Theory and Praxis of Capillary Viscometry - An Introduction –
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.
1
Table of contents Page
1 Viscosity – Rheology ................................................... 2
2 Basics of capillary viscometry ................................. 5
2.1 Measurement principle ................................................. 5 2.2 Designs of glass capillary viscometers ......................... 5
3 Measurement of flow time .......................................... 7
3.1 Manual time measurement ........................................... 7 3.2 Automatic time measurement ....................................... 7 3.2.1 Tasks and particularities ............................................... 7 3.2.2 Detection of the meniscus passage ............................. 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 General guidelines for the selection of the measurement system ........................ 15 6.2 Cleaning of capillary viscometers ............................... 16 6.3 Preparation of the measurement ................................ 17 6.4 Performing the measurement ..................................... 19
7 Causes of errors and special corrections ......... 23
7.1 Correctable errors and corrections ............................. 23 7.2 Uncorrectable errors .................................................. 24 7.3 Frequently occurring error symptoms, possible causes of errors, and ways of elimination ..................................................... 26
8 Special applications .................................................... 28
8.1 Testing of plastics ....................................................... 28 8.2 Determination of the viscosity of oils and additives .... 30 8.3 Testing of food ........................................................... 31
9 Formula signs and units used ................................ 33
10 Bibliography ................................................................... 35
11 Standards used in capillary viscometry ............. 37
2
1 Viscosity - Rheology Viscosity characterises the flow properties, the inher-ent friction of liquids and gases.
If a fluid is trapped between two plane-parallel plates, it will require some amount of force to displace the upper plate.
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 recip-rocal dislocation of the individual layers.
F
v
y
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 � (also referred to as �1,2) refers the quotient of force F and the boundary surface A of the liquid:
� = FA
(1.1)
The speed drop, i.e. the shear rate D, is the differ-ential quotient:
D =dvdy
(1.2)
According to Newton's Viscosity Law there is pro-portionality between the shear strain � and the shear rate D.
� = � • D (1.3)
The proportionality factor � is referred to as dynamic viscosity coefficient or, in short, as dynamic vis-cosity.
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
= [Ns / m 2] = [Pa • s] (1.4)
The relationship between dynamic viscosity ���� and density ���� is referred to as kinematic viscosity ����:
��
� = = [m 2 / ]s (1.5)
For reasons of convenience, the unit of mm2/s is used which then numerically corresponds to the for-mer cSt (Centistoke) unit.
In case of Newtonian liquids � 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 rela-tionship if Maxwellian Boltzmann velocity distribution is being applied:
� = k e E
RTvisk
� (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, � may change within very wide limits in the case of pure liq-uids.
Examples: n-pentane 0.230 mPa • s (20 °C) Water 1.002 mPa • s (20 °C) Propane triol 1480 mPa • s (20 °C) (Glycerine)
In the case of liquids, and in contrast to gases, � 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 inter-molecular interactions are decreasing with the mag-nifying 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.
3
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 aggre-gates are being formed the reciprocal friction of which is lower.
In the case of liquid miscible phases � is in general not made up by the addition of �-values of the pure components.
The viscosity of the miscible phase may be greater or smaller than � of the isolated components, or may be in between.
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 con-centration-dependability of viscosity of electrolyte so-lutions.
If the liquid layers are moving at different velocities, the deformation of the ion cloud will cause the occur-rence of additional inter-ionic interacting forces which will affect friction between the individual layers.
H. Falkenhagen used the theory of inter-ionic interac-tions, applicable to highly diluted electrolyte, solutions to derive the Limit Law of Viscosity: � �
C = + K c0 (1.7)
�c Viscosity at ion concentration c
�0 Viscosity of the pure solvent
at same temperature
K Constant depending on
the following influencing variables:
- Temperature
- Relative permittivity
- Ionic valence
- Ionic mobility
Non-Newtonian flow behaviour
Disperse systems, concentrated polymer solutions, and melts of macro molecules show a marked non-Newtonian behaviour with increasing shear rates. In their case there is a non-linear dependency be-tween shear strain and shear rate.
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
a
c
Figure 2 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: � = f (D) is linear above the yielding point.
CASSON substances: � = f (D) is non-linear above the yielding point.
Pseudo-plasticity (intrinsic viscosity) These substances are characterised by Newtonian behaviour at low shear rates.
At high shear rates � will increase with the shear rate (please refer to Figure 2, curve c).
Examples: - Lacquer/varnish - Thermoplastics - Lubricating oils (multigrade oils) - Glues - Additives
4
In addition to these effects a shear-time dependent flow behaviour can be observed with some non-Newtonian matters:
� = f (D, t) � = f (D, t)
This means that shear viscosity is influenced by the duration of the shearing action (please refer to Figure 3).
b
a
c
ts
�
Figure 3 Dependency of shear viscosity on the shear time a = shear-time independent flow behaviour b = Rheopexy c = Thixotropy
The following distinction is made:
Thixotropy
Shear viscosity decreases at constant shear rate with increasing shear time (typical for sol/gel transforma-tion).
Rheopexy
Shear viscosity increases at constant shear rate with increasing shear time.
Rheopexy can, for instance, be seen with PVC plas-tisols. They are used for corrosion protection on met-als. If the coating rate is increased the material be-comes more thick-flowing. Rheopex liquids are char-acterised by a gradual structure formation under shearing strain.
In addition to these viscous properties one can ob-serve 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. Poly-mer solutions, and recently also biopolymers exhibit-ing molecular-structure dependent viscoelastic prop-erties of this kind meet with more and more techno-logical interest, e.g. in the production of paints and coatings, food, cosmetics, and pharmaceutics.
The complex nature of this field of work has lead to the crystallisation of an original term, i.e. rheology (science of flow behaviour).
Rheometry deals with the specific methods and pro-cedures of determining rheological characteristics. Within this nomenclature viscometry is a partial dis-cipline of rheometry.
Principles of viscosity measurement
Rheological measurement procedures are mainly based on mechanical methods, since tension and elongation are mechanical values which are deter-mined 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.
Figure 4 shows the major manners of realising the deformation of the sample.
v
1
2
v
2
M1
5
6
M2
4
3
2
a b c
Figure 4 Measurement principles of viscometers a = Capillary viscometer b = Rotational viscometer c = Falling-ball viscometer
1 = Capillary 5 = Measurement ball 2 = Sample 6 = Glass cylinder 3 = Coaxial cylinder M1, M2 = Measurement marks 4 = Torque sensor
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 measure-ments with Newtonian liquids with a kinematic viscos-ity of more than 0.3 mm2/s.
Perfection in the manufacture and the sophisticated quality-assurance methods form the basis of stan-dardised measurement systems which are meeting today highest accuracy requirements as to reproduc-tion incertainties and absolute measurement incer-tainty.
5
2 Basics of capillary viscometry 2.1 Measurement principle
Inside the capillary viscometers, the velocity drop re-quired for viscosity measurement is built up in the form of a laminar tube flow within a measurement capillary.
Under idealised conditions
� laminar, isothermal flow � stationary flow condition � Newtonian flow behaviour of the liquid � pressure-independence of viscosity � incompressibility of the liquid � wall adherence of the liquid � neglect of the flow influences at the entry and exit of capillary of sufficient length
the liquid flows in coaxial layers towards the pressure drop through the capillary. A parabolic velocity flow occurs (please refer to Figure 5).
vvmax
v = 0
R r
Figure 5 Velocity profile with laminar tube flow
The Hagen-Poiseuille Law is the physical basis of viscometers working according to the capillary princi-ple /1, 2, 3, 4/:
Vt
= R8L
4�
�
�p (2.1)
With regard to viscosity measurement, this results in two different fundamental measurement principles:
� Measurement of the differential pressure at a con-stant volume flow of the sample through the cap-illary
� Measurement of the volume flow through the cap-illary at a given differential pressure.
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 vol-ume flow.
This issue is approached in a satisfactory manner the design of device in the form of comparison meas-urement methods.
An application of this can be found in solution vis-cometry 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 Wheat-stone bridge”.
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).
2.2 Designs of capillary viscometers
In the case of low-pressure capillary viscometers the imaging signal used for viscosity is the time re-quired by a defined liquid volume to flow through a measurement capillary.
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 en-ables the passage time of a product volume re-stricted in such a manner to be measured with measurement incertainties < 1/10 s.
__________________________________________
1) National Bureau of Standards, USA, 1953 6
Figure 6 shows the two fundamentally different vis- cometer types after OSTWALD and UBBELOHDE.
a)
10
L
6
7
b)
hm
4
7
L
8M1
M2
2 3
Figure 6 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 con-tainer (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 con-tainer (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).
After venting tube (1), the liquid column in the level-ling bulb breaks off. At the exit of the capillary the so-called suspended level develops (also refer to Fig-ure 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 cap-illary will flow off along the inner wall of the levelling bulb (6) in the form of a film.
In this way the hydrostatic pressure of the liquid col-umn is independent of the sample quantity being filled in.
In addition, owing to the geometrical shaping of the levelling bulb (6), the influence of surface tension on the measurement result is almost eliminated.
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 measure-ment 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 menis-cus passage through the measurement marks is im-possible owing to the wetting of the tube. For manual operation, the Reverse-Flow Viscometer (please re-fer to Figure 7) is used in such cases.
hm 2
h m 1
3 = M1
5 = M2
7 = M3L
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 re-verse-flow (1).
The standard viscometer introduced was the CANNON-Master instrument with a capillary di-ameter of 0.45 mm and a capillary length of 400 mm.
With the determination of the viscosity of water � = 1.0019 [cP] ± 0.0003 [cP] 1) (20 °C), it was possible to define a viscosity scale.
The capillaries of viscometers used for industrial ap-plications are usually shorter (70 - 250 mm).
__________________________________________
1) National Bureau of Standards, USA, 1953 7
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 meas-urement marks burnt in above and below the meas-urement sphere (please refer to Figures 6, 7).
The disadvantages of this method are obvious:
� 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.
� 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 pas-sage of the air/sample or sample/air boundary layer, respectively, through the measurement marks. This electrical signal is required as
� a start and stop signal for the timing process and as
� 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 incertain-ties are determined by the fluid-dynamic circum-stances 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 calibra-tion temperature).
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 deci-sive advantage over other viscosity measurement procedures.
The well-adapted selection of materials, the engi-neering-technological mastery of the production processes, and the sophisticated methods of quality assurance enable a calibration of the viscometers to be made.
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 pas-sage 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 ra-diation intensity of the light arriving from the transmit-ter 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 meas-urement. 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, espe-
cially those which adhere strongly to the wall, cannot me measured.
On the viscometers from SCHOTT-GERÄTE all opti-cal 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 ar-rangement of the optical sensors within the meas-urement tripod on the viscometer.
The light is guided out of the tripod head through fi-bre optics into the tripod legs up to the upper and lower measurement plane. The watertight sealing enables the measurement tripods to be placed in liq-uid thermostats.
Owing to high precision in the glass-technological and mechanical production as well as through meas-ures of quality assurance it is ensured that the glass bodies and tripods are freely interchangeable, with the certified viscometer constants remaining valid.
21
Figure 8 Arrangement of the optical sensors on the viscometer 1 = Optical fibre input 2 = Optical fibre output
8
Conductivity sensors
Electrolytically conductive measurement liquids (solu-tions 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 electrocon-ductive; the supply lines to the sen-sors are to be protected against wa-ter 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 inde-pendent 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 SCHOTT-GERÄTE. In the tube axis the thermistors with a di-ameter of < 1 mm in the sealed-in head portion are clearly visible.
lower NTC sensor
upper NTC sensor
Figure 9 TC Viscometer from SCHOTT-GERÄTE
The essential factor for safe operation is a good dy-namic behaviour. Figure 10 shows the signal course resulting developing during filling and run-off (meas-urement process) through the changing thermal con-ductivity in the surrounding of the sensor.
To compensate the influence of the sample on dy-namics, the SCHOTT-GERÄTE viscosity measure-ment 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 deter-mined dynamic ID value.
b
a
t [ s ]
U [ V ]1 4
1 2
4
6
8
1 0
20 1 2 3 4
s
Figure 10 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 re-flected 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 re-ceiving modulators located at opposite tube posi-tions.
Advantage: The signal formation is independent of other sample properties, i.e. the application of the process is versa-tile; no sealing in the glass required
Disadvantage: Coupling of the sound heads bears production-technological difficulties, especially in the case of an applica-tion 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 re-quires extensive insulation.
9
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 determina-tion 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 �:
��
�
� =
=
R g h
8 L V t
4m (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 viscome-ter constant K:
� = K • t (4.2)
In order to take into account the tolerances which are inevitable in the manufacture of the devices, K is de-termined for each individual viscometer by way of a calibration (please refer to Chapter 5).
According to equation (4.2) there is a linear correla-tion between kinematic viscosity and flow time. Fig-ure 11 shows this correlation in the form of a charac-teristic (curve a).
ba
ttgt
�
�
Figure 11 a ideal and b real viscometer characteristic
When applying the flow model in the form of the Hagen-Poiseuille Law, additional pressure losses oc-curring 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.
The basic hydrodynamic process was first examined by Hagenbach /5/ and Couette /6/.
The difference between the measured and theoreti-cal flow time tH is therefore referred to as Hagen-bach-Couette Correction Time (or, in short, HC correction or Hagenbach correction):
tH = tg - t (4.3)
This results in the following corrected working equa-tion for glass capillary viscometers:
� = 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 measurement there are in prin-ciple three ways to take into account the Hagenbach-Couette Correction and thus to deter-mine the kinematic viscosity of the product being analysed.
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 ana-lysed, involves long flow times. In this case HC cor-rection 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 ne-glected in order not to exceed a relative error e can be calculated according to equation (4.5) or equation (4.6), respectively:
tg � 19.95 m V L K�
���
���
1
2 (4.5)
tg � 4.9 VK
���
���
1
2 (� L)
- 1
2-
1
3 R (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/.
10
4.1.2. Calculation of HC correction resp. use of given table values
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 de-scriptions.
Understanding the calculation algorithm requires first an explanation of the theoretical basics of Hagen-bach-Couette Correction.
Figure 12 shows the true march of pressure in the capillary /7/.
The deviations from the ideal march result from hy-drodynamic 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 addi-tional terms.
Lle
l
�p
Figure 12 Axial march of pressure in the capillary
Figure 13 Flow model with correction terms
The mean flow rate v in the capillary results from:
v = �V
R2 � (4.8)
In this way the following corrected Hagen-Poiseuille Law for the determination of viscosity results from equation (4.7), Figure 13:
�� �
�
� =
p R
V L -
V
8 L -
p R
V L
4c
4� �
8 8�
�
� (4.9)
Couette did already take into account the pressure loss �pc by way of adding a fictitious length n � R to the capillary length L in equation (4.10).
This correlation was confirmed by Kerstin, Solokov, and Wakeham /8/ by a numerical solution of the Na-vier Stokes' equations.
�� �
� =
p R
V (L + n R) -
m V
8 (L + n R)
4�
8 �
�
(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. Cou-ette 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/.
Hagen-Poiseuille Law
� p = 8 V L
R4
�
�
�
� ��
2
2
V�
�
2� pC (4.7) +
Pressure loss owing to the formation of the para-bolic velocity profile in the flow path Ie
Hagenbach-Couette Correction
�
Viscous portion Pressure loss owing to the increase in the kinematicenergy of the liquid when flowing into the capillary
Pressure loss owingto the increased wall friction inside the flow-in path Ie
+ +
11
For a given glass capillary viscometer
� p = g hm� (4.11)
and
�V = Vtg
, (4.12)
with equation (4.13) being derived as working equa-tion.
��
� =
R g h
V L t -
m V8 L t
4m
gg8
(4.13)
Parameter m mainly depends on the shape of the capillary ends and the Reynolds number (Re).
The Reynolds number is an important non-dimensional similitude characteristic for fluidic de-scription of incompressible fluids:
Re�
= V v
= 2 V
R t g
�
� � � (4.14)
It characterises the flow shape, i.e. laminar or turbu-lent, conditioned by inertia and friction (viscosity).
Depending on the production technology the capillary ends of viscometers may be sharp-edged or funnel-shaped (please refer to Figure 14).
a b
Figure 14 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 ba-sis /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.
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 me-trologically utilised flow-time range.
Cannon, Manning, and Bell /14/ arrived at the follow-ing functional correlation:
Re 0.037 = m (4.15)
Equation (4.15) forms the basis of the calculation of HC correction according to the applicable standards /N6, N8, N10/.
In this way the following working equations result for viscometers with sharp-edged or funnel-shaped cap-illary ends:
sharp-edged capillary ends
� = K t - Bt
g
�
(4.16)
L 8
V1.12 = B
�
UBBELOHDE Viscometer: B = 2.5 /N6/
tH = B
K tg
(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:
2
1
2
3
2g
R)K (2 L
V 1.66 = E
t
E - t K = ��
(4.18)
tH = E
K tg2
(4.19)
12
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 vis-cometers from SCHOTT-GERÄTE have funnel-shaped capillary ends. The correction times tH are given in the operation instructions.
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 re-sult. In addition, owing to after-flow effects of the liq-uid and the beginning of the deformation of the sus-pended level, the viscometer characteristic of UBBELOHDE Viscometers is affected.
If falling short of the measurement range as recom-mended 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 stan-dard liquids. The smaller the difference between the viscosities, the more accurate the result of the cor-rection procedure.
Realisation of the correction procedure:
1. Determination of individual values for the Hagenbach correction with the standard liquids:
K -t = t i
g H ii
�
i = {1;2} (4.20)
2. Determination of the Hagenbach correction tH for the flow time tg by way of linear interpolation between the values tH1
und tH 2:
t
1 -
t
1 K - t = t
12
1 2
g g12HH �
�
�
�
��
�
� (4.21)
2g1g
H H12
t
1 -
t
1
t - t = K 21 (4.22)
Figure 15 illustrates the correction procedure:
t H
t H 2
1 / t
t H 1
t H
Figure 15 individual Hagenbach correction /N9/ a Hagenbach curve according to equation (4.19) b real course of the individual Hagenbach- correction c interpolation straight line
b
a
c
13
Examples of viscosity determination
Viscosity measurement of n-decane at � = 23 °C (� � 1.21 mm2/s) with UBBELOHDE Viscometers 1. Case
Selection of a viscometer with capillary 0 K = 0.00098 mm2/s2
L = 90 mm V = 5.7 ml hm = 130 mm D = 0.36 mm Measurement range according to operating instructions: 0.2 ... 1.2 mm2/s mean measured flow time: tg = 1234.57 s HC correction time is approx. 0.3 s. This corresponds to approx. 0.024% of the flow time. This means that neglecting the HC correction time would not cause any significant change of the measurement result. Calculation of viscosity: � = K · tg � = 0.00098 mm2/s2 � 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 hm = 130 mm D = 0.84 mm 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: � = K · (tg - tH)
� = 0.0105 mm2/s2 � (116.05 - 0.69) s = 1.211 mm2/s
3. Case
Selection of a viscometer with capillary Ic K = 0.0303 mm2/s2
L = 90 mm V = 5.7 ml hm = 130 mm D = 0.84 mm Measurement range according to operating instructions: 3 ... 30 mm2/s mean measured flow time: tg = 39.95 s Calculated HC correction according to equation (4.19): tH = 1.03 s
The measurement range of the viscometer was fallen short of. Furthermore, the HC correction time is above the max. correction time of tH = 0.66 s as indi-cated in /16/ for precision measurements.
In this case a viscometer with a smaller capillary di-ameter should be resorted to. If this is impossible, the individual HC correction time for precision meas-urements has to be determined in an experimental manner.
14
5 Calibration The viscometer constant K is determined individually for each glass capillary viscometer by way of calibra-tion.
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 reproducibil-ity incertainties of calibration have a direct influence on the measurement incertainty of the viscometers.
Measurement principle The determination of the constants is done by a si-multaneous flow-time measurement in the viscome-ters to be calibrated (test specimens) and in the ref-erence standard sources the constants of which were determined by the "Physikalisch-Technische Bunde-sanstalt (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 multi-tude 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.
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).
To ensure a high statistical certainty, two measure-ment cycles involving seven flow-time measurements each are run, with the first measurement of the re-spective measurement cycle being considered as preliminary test.
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 cor-rectness of the viscometer constants only for a lim-ited 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 measure-ments using reference standard sources (please see above) or with calibrating oils from the ”Deutsche Ka-librierdienst (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 measure-ments.
Please refer also to DIN 51 561 - 4, Part 4: Viscome-ter calibration and determination of measurement in-certainty, taking into account the user note /N9/.
Test specimens Reference Viscometer
Figure 16 Calibration of glass capillary viscometers
R1 R2P3P2 P1
1P1P
1
HgP
t - t = K
�
)t - (t K = 1R1R1 HgR1�
2
+ =
21 ��
�
)t - (t 2R2R2R HgK = 2�
15
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 trans-parent liquids:
� UBBELOHDE Viscometer � OSTWALD Viscometer � 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 re-ferred to in chapter 2, UBBELOHDE Viscometers should be preferred over the other types in most ap-plications.
In the case of measurements involving low-foaming or bubbling liquids one should use OSTWALD or TC-UBBELOHDE Viscometers, since foam of bubbles affect the functioning of the photoelectric barriers. In the case of highly foaming liquids, however, TC-UBBELOHDE 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 in-tense 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 rec-ommended.
If only sample or solvent small quantities are avail-able, 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 liq-uids, or BS/IP/RF U-Tube Reverse Flow Viscometers
(from approx. 6000 mm2/s) for highly viscous sub-stances are available.
For automatic viscosity determination, to be used in particular with opaque oils and emulsions, TC-UBBELOHDE Viscometers are the choice. Ow-ing to the fact that the thermistor sensors are glass-sealed and melted hermetically tight in the viscome-ters, it is, for instance, also possible to measure con-ductive and highly aggressive liquids.
Capillary selection
The measurement range of the viscometers is de-termined 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 calcula-tion 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 re-search results, even flow times down to approx. 10 s /15, 34, 35/ are possible if individual Hagenbach-Couette Correction with automatic flow-time meas-urement is applied.
In the operating instructions of the viscometers the min. flow times are stated as a function of the capil-laries.
Table 1 shows as an example the measurement ranges as a function of the capillary diameter for UBBELOHDE Viscometers.
16
Table 1 Measurement ranges of UBBELOHDE Viscometers /16/
Capillary no.
Capillary diameter [mm]
K (guidance value)[mm2/s2]
Measurement range[mm2/s]
0 0.36 0.001 0.2 ... 1.2
0c 0.46 0.003 0.5 ... 3
0a 0.53 0.005 0.8 ... 5
I 0.63 0.01 1.2 ... 10
Ic 0.84 0.03 3 ... 30
Ia 0.95 0.05 5 ... 50
II 1.13 0.1 10 ... 100
IIc 1.50 0.3 30 ... 300
IIa 1.69 0.5 50 ... 500
III 2.01 1 100 ... 1000
IIIc 2.65 3 300 ... 3000
IIIa 3.00 5 500 ... 5000
IV 3.60 10 1000 ... 10000
IVc 4.70 30 3000 ... 30000
IVa 5.34 50 6000 ... 30000
V 6.40 100 > 10000
6.2 Cleaning of capillary viscometers Careful cleaning of viscometers is an essential pre-requisite 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 quan-tities 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 particu-larly 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 fi-bres and are thus not recommendable.
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: � concentrated sulphuric acid with an addition of po-
tassium dichromate (chromic-sulphuric acid mix-ture); when working with chromic-sulphuric acid mixture, extreme care has to be taken; chromium-(VI) compounds are toxic
� 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 irre-versible leaching in the glasses which may even cause a change in the viscometer constant.
In addition, SCHOTT-GERÄTE offers a KPG utility pipette for determining the optimally suited capillary number for the respec-tive measurement task.
17
Initial 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.
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 addi-tional 20 to 30 minutes prior to the beginning of the cleaning cycle. If measurements are not made im-mediately subsequent one to another, the cleaned viscometers are to be stored in a dust-free environ-ment. 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 elimi-nated 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 clean-ing is also recommended at larger timely intervals.
Automatic cleaning
Especially for examinations of mineral oils in UBBELOHDE or CANNON-FENSKE Routine Vis-cometers, 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 spe-cial viscometers with an attached rinsing tube.
The AVS 26 Viscometer Cleaner works in combina-tion with the automatic viscosity-measurement de-vices of the AVS series. Several rinsing programs are available. During the rinsing process the vis-cometer 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 clean-ing, 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 exam-ined have a similar effect on the measurement result as contamination in the viscometer
For this reason, you should immediately prior to per-forming the measurement: � Carefully clean and dry all parts coming in contact with the substance to be measured, � filter the samples - low-viscosity samples: glass filter, porosity 2 to 4 (10 - 100 �m) - highly viscous samples: sieve, mesh width 0.3 mm.
Paraffin or resin-containing products as well as sub-stances 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.
18
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 quan-tity, 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 dos-ing 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.
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 at-tached glass-tip filter. When using syringe filters, prior filtration is not necessary.
Especially when filling in substances of a higher vis-cosity into OSTWALD Viscometers the pipette should be immersed deeply into the filling tube in order to prevent after-flow errors.
Table 2 Filling quantities for various viscometer types
Viscometer type Filling quantity[ml]
OSTWALD 3 Micro OSTWALD 2 UBBELOHDE 15 - 22 Micro UBBELOHDE 3 - 4 CANNON-FENSKE Routine 5 - 12 CANNON-FENSKE Reverse Flow
approx. 12
BS/IP/RF U-Tube Reverse Flow
approx. 20
Filling CANNON-FENSKE Routine Viscometers
CANNON-FENSKE Routine Viscometers (please re-fer 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. Af-ter filling, the viscometer is restored to normal meas-uring 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.
Figure 17 CANNON-FENSKE Routine Viscometer
1 tube with capillary 2 venting tube 3 reservoir 4 lower timing mark M2 5 upper timing mark M1 6 pre-run sphere 7 capillary 8 measuring sphere 9 tube extension
19
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 vis-cometers from breaking.
Prior to the measurement, UBBELOHDE Viscome-ters are to be suspended in the racks provided for this purpose, and fixed in position by pressing the spring downwards.
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 high-est position.
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. Out-side the indicated temperature range major fluctua-tion cannot be avoided in each case, but these fluc-tuations 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 vis-cometry, meet the requirements with regard to the timely and local constancy of the temperature of the bath liquid. They are equipped with openings or in-serts, 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 ther-mostats of the CT series, special viscometer-rack in-serts for manual measurement are available.
Subsequently, the sample is exposed to thermostat treatment in the viscometer.
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:
� 10 min: low-viscosity substances; � 20 min: high-viscosity substances,
low-viscosity substances in the case of Reverse-Flow Viscometers;
� 30 min: high-viscosity substances in the case of Reverse-Flow Viscometers.
20
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 viscome-ters 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 Viscome-ters are used, the venting tube should be closed with a finger tip prior to starting sucking in. Upon comple-tion 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 re-leased.
When measuring highly viscous samples it is rec-ommendable 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 rec-ommended 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 analo-gously.
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.
Figure 19 (c) shows the proper detection of the meniscus passage.
Figure 19 Detection of the meniscus passage in the case if manual measurement (a), (b) - wrong (c) – correct
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 re-newed 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 applica-ble. To perform the measurement, the tube which was closed after filling, is opened on the side of the measurement sphere, and subsequently one meas-ures the time over which the liquid rises from the lower to the upper annular mark. The CANNON-FENSKE 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 measure-ment.
If the repeatability limit of a measurement series (2.8 times the standard deviation) exceeds the re-producibility limit indicated for the specific vis-cometer, one has to assume the presence of exter-nal 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 measure-ment 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
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 pro-gram.
The selection of the AVS/S, AVS-SK, and AVS/S-CF measurement tripods for automatic viscosity meas-urement with optical detection is determined by:
� Viscometer type � 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 Vis-cometer no measurement tripod is required. The vis-cometer 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.
21
Table 3 Automatic viscometer measurement devices from SCHOTT-GERÄTE
Type of device AVS 310 AVS 350 AVS 360 AVS 450 AVSPro
Meniscus detection Photoelectric barrier
Photoelectric barrier NTC sensor
Photoelectric barrier NTC sensor
Photoelectric barrier NTC sensor
Photoelectric barrier NTC sensor
Working mode pressing pressing sucking sucking sucking
nmax 10 10 10 999 10
Interface RS-232-C RS-232-C RS-232-C RS-232-C RS-232-C
Special features software control (optimal)
built-in printer fully automatic viscosity measurement system
nmax = max. number of programmable single measurements in repetitive operation
The viscometers are pneumatically connected to the AVS device via silicone or PTFE hoses.
All automatic devices are microprocessor-controlled. An interface enables an external printer or computer to be connected.
Parameterisation and the triggering of the automatic measurement cycle are done on the control unit.
The displacement of the measurement liquid within the viscometer is done via an internal diaphragm pump with pressing or sucking action. The pump is controlled in such a manner that an optimal pumping pressure for a reproducible filling of the measure-ment systems is built up as a function of the viscosity of the sample being analysed.
For the Viscosity Measuring Units AVS 350 and AVS 360 a PC software is available which enables the control of up to 8 measurement devices and an evaluation of the measurement data.
Figure 20 shows a viscosity measurement station with 4 AVS 350 Viscosity Measuring Units.
Figure 20 AVS 350 Viscosity Measuring Units with UBBELOHDE and TC Viscometer and Viewing Thermostat
22
The AVSPro Automatic Viscosity Sampler is a fully automatic viscosity measurement system for routine measurements.
This device performs measurements of kinematic and relative viscosity up to calculation and documen-tation work in an independent manner.
Filling, emptying, and rinsing of the viscometers are integrated in the automatic course of the measure-ment.
Operating guidance is via menu-control using a monitor, a mouse, and a computer keyboard.
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.
The AVSPro Automatic Viscosity Sampler may be operated with a maximum of eight Micro UBBE-LOHDE Viscometers equipped with TC Sensors in two thermostat baths at two different measurement temperatures simultaneously.
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 AVSPro Automatic Viscosity Sampler equipped with 8 Micro UBBELOHDE Viscometers with TC Sensors in 2 Viewing Thermostats CT 53
23
7 Causes of errors and special corrections
7.1 Correctable errors and corrections Rising-height error
Surface tension causes the liquid which is wetting the tube wall to climb by a distance of �h.
The size of the relative rising-height error � in terms of % can be calculated on the basis of the following formula:
��
�
�
� =
2
g h (
1
r -
1
r) ( - ) · 100 %
m 1 2
0
0 (7.1)
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 � - surface tension of the measurement substance �0 - surface tension of the calibration substance � - density of the measurements substance �0 - density of the calibration substance
In the case of precision measurements the influence of the rising-height error is to be noted with the fol-lowing viscometer types, if the relation between sur-face 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 correc-tion will in general be no more than 0.1 to 0.2 % and can thus be neglected in most cases.
Thermal expansion of the capillaries and the measurement vessel
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 viscome-ter constant has to be corrected in the case of preci-sion measurements.
The corrected device constant according to the equa-tion (7.2):
K´ = K (1 + � (� - �0)) (7.2)
Viscometers from SCHOTT-GERÄTE are calibrated at a temperature of �0 = 23 °C. The coefficient � of longitudinal expansion of the DURAN�-glass2) used
for production is 3.3 • 10-6 K-1.
Thermal expansion of the measurement substance
In the case of UBBELOHDE Viscometers no correc-tion is required, since the measurement result is largely independent of the substance quantity being filled in. If, in the case of viscometers without sus-pended level, the substance temperature should de-viate 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 tem-perature adaptation.
In this case the constants are to be corrected accord-ing to equation (7.3) for OSTWALD and CANNON-FENSKE Routine Viscometers, or according to equa-tion (7.4) for Reverse-Flow Viscometers.
)
p hD
)p - (p V 4 + (1K = K
2m 2
m
12
�
� (7.3)
)
p h D
)p - (p V 4 - (1K = K
2m2
m
12
�
� (7.4)
Dm - mean diameter of the liquid meniscus in the reservoir vessel �1 - density of the measurement substance at filling temperature �2 - density of the measurement substance at measurement temperature
2) Registered trademark of SCHOTT GLAS, Mainz, Germany
24
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 devi-ates from normal position, the mean pressure height of the viscometer will change. If, instead of the initial angle �0 the connection line compared to perpen-dicular is at an angle of � the corrected device con-stant is to be calculated according to:
�K = K cos
cos 0
�
� (7.5)
The fixation racks or holders offered by SCHOTT-GERÄTE 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 dif-ferent.
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 begin-ning the measurements the watch should be wound up to exclude variations of the spring force. It is rec-ommended to check the accurate march of the watches regularly using a time standard.
If the time is measured electronically using a corre-sponding 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 adjust-ment or insufficiencies in the temperature stability or temperature measurement are frequently very large, since the viscosity of most of the liquids var-ies largely as a function of temperature /24/.
In the case of a temperature error of �s� 1K, the relative error in the viscosity measurement is:
� = U� • s • 100 % (7.7)
The temperature coefficient U� is determined accord-ing to the corresponding DIN standard /N4/.
The temperature measurement should only be made fully in mass in gauged thermal metres with a resolu-tion 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:
2gt K R
V 63.7 = Re
��
� (7.8)
V = [cm3] 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 er-rors, since the average pressure height of the vis-cometer 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 influ-ence of surface tension on the measurement result will increase.
25
Figure 22 shows various stages of level disturbance.
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 (nor-mal 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.
Table 4 Limit values of tg and Re (UBBELOHDE Viscometer) /N9/
Capillary no. 0c 0a I Ic
tg [s] 100 75 60 60
Re 500 500 300 100
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 forma-tion of the profile is considerably smaller than the capillary length. According to Schiller /10/ the start-up length can be calculated as follows:
l = 0,115 V
teg� �
(7.9)
Drainage errors
Drainage errors are caused by the fact that a small liquid volume �V is adhering to the wall of the vis-cometer above the sinking liquid meniscus. �V will increase with the viscosity and the sinking velocity of the meniscus. The magnitude of the error is also in-fluenced by the wettability of the wall, the surface tension of the liquid, and the geometry of the vis-cometer. Depending on the constructional shape of the device a shortening or extension of the flow times may occur.
Radiation heat
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 pre-mounted infra-red filter should be used for illumina-tion preferably.
Figure 22 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
26
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 measure-ment 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: flow time too small with (Ostwald, CANNON-FENSKE or BS/IPRF U-Tube Reverse Flow Viscometer)
substance quantity filled in was too small
empty, clean and refill viscometer (please refer to Chapter 6.2 / 6.3)
systematic measurement error: flow time too large (Ostwald, CANNON-FENSKE or BS/IP/RF-U-Tube Reverse Flow Viscometer)
substance quantity filled in was too great
as above
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
temperature of the bath liquid too low
check temperature, if necessary, readjust thermostat
drift of the flow times 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 measurement substance not completed
continue temperature adjustment until the time values are stable (please refer to Chapter 6.4)
evaporation of a highly volatile component; reaction of the product being analysed with the air
apply pressing operating mode
27
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 Chap-ter 6.2); repeat measurement
contamination in the product being analysed
empty and clean viscometer; repeat the measure-ment 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 Chap-ter 6.2); during refilling, ensure absence of bubbles (please refer to Chapter 6.3)
excessive stochastic scattering oc-curring during automatic meas-urements using optoelectric barriers
contamination of the optical sensors
remove the viscometer tripod from the thermostat bath; clean optical system using non-denatured al-cohol on a soft cloth
(Baron possibility of total malfunction)
errors triggered by the opto-electric barriers as a result of the formation of bubbles, foam, or liquid lamellae
use a TC-UBBELOHDE, OSTWALD, or CANNON-FENSKE Routine Viscometer (please refer to Chapter 6.1)
excessive stochastic scattering oc-curring during automatic meas-urements using TC Viscometers (possibility of total malfunction)
Incrustation of the sensors (in the case of thermally instable media)
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 bath-liquid temperature (defective thermostat)
replace the thermostat (please refer to Chapter 6.4)
malfunction caused by air bubbles during the sucking-in process of the liquid into the delivery vessel
substance quantity filled in was too small
UBBELOHDE Viscometer: fill up the measurement substance; others: empty and clean viscometer; repeat measurement
28
8 Special application
8.1 Testing of plastics Measurement problem
One of the major quality features of synthetic materi-als 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.
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 cir-cumstances the properties of the finished part might be changed to such an extent that it is no longer suit-able 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 mole-cules is of essential importance as to the characteri-sation of the finished product.
This results in the following measurement tasks:
Polymer research and development
� Determination of the mean chain length of mean polymerisation degree of the polymer molecules � 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)
� Determination of the mean chain length or mean degree of polymerisation of the finished product (raw granules) � Objectives: - Characterisation of the finished product - Quality assurance - Optimisation of the process parameters - Prevention of the production of spoiled batches
Polymer processing
� Characterisation of the properties and the capabili- ties of the starting material (raw granules) � Objectives: - Rating of plants for polymer processing - Determination of optimum process parameters
� Determination of the chemical and physical proper- ties of the finished part � Objectives: - Quality assurance - Optimisation of the process parameters
Solution
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 vis-cometers (solution viscometry). Table 6 will inform you about the solvents, viscometers, and the applica-tion of the relevant standards.
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 addi-tion, 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 viscos-ity of the solvent and of the plastic solution (concen-tration 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 vis-cosity number (please refer to Table 7). It is of par-ticular importance in the range of research and de-velopment of polymers and of procedures and instal-lations for their production and processing. In addi-tion, it is an important feature as regards quality as-surance in the case of special applications, such as plastic recycling and the processing of recycled plas-tics.
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.
29
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
Polyethyleneterephtalate Polybutyleneterephthalate
PET PBT
Phenol / 1.2- dichlorobenzene(1:1 parts by weight) 2- chlorophenol m-cresol Dichloroacetic acid
Ic Ic II II, Micro IIc
53 728, Part 3
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 2) Measurement temperature: 135 °C 3) c = 0,26 g/l
Table 7 Definition of the terms used in dilute viscometry /18, N2/
Calculated value Description
dynamic viscosity
� = / � kinematic viscosity
r = / S relative viscosity, viscosity ratio
( - S) / S = r - 1 relative viscosity change, specific viscosity
Jv = 1 / c · ( - S) / S Staudinger function, viscosity number
Ln ( / S) / c inherent viscosity
Jg = lim [1 / c � ( - S) / S] c�0
Staudinger index, limiting viscosity number, intrinsic viscosity
30
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 im-proved 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 lubri-cating 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 lubricat-ing 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 vis-cosity of the oil must still be low enough to enable the oil being pumped to the rubbing parts inside the en-gine.
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 for-mation of lubricating film has to be ensured, so that the lubricating film will not break as a result of the in-sufficient 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, oxi-dation, and thermal strain) /20, 21, 22/.
The determination of viscosity is playing a major role in the production and development of doped oils (ba-sic oil / additive mixtures). In the course of produc-tion, regular viscosity measurement ensures ade-quate quality control. As regards development on the other side, the focus is on the examination of the vis-cosity-temperature behaviour of new oil/additive mix-tures.
In the case of used engine oils the determination of viscosity can be used to determine whether the for-mation of the lubricating film will still be sufficient even at higher temperatures.
Solution
One of the frequently used characteristics of viscos-ity-temperature behaviour (VT behaviour) of a lubri-cating 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 magni-tude of the viscosity drop occurring with increasing temperature depends on the chemical composition of the oil under concern. A minor temperature-dependence of the viscosity will lead to a higher vis-cosity index. Multigrade, engine, and gear oils are characterised by a high VI /23/.
The classification of an engine lubricating oil in so-called 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/.
31
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 manual measurement
Viscometer � UBBELOHDE � CANNON-FENSKE Routine � TC Viscometer (for dark oils)
� UBBELOHDE � CANNON-FENSKE Routine � CANNON-FENSKE Reverse Flow Viscometer (for dark oils) � BS/IP/RF U-Tube Reverse Flow Viscometer (for viscid and / or dark oils)
Viscosity measurement device
� AVS 350, AVS 360, AVS 450 � AVSPro (up to � 1200 mm2/at room temperature)
� Stop watch
Accessories � Thermostat and cooler � Viscometer Cleaner AVS 26 (optional)
� 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 charac-terised by very much different rheologic properties. Provenience, temperature, water percentage, inten-sity of the mechanical processing, storage time, and conditions of transportation are some of the factors influencing the mainly non-Newtonian flowing behav-iour of food masses.
But a number of fluids involved in food production also presents Newtonian behaviour.
In food technology and machine engineering, knowl-edge of viscosity is of importance in multiple ways, e.g. for: � controlling technological processes � evaluating the products’ quality � designing food dispensers and conveying apparatus � selecting and operating packaging installations.
Within the framework of food-technological research and development the measured viscosities can be used to draw valuable information about � molecular structure � chemical composition � efficiency of enzymes ���� percentage of viscosity-influencing constituents and additives
Examples of measurement tasks in food 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 ef-fect on the full-bodiedness and the stability of the foam.
Objectives of viscosity measurement: � optimisation of the mashing properties � selection of filtration strategy � 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 per-centage 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 ad-just an optimum pectin percentage /27/.
Objectives of viscosity measurement: � gathering of control parameters for the pectinological process of optimising of optimising clarification and fining � quality surveillance � characterisation of the jellying capabilities of pectins, inter alia by the determination of the limiting viscosity number /28/.
c) Viscosity determination in sugar industry
In the extraction and technical processing of saccha-rarose solutions, information about viscosity is essen-tial /29/. It increases in the form of an exponential curve with rising concentration and has thus a sub-stantial influence on the crystallisation readiness of sugar solutions.
32
So it is that the crystallisation of sacchararose solu-tions 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, glu-cose syrup /30/) and can be calculated as follows as regards saccharide solutions: = wA log A + wB log B (8.1) w - Mass portions in the total mixture A, B - Components
Glucose syrups are characterised by different sac-charide fractions with one and the same saccharifica-tion degree, a fact which results in diverging viscous behaviour patterns. Considering that they are used as crystallisation inhibitors in the production of con-fectionery, viscosity is a major technological parame-ter.
Objectives of viscosity measurement: � gathering of control parameters for processing sugar solutions � quality surveillance � development of recipes � 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 proc-essing conditions, e.g. by homogenisation.
On the other side it was possible to show that the homogenisation effects can be improved through vis-cosity control.
An addition of hydrocolloids (thickening, binding, and jellying agents) and stabilisers has a highly viscosity-raising effect. Viscosity measurement provides valu-able information required to reveal their chemical structure and their effect in combination with compo-nents of the milk.
Objectives of viscosity measurement: � Technology surveillance � Quality evaluation � 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 viscome-ters 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 af-ter-flow effects, an optical detection of dairy products is problematic.
The use of TC Viscometers requires frequent, thor-ough cleaning, since the thermistors tend to soil as a result of incrustation.
There are less problems in the viscosity measure-ment on beer, fruit juices and the like. Owing to the fact that these fluids have a tendency of foam forma-tion, 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.
33
9 Formula signs and units used
A Surface being parallel with flow direction m2
B Constant of Hagenbach correction with mm2 s sharp-edged capillary ends
c Concentration g/cm3
D Shear rate 1/s
E Constant of Hagenbach correction with mm2 s funnel-shaped capillary ends
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
�h 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 -
�p Acting pressure mbar
�pC 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
34
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
U� Temperature coefficient of kinematic viscosity 1/K
V Flow through volume cm3
�V Flow volume cm3/s
�V 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
� Longitudinal expansion coefficient of the glass grade 1/K used for the production of glass capillary viscometers
� Relative error of the measurement value %
Dynamic viscosity mPa s
r Relative viscosity -
S Dynamic viscosity of the solvent mPa s
� Kinematic viscosity mm2/s
� Density of the liquid to be measured g/cm3
�0 Density of the normal liquid g/cm3
� Surface tension of the liquid to be measured mN/m
�0 Surface tension of the normal liquid mN/m
� Temperature °C
� Shearing strain Pa
� Angle between the perpendicular and the connection line o of the upper and lower central point of the reference level vessel during measurement
�0 Angle between the perpendicular and the connection line o
of the upper and lower central point of the reference level vessel during calibration
35
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
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/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
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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
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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 Polybutylen- terephthalat (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
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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
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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. British Standard (BS)
/N54/ BS 188 Methods for Determination of the Viscosity of Liquids
5. Norme Française Enregistrée
/N55/ NF T 60 - 100 Mesure de la viscosité cinématique 6. 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.
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