Pressure loss resulting from Couette correction
mbar
R
Radius of the capillaries
cm
Re
Reynolds number
-
r1
Radius of the upper reservoir vessel on the liquid meniscus
cm
r2
Radius of the lower reservoir vessel on the liquid meniscus
cm
s
Temperature error
K
t
Flow time
s
tg
Measured flow time
s
tgP
Measured flow time (device being tested)
s
33
tgR
Measured flow time (reference viscometer)
s
tH
Hagenbach-Couette correction
s
tHP
Hagenbach-Couette correction (device being tested)
s
tHR
Hagenbach-Couette correction (reference viscometer)
s
ts
Shear time
s
T
Measurement temperature
K
T0
Calibration temperature
K
U
Voltage
V
Un
Temperature coefficient of kinematic viscosity
1/K
V
Flow through volume
cm3
V
Flow volume
cm3/s
DV
Liquid volume adhering to the inner wall surfaces of the viscometer
cm3
v
Mean flow velocity
m/s
x
Co-ordinate in flow direction
m
y
Co-ordinate perpendicular to flow direction
m
a
Longitudinal expansion coefficient of the glass grade
used for the production of glass capillary viscometers
1/K
e
Relative error of the measurement value
%
h
Dynamic viscosity
mPa s
hr
Relative viscosity
-
hS
Dynamic viscosity of the solvent
mPa s
n
Kinematic viscosity
mm2/s
r
Density of the liquid to be measured
g/cm3
r0
Density of the normal liquid
g/cm3
s
Surface tension of the liquid to be measured
mN/m
s0
Surface tension of the normal liquid
mN/m
J
Temperature
°C
t
Shearing strain
Pa
f
Angle between the perpendicular and the connection line
of the upper and lower central point of the reference level vessel
during measurement
o
f0
Angle between the perpendicular and the connection line
of the upper and lower central point of the reference level vessel
during calibration
o
34
10 Bibliography
/1/
Hagen, G.
Poggendorffs Annalen der Physik 46 (1839), 423
/2/
Poiseuille, J. L.
Comptes rendus 11 (1840), 961; Mémoires des Savants Etrangers 9 (1846), 433
/3/
Prandtl, L.
Strömungslehre
Friedrich Vieweg u. Sohn, Braunschweig 1960
/4/
Eck, B.
Technische Strömungslehre
B.I; 75; Springer-Verlag, Berlin 1978
/5/
Hagenbach, E.
Poggendorffs Annalen der Physik 109 (1860), 385
/6/
Couette, M.
Annales de Chimie et Physique 21 (1890), 433
/7/
Hengstenberg, J.; Sturm, B.; Winkler, O.
Messen, Steuern und Regeln in der chemischen Technik
B. II, 432 - 499; Springer-Verlag, Berlin 1980
/8/
Kestin, J.; Sokolov, M.; Wakeham, W.
Applied scientific research 27 (1973), 241
/9/
Boussinesq, V. S.
Comptes rendus 110 (1890), 1160, 1238
/10/
Schiller, L.
Forschung auf dem Gebiete des Ingenieurwesens (1922), H. 248
/11/
Riemann, W.
Journal of the American Chemical Society 50 (1928), 46
/12/
Weber, W.; Fritz, W.
Rheologica Acta 3 (1963), 34
/13/
Dorsay, N. E.
The physical review 28 (1926), 833
/14/
Cannon, M. R.; Manning, R. E.; Bell, J. D.
Analytical Chemistry 32 (1960), 355
/15/
Kryk, H.; Wilke, J.
Möglichkeiten zur Meßbereichserweiterung von Mikro-UBBELOHDE-Viskosimetern
Vortrag anläßlich der Jahrestagung der Deutschen Rheologischen Gesellschaft,
Karlsruhe 1993
/16/
Gebrauchsanleitung
UBBELOHDE-Viskosimeter mit hängendem Kugelniveau
SCHOTT-GERÄTE GmbH, Hofheim am Taunus
/17/
Doerffel, K.
Statistik in der analytischen Chemie
Deutscher Verlag für Grundstoffindustrie, Leipzig 1982
/18/
Brown, R. P.
Taschenbuch der Kunststofftechnik
Carl Hanser Verlag, München 1984
35
/19/
Streitwieser, A.; Heathcock, C. H.
Organische Chemie
Verlag Chemie, Weinheim 1980
/20/
Jentsch, C.
Chemie in unserer Zeit 12 (1978), 57
/21/
Klein, J.; Müller, H. G.
Erdöl und Kohle, Erdgas, Petrochemie 32 (1979), 394
/22/
Klein, J.; Müller, H. G.
Erdöl und Kohle, Erdgas, Petrochemie 35 (1982), 187
/23/
Stepina, V.; Vesely; V.; Trebicky, Vl.
Tribologie und Schmierungstechnik 34 (1987), 113
/24/
Werner, S.
Zur Temperaturabhängigkeit der Viskosität niedrigviskoser Newtonscher Fluide
Diplomarbeit; TH Köthen 1993
/25/
Wilke, J.; Kryk, H.
Temperaturkonstanz und Temperaturverteilung in Flüssigkeitsthermostaten
VDI/VDE-GMA-Tagung TEMPERATUR ´92
VDI Berichte 982 (1992), 265 - 268
/26/
Greif, P.
Monatsschrift für Brauerei 32 (1979), 356
/27/
Köller, M.; Grandke, I.
Lebensmittelindustrie 24 (1977), 162
/28/
Kunzele, H.; Kleiber, U.; Bergemann, U.
Lebensmittelindustrie 36 (1989), 78
/29/
Hoffmann, H.; Mauch, W.; Untze, W.
Zucker und Zuckerwaren
Verlag Paul Parey, Berlin 1985
/30/
Schiweck, H.; Kolber, A.
Gordian 72 (1972), 41
/31/
Kessler, H. G.
Lebensmittel- und Bioverfahrenstechnik/ Molkereitechnologie
Verlag A. Kessler, Freising 1988
/32/
UBBELOHDE, L.
Zur Viskosimetrie
S. Hirzel Verlag, Stuttgart 1965
/33/
UBBELOHDE, L.
Öl und Kohle vereinigt mit Erdöl und Teer 12 (1936), 949
/34/
Kryk, H; Wilke J.
GIT Fachzeitschrift für das Labor 5 (1994), 463
/35/
Kryk, H; Wilke J.
Erdöl und Kohle, Erdgas, Petrochemie 47 (1994), 467
/36/
Schurz, J.
Viskositätsmessungen an Hochpolymeren
Verlag Berliner Union GmbH, Stuttgart 1972
36
11 Standards used in capillary viscometry
1.
National Standards
Basics
/N1/
DIN 1342 Teil 1
Rheologische Begriffe
/N2/
DIN 1342 Teil 2
Newtonsche Flüssigkeiten
/N3/
DIN 51 550
Bestimmung der Viskosität
Allgemeine Grundlagen
/N4/
DIN 53 017
Bestimmung des Temperaturkoeffizienten der Viskosität
Measuring techniques
/N5/
DIN 51 366
Messung der kinematischen Viskosität mit dem CANNON-FENSKE-Viskosimeter
für undurchsichtige Flüssigkeiten
/N6/
DIN 51 562 - 1
Messung der kinematischen Viskosität mit dem UBBELOHDE-Viskosimeter
Normal-Ausführung
/N7/
DIN 51 562 - 2
Messung der kinematischen Viskosität mit dem UBBELOHDE-Viskosimeter
Mikro-UBBELOHDE-Viskosimeter
/N8/
DIN 51 562 - 3
Messung der kinematischen Viskosität mit dem UBBELOHDE-Viskosimeter
Relative Viskositätsänderungen bei kurzen Durchflußzeiten
/N9/
DIN 51 562 - 4
Messung der kinematischen Viskosität mit dem UBBELOHDE-Viskosimeter
Teil 4: Viskosimeter-Kalibrierung und Ermittlung der Meßunsicherheit
/N10/
DIN 53 012
Kapillarviskosimetrie Newtonscher Flüssigkeiten, Fehlerquellen und Korrektionen
Test of mineral oils and related products
/N11/
DIN / ISO 2909
Berechnung des Viskositätsindex aus der kinematischen Viskosität
/N12/
DIN 51 511
SAE-Viskositätsklassen für Motoren-Schmieröle
/N13/
DIN 51 512
SAE-Viskositätsklassen für Kraftfahrzeug-Getriebeöle
/N14/
DIN 51 519
ISO-Viskositätsklassifikation für flüssige Industrie-Schmierstoffe
/N15/
DIN 51 563
Bestimmung des Viskositäts-Temperatur-Verhaltens
Richtungskonstante m
/N16/
DIN 51 564
Berechnung des Viskositätsindex aus der kinematischen Viskosität
37
Test of polymers
/N17/
DIN/ISO 1628 Teil 1
Richtlinien für die Normung von Verfahren zur Bestimmung der Viskositätszahl
und der Grenzviskositätszahl in verdünnter Lösung
Teil 1: Allgemeine Grundlagen
/N18/
DIN 7741 Teil 2
Polystyrol (PS)-Formmassen
Herstellung von Probekörpern und Bestimmung von Eigenschaften
/N19/
DIN 7744 Teil 2
Polycarbonat (PC)-Formmassen
Bestimmung von Eigenschaften
/N20/
DIN 7745 Teil 2
Polymethylmethacrylat (PMMA)-Formmassen
Herstellung von Probekörpern und Bestimmung von Eigenschaften
/N21/
DIN 53726
Bestimmung der Viskositätszahl und des K-Wertes von Vinylchlorid (VC)-Polymerisaten
/N22/
DIN 53 727
Bestimmung der Viskositätszahl von Thermoplasten in verdünnter Lösung
Polyamide (PA)
/N23/
DIN 53 728 Blatt 1
Bestimmung der Viskosität von Lösungen
Celluloseacetat in verdünnter Lösung
/N24/
DIN 53 728 Blatt 2
Bestimmung der Viskosität von Lösungen
Polyamid (PA) in konzentrierter Lösung
/N25/
DIN 53 728 Blatt 3
Bestimmung der Viskositätszahl von Polyethylenterephthalat (PETP) oder Polybutylenterephthalat (PBTP) in verdünnter Lösung
/N26/
DIN 53 728 Blatt 4
Bestimmung der Viskosität von Polyethylen (PE) und Polypropylen (PP) in verdünnter Lösung
/N27/
DIN 54 270
Bestimmung der Grenzviskosität von Cellulosen
2.
International Organization for Standardization (ISO)
Viscometers
/N28/
ISO 3105
Glass capillary kinematic viscometers
Specification and operating Instructions
Petroleum Products
/N29/
ISO 3104
Transparent and opaque liquids
Determination of kinematic viscosity and calculation of dynamic viscosity
/N30/
ISO 3448
Industrial Liquid Lubricants
ISO Viscosity Classification
38
Plastics
/N31/
ISO/R 175
Determination of Viscosity Number of Polyvinylchloride Resin in Solution
/N32/
ISO/R 307
Polyamides
Determination of Viscosity Numbers
/N33/
ISO/R 600
Determination of Viscosity Ratio of Polyamides in concentrated Solution
/N34/
ISO/R 1157
Cellulose Acetate in dilute Solution
Determination of Viscosity Number and Viscosity Ratio
/N35/
ISO/R 1191
Determination of Viscosity Number and Limiting Viscosity Number of Polyethylenes
and Polypropylenes in dilute Solution
/N36/
ISO/DIS 1228
Determination of Viscosity Number of Alkylene Terephthalate Polymers and Copolymers
in dilute Solution
/N37/
ISO/R 1336
Determination of Viscosity Number of Methylmethacrylate Polymers and Copolymers
in Solution
/N38/
ISO/R 1599
Determination of Viscosity Loss on Moulding of Cellulose Acetate
/N39/
ISO 1628 / 1
Guidelines for the Standardization of Methods for the Determination of Viscosity Number
and Limiting Viscosity Number of Polymers in Dilute Solution - General Conditions
/N40/
ISO 1628 / 2
Plastics - Determination of Viscosity Number and Limiting Viscosity Number
Part 2: Poly (Vinyl Chloride) Resins
/N41/
ISO 1628 / 3
Plastics - Determination of Viscosity Number and Limiting Viscosity Number
Part 3: Polyethylenes and Poly Propylenes
/N42/
ISO 1628 / 4
Plastics - Determination of Viscosity Number and Limiting Viscosity Number
Part 4: Polycarbonate (PC) Moulding and Extrusion Material
/N43/
ISO 1628 / 5
Determination of Viscosity of Polymers in Dilute Solution using Capillary Viscometers
Part 5: Thermoplastic Polyester (TP) Homopolymers and Copolymers
/N44/
ISO 1628 / 6
Determination of Viscosity Number and Limiting Viscosity Number
Part 6: Methyl methacrylate polymers
39
3.
American National Standard (ASTM)
Basics
/N45/
D 445 - 88
Standard Test Method for Kinematic Viscosity of Transparent and Opaque Liquids
(and the Calculation of Dynamic Viscosity)
Viscometers
/N46/
D 446 - 89 a
Standard Specifications and Operating Instructions for Glass Capillary Viscometers
/N47/
D 2515 - 86
Standard Specifications and Operating Instructions for Glass Capillary Kinematic Viscometers
Plastics
/N48/
D 789
Standard Test Methods for Determination of Relative Viscosity, Melting Point, and Moisture
Content of Polyamide (PA)
/N49/
D 1243
Standard Test Method for Dilute Solution Viscosity of Vinyl Chloride Polymers
/N50/
D 1601
Standard Test Method for Dilute Solution Viscosity of Ethylene Polymers
/N51/
D 2393
Standard Test Method for Viscosity of Epoxy Resins and Related Components
/N52/
D 4603
Standard Test Method for determining inherent Viscosity of Poly (ethylene terephthalate)
(PET)
/N53/
D 4878
Standard Test Method for Polyurethane Raw Materials:
Determination of Viscosity of Polyols
4.
/N54/
5.
/N55/
6.
British Standard (BS)
BS 188
Methods for Determination of the Viscosity of Liquids
Norme Française Enregistrée
NF T 60 - 100
Mesure de la viscosité cinématique
Normen zu Flüssigkeits-Thermostaten
/N56/
DIN 58 966, Teil 1, Thermostate, Allgemeine Begriffe
/N57/
DIN 58 966, Teil 2, Thermostate, Flüssigkeitsthermostate, Begriffe und Bestimmung
der Kenndaten
These standards are valid as they are at the time of printing; newer standards are in process.
40
55034 e 12990.2 Printed in Germany
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