theory and praxis of capillary viscometry

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 reciprocal 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 t (also referred to as s 1,2 ) refers the quotient of force F and the boundary surface A of the liquid: J = F A (1.1) The speed drop, i.e. the shear rate D, is the differential quotient: D = dv dy (1.2) According to Newton's Viscosity Law there is proportionality between the shear strain t and the shear rate D. t = h • D (1.3) The proportionality factor h is referred to as dynamic viscosity coefficient or, in short, as dynamic viscosity. The unit of measurement is Pa • s, with the indication being made in mPa • s i.e. in numerical conformity with the former unit cP (Centipoise): D J = D = [Ns / m 2 ] = [Pa • s] (1.4) The relationship between dynamic viscosity h hh h and density r rr r is referred to as kinematic viscosity n nn n: n h r = = [m 2 /]s (1.5) For reasons of convenience, the unit of mm 2 /s is used which then numerically corresponds to the former cSt (Centistoke) unit. In case of Newtonian liquids h will remain invariant if the shear rate changes with all other test conditions remaining unchanged. Moving a liquid molecule requires a potential hill to be surmounted which will lead to the following relationship if Maxwellian Boltzmann velocity distribution is being applied: D = k e E RT visk × (1.6) k Potentiality factor E visk Measure of the height of the energy maximum (activation energy of viscous flow) R Gas constant T absolute temperature As a consequence of the differences in size, shape, and interaction between the molecules, h may change within very wide limits in the case of pure liquids. 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, h will decrease in a strongly exponential manner with rising temperatures. As a rule, the decrease will be the higher, the higher the absolute values of viscosity are and the lower the temperature is, since the 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 h is in general not made up by the addition of h-values of the pure components. The viscosity of the miscible phase may be greater or smaller than h 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 concentration-dependability of viscosity of electrolyte solutions. If the liquid layers are moving at different velocities, the deformation of the ion cloud will cause the occurrence of additional inter-ionic interacting forces which will affect friction between the individual layers. H. Falkenhagen used the theory of inter-ionic interactions, applicable to highly diluted electrolyte, solutions to derive the Limit Law of Viscosity: DD C = + K c 0 (1.7) D c Viscosity at ion concentration c D 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 between 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 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: t = f (D) is linear above the yielding point. CASSON substances: t = 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 h 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: t = f (D, t) h = f (D, t) This means that shear viscosity is influenced by the duration of the shearing action (please refer to Figure 3). b a c t s h 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 transformation). 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 characterised 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 properties of this kind meet with more and more technological 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 procedures 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 determined on the basis of a defined deformation of the sample. The simultaneous measurement of the electrical, magnetic, and optical properties which may change during the deformation or flow process of the fluids is becoming more and more interesting. Figure 4 shows the major manners of realising the deformation of the sample. v 1 2 v 2 M 1 5 6 M 2 4 3 2 a bc 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 M 1 , M 2 = 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 measurements with Newtonian liquids with a kinematic viscosity of more than 0.3 mm 2 /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 incertainty. 5 2 Basics of capillary viscometry 2.1 Measurement principle Inside the capillary viscometers, the velocity drop required for viscosity measurement is built up in the form of a laminar tube flow within a measurement capillary. Under idealised conditions  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). v v max 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 principle /1, 2, 3, 4/: V t = R 8L 4 F D ,p (2.1) With regard to viscosity measurement, this results in two different fundamental measurement principles:  Measurement of the differential pressure at a constant volume flow of the sample through the capillary  Measurement of the volume flow through the capillary 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 volume flow. This issue is approached in a satisfactory manner the design of device in the form of comparison measurement methods. An application of this can be found in solution viscometry where the viscosity of the pure solvent is used as a reference liquid. The measurement itself is made, inter alia, on the basis of a ”pneumatic 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 required 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 enables 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 viscometer types after OSTWALD and UBBELOHDE. a) 10 L 6 7 b) h m 4 7 L 8 M 1 M 2 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 M 1 to measurement mark M 2 (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 levelling 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 capillary 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 column 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 measurement mark M 1 down to the annular measurement mark M 2 . In the case of very strongly tinted, opaque liquids, it can be possible that a visual detection of the meniscus passage through the measurement marks is im- possible owing to the wetting of the tube. For manual operation, the Reverse-Flow Viscometer (please refer to Figure 7) is used in such cases. h m 2 h m 1 3 = M 1 5 = M 2 7 = M 3 L Figure 7 CANNON-FENSKE Reverse-Flow Viscometer The sample is filled into the spherical extension of the capillary tube (2). The tube (1) is closed during thermostatisation and opened at the beginning of the measurement. The imaging signal used for viscosity is the time required by the meniscus to flow through the measurement marks M 1 , M 2 and M 3 at the reverse-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 h = 1.0019 [cP] ± 0.0003 [cP] 1) (20 °C), it was possible to define a viscosity scale. The capillaries of viscometers used for industrial applications 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 measurement marks burnt in above and below the measurement 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 passage 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 incertainties are determined by the fluid-dynamic circumstances and the detection of the meniscus passage through the measurement marks. The manufacturer of the measurement device has to ensure by design and production measures that the viscometer constant will not change even if the measurement conditions should deviate from the calibration conditions (e.g. measurement and calibration temperature). 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 passage of the meniscus through the measurement marks. Optical sensors During the meniscus passage the optical conditions such as refraction and reflection within the detection plane are changing. This leads to a change n the radiation intensity of the light arriving from the 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 measurement. Specific threshold values of the analogous signal may be defined for the "filled" or "empty" status. Advantage: Versatile application, simple set-up Disadvantage: Highly tinted or opaque liquids, especially those which adhere strongly to the wall, cannot me measured. On the viscometers from SCHOTT-GERÄTE all optical sensors are accommodated in a measurement tripod made of metal or plastic. Within the tripod the fixation rack and the glass viscometer are fastened using a clamping mechanism. Figure 8 shows the arrangement of the optical sensors within the measurement tripod on the viscometer. The light is guided out of the tripod head through fibre optics into the tripod legs up to the upper and lower measurement plane. The watertight sealing enables the measurement tripods to be placed in liquid thermostats. Owing to high precision in the glass-technological and mechanical production as well as through measures of quality assurance it is ensured that the glass bodies and tripods are freely interchangeable, with the certified viscometer constants remaining valid. 2 1 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 (solutions of salts, acids, bases) can be detected using small-sized electrodes melted into the measurement plane in the glass wall. For signal generation the electrical resistance is measured. Advantage: Simple set-up; detection of tinted and opaque liquids Disadvantage: The sample must be electrocon- ductive; the supply lines to the sensors are to be protected against water penetration if liquid thermostats are being used. Thermal-conductivity sensors Small-sized thermistors (NTC resistors), melted in on the level of the measurement plane, are heated up. As a result to the improved thermal conductivity of the liquid the thermistor will cool down at the air/sample transition, and its electrical resistance will diminish. Advantage: Measurement-signal generation is independent of the tint, transparency, and conductivity of the product being analysed. Disadvantage: More demanding production owing to the required melting-in of the sensors; incrustation and contamination hazard in the case of thermally decomposable samples. Figure 9 shows a TC Viscometer from 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 dynamic behaviour. Figure 10 shows the signal course resulting developing during filling and run-off (measurement process) through the changing thermal conductivity in the surrounding of the sensor. To compensate the influence of the sample on dy- namics, the SCHOTT-GERÄTE viscosity measurement devices perform an automatic calibration. The working point of the start/stop timing is adaptively set by the device software during the filling process of the capillaries on the basis of a respectively determined dynamic ID value. b a t [s] U[V] 14 12 4 6 8 10 2 0 1 23 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 versatile; no sealing in the glass required Disadvantage: Coupling of the sound heads bears production-technological difficulties, especially in the case of an application in liquid thermostats; greater signal-processing efforts required; higher price Gas-ionisation spark-discharge detection The electrodes melted in on the level of the detection planes are connected to a high-voltage generator. If the liquid, acting as an electrical insulator, uncovers the electrodes a spark discharge will occur in the gas chamber if a sufficiently high breakdown voltage is selected. The electrical pulse is used as a control signal. Advantage: Detection is possible in dull, opaque liquids Disadvantage: The process cannot be used in the presence of least traces of water in the product being analysed (water contents > 0.5 %); high-voltage requires extensive insulation. [...]... smallest quantities of microscopically small particles of dust within the viscometer may lead to standard deviations of up to several per cent Particles which adhere firmly to the capillary wall and are frequently almost invisible are often the cause of systematic measurement errors Errors of this type, leading to an increase of the flow times, can hardly be told from the individual values of a measurement... 53 7 Causes of errors and special corrections 7.1 Correctable errors and corrections Rising-height error Thermal expansion of the capillaries and the measurement vessel Surface tension causes the liquid which is wetting the tube wall to climb by a distance of Dh During high- and low-temperature measurements the radius and the length of the capillaries, the volume of the measurement sphere, and the average... 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... /N21/ The determination of the mean molecular weight of the polymer molecules is done via the limiting viscosity number (please refer to Table 7) It is of particular importance in the range of research and development of polymers and of procedures and installations for their production and processing In addition, it is an important feature as regards quality assurance in the case of special applications,... 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... explanation of the theoretical basics of Hagenbach-Couette Correction ,p Figure 12 shows the true march of pressure in the capillary /7/ The deviations from the ideal march result from hydrodynamic processes in the in- and outflow zone of the capillary They are taken into account in the flow model (please refer to Figure 13) in the form of additional terms l Figure 12 Axial march of pressure in the capillary. .. 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 capabilities of the starting material (raw granules) Objectives: - Rating of plants for polymer processing - Determination of optimum... surface tension of the liquid and the shape of the capillary outflow, disturbances of this kind may even occur in the case of somewhat longer flow times Drainage errors are caused by the fact that a small liquid volume DV is adhering to the wall of the viscometer above the sinking liquid meniscus DV will increase with the viscosity and the sinking velocity of the meniscus The magnitude of the error is... processes evaluating the products quality designing food dispensers and conveying apparatus selecting and operating packaging installations 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... by the wettability of the wall, the surface tension of the liquid, and the geometry of the viscometer Depending on the constructional shape of the device a shortening or extension of the flow times may occur Table 4 Limit values of tg and Re (UBBELOHDE Viscometer) /N9/ Capillary no Radiation heat 0c 0a I Ic tg [s] 100 75 60 60 Re 500 500 300 100 To avoid an uncontrolled heating up of the liquid to be . Theory and Praxis of Capillary Viscometry - An Introduction – Authors: Prof. Dr Ing. habil. Jürgen Wilke Hochschule Anhalt Food and biotechnology (Process and environmental. 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. 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