Theory and Praxis of Capillary Viscometry - An Introduction – Authors: Prof. Dr.-Ing. habil. Jürgen Wilke Hochschule Anhalt Food and biotechnology (Process and environmental Technology Faculty) Dr.-Ing. Holger Kryk Magdeburg Dr.-Ing. Jutta Hartmann Rheinfelden Dieter Wagner SCHOTT-GERÄTE GmbH Viscometry development dept. Table of contents Page 1 Viscosity – Rheology ................................................... 2 2 Basics of capillary viscometry ................................. 5 2.1 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 1 1 Viscosity - Rheology Viscosity characterises the flow properties, the inher- The relationship between dynamic viscosity h and ent friction of liquids and gases. density r is referred to as kinematic viscosity n: If a fluid is trapped between two plane-parallel plates, h n = = [m2 /]s (1.5) it will require some amount of force to displace the r upper plate. The fluid particles which are directly adjacent to the For reasons of convenience, the unit of mm2/s is plates are firmly bonded to the surface by adhesion used which then numerically corresponds to the for- forces. In this process the fluid layer neighbouring the mer cSt (Centistoke) unit. plate being displaced adopts the velocity of the plate. All neighbouring layers stay more and more behind In case of Newtonian liquids h will remain invariant with the increasing distance to the plate being if the shear rate changes with all other test conditions moved. The cause for this phenomenon can be remaining unchanged. found in cohesion forces which counter-act the recip- rocal dislocation of the individual layers. Moving a liquid molecule requires a potential hill to y be surmounted which will lead to the following rela- F tionship if Maxwellian Boltzmann velocity distribution is being applied: v Evisk RT D = k × e (1.6) x Figure 1 Basic model of the shearing operation in k Potentiality factor the case of laminar, stationary layer flow Evisk Measure of the height of the energy maximum (activation energy of viscous flow) The fluid starts to flow inside the gap. A layered flow R Gas constant builds up (please ref. to Figure 1). T absolute temperature t s The shear strain (also referred to as 1,2) refers As a consequence of the differences in size, shape, the quotient of force F and the boundary surface A of and interaction between the molecules, h may the liquid: change within very wide limits in the case of pure liq- uids. F J = (1.1) A Examples: The speed drop, i.e. the shear rate D, is the differ- n-pentane 0.230 mPa • s (20 °C) ential quotient: Water 1.002 mPa • s (20 °C) Propane triol 1480 mPa • s (20 °C) dv D = (1.2) (Glycerine) dy According to Newton's Viscosity Law there is pro- In the case of liquids, and in contrast to gases, h will portionality between the shear strain t and the shear decrease in a strongly exponential manner with rate D. rising temperatures. As a rule, the decrease will be the higher, the higher the absolute values of viscosity t h = • D (1.3) are and the lower the temperature is, since the inter- The proportionality factor h is referred to as dynamic molecular interactions are decreasing with the mag- viscosity coefficient or, in short, as dynamic vis- nifying thermal movement of the molecules. cosity. The unit of measurement is Pa • s, with the indication This effect indicates the major practical significance being made in mPa • s i.e. in numerical conformity of viscosity, for instance, with regard to lubrication with the former unit cP (Centipoise): technology, as will be shown below. J 2 D = = [Ns / m] = [Pa • s] (1.4) D 2 In the case of liquids a complex molecule structure Shear-rate dependent flow behaviour: and an increasing pressure lead to an increase in viscosity. Dilatancy The shear viscosity increases with rising shear rate (for As regards water, an anomaly occurs owing to the work hardening, please refer to Figure 2, curve b). particular structure. If pressure increases, viscosity will pass through a minimum, since molecule aggre- D gates are being formed the reciprocal friction of b which is lower. In the case of liquid miscible phases h is in general a not made up by the addition of h-values of the pure components. c The viscosity of the miscible phase may be greater or smaller than h of the isolated components, or may be D in between. Figure 2 Viscosity curves of fluids The viscosity of the solutions of solid matters is a - Newtonian fluid frequently greater than the one of the pure solvent. b - Fluid with dilatant flow behaviour The indication is mostly given in terms of relative or c - Intrinsic viscous fluid specific viscosity (please refer to chapter 8). A particular behaviour can be observed with the con- Plasticity centration-dependability of viscosity of electrolyte so- The flow of the liquids begins only from a minimum lutions. shear strain. Below this yielding point the substance behaves like a solid matter. If the liquid layers are moving at different velocities, the deformation of the ion cloud will cause the occur- Examples: rence of additional inter-ionic interacting forces which - Paints, varnish/lacquer will affect friction between the individual layers. - Food (mayonnaise) - Toothpaste H. Falkenhagen used the theory of inter-ionic interac- - Vaseline tions, applicable to highly diluted electrolyte, solutions to derive the Limit Law of Viscosity: BINGHAM substances: t = f (D) is linear above the yielding point. DD = + K c (1.7) C 0 CASSON substances: D t = f (D) is non-linear above the yielding point. c Viscosity at ion concentration c D 0 Viscosity of the pure solvent at same temperature Pseudo-plasticity (intrinsic viscosity) K Constant depending on These substances are characterised by Newtonian the following influencing variables: behaviour at low shear rates. - Temperature At high shear rates h will increase with the shear rate - Relative permittivity (please refer to Figure 2, curve c). - Ionic valence - Ionic mobility Examples: - Lacquer/varnish Non-Newtonian flow behaviour - Thermoplastics Disperse systems, concentrated polymer solutions, - Lubricating oils (multigrade oils) and melts of macro molecules show a marked non- - Glues Newtonian behaviour with increasing shear rates. - Additives In their case there is a non-linear dependency be- tween shear strain and shear rate. 3 In addition to these effects a shear-time dependent The complex nature of this field of work has lead to flow behaviour can be observed with some non- the crystallisation of an original term, i.e. rheology Newtonian matters: (science of flow behaviour). t = f (D, t) Rheometry deals with the specific methods and pro- h = f (D, t) cedures of determining rheological characteristics. This means that shear viscosity is influenced by the Within this nomenclature viscometry is a partial dis- duration of the shearing action (please refer to Figure cipline of rheometry. 3). Principles of viscosity measurement h Rheological measurement procedures are mainly based on mechanical methods, since tension and b elongation are mechanical values which are deter- mined on the basis of a defined deformation of the a sample. The simultaneous measurement of the electrical, c magnetic, and optical properties which may change during the deformation or flow process of the fluids is