8.62 Viscometers Application and Selection

Transcription

1 8.62 ViscometersApplication and Selection C. H. KIM (1969, 1982) B. G. LIPTÁK (1995, 2003) Definition of Viscosity: Viscosity Units: Types of Viscous Behavior: Absolute viscosity is the ratio of applied stress to resulting shear velocity; kinematic viscosity is absolute viscosity divided by density. Dynamic (absolute), poise = 1.0 dyne-sec/cm 2 = 100 centipoise (cp) = 0.1 pascalsecond (Pas or PI); Pas = 1.0 newton-second/m 2 = 1.0 poiseuille (PI) = 1000 cp = 0.67 lbm/ft-sec Kinematic viscosity, stoke = 1.0 cm 2 /sec = 100 centistokes (cst) = ft 2 /sec Newtonian or non-newtonian; non-newtonian fluids include pseudoplastic, dilatant, plastic solid, thixotropic, and rheopectic types. INTRODUCTION In industrial plants, viscosity measurements serve to determine the resistance of fluids to flow, define the behavior of various concentrations of slurries, or measure the molecular weight of polymers. Absolute viscosity is the ratio of applied stress to resulting shear velocity, as kinematic viscosity is absolute viscosity divided by density. Viscometers are available to evaluate these and other characteristics in the laboratory and on line in a producing plant environment. Sections 8.62 through 8.64 deal with viscosity measurement. This section provides some general orientation on viscometer selection and application, Section 8.63 discusses laboratory units, and Section 8.64 covers industrial viscometers. In addition, the reader is referred to the related detectors that measure consistency (Section 8.18) and molecular weight (Section 8.35). This section begins with the discussion of viscous behavior as it is governed by the laws of Stokes and Hagen Posieuille. This is followed by an orientation table that provides guidelines to assist the reader in the selection and application of viscometers, in the form of a listing of the features and capabilities of both laboratory and industrial viscometers. Finally, the section is concluded with some definitions of terms and units that are used in connection with viscometry and with definitions of the different types of viscous behavior exhibited by industrial fluids. F FIG. 8.62a Viscosity is a fluid property that describes the amount of deformation (V/L) that will result from a particular shear (F/A) that is applied to the fluid. resistance offered by the fluid, termed its viscosity. For gases and newtonian liquids at constant pressure and temperature, this resistance to deformation is called absolute viscosity. The viscosity of non-newtonian fluids varies, even when the static pressure and temperature are fixed, because it also changes as a function of the applied shear stress. In some cases, viscosity may also vary with duration of the applied shear stress. The viscosity of non-newtonian fluid therefore is frequently called apparent viscosity. STOKE S LAW L V MOVING PLATE LIQUID LAYER STATIONARY PLATE F µv F/A = : µ = A L V/L Stoke s falling ball principle, published in 1851, was based on his investigations of spheres falling through liquids. F THEORY OF VISCOUS BEHAVIOR Viscosity is a fluid property that defines the fluid s behavior when in motion. Because a fluid is a substance that is in a state of continuous deformation when subjected to a shear stress (Figure 8.62a), the rate of that deformation is a function of the 1700 ρ ρ υ = 2r 2 ( g S L) pµ ν = terminal velocity of fall, cm/sec r = radius of sphere, cm ρ s = density of sphere, g/cm (1)

2 8.62 ViscometersApplication and Selection 1701 ρ L = density of liquid, g/cm 3 g = gravity, cm/sec 2 µ = coefficient of viscosity, poise Hagan Poiseuille Law Capillary viscometers measure viscosity by detecting the flow or the pressure drop of newtonian process liquid through a capillary under isothermal laminar flow conditions. According to the Poiseuille law, the pressure drop of a newtonian liquid passing through a capillary tube is directly proportional to its viscosity if the fluid s temperature and flow rate are kept constant. µ = (Kd 4 P)/VL 8.62(2) µ = absolute viscosity, centipoise K = a constant d = inside diameter of a capillary tube, inches P = pressure drop across the capillary tube, PSI V = flow rate, GPH L = length of the capillary tube, inches Kinematic Viscosity The capillary-tube viscometer can detect the kinematic viscosity in stokes by measuring both the pressure gradient and the volumetric flow rate in a cylindrical tube of precisely known dimensions. The following equation describes the Hagen Poiseuille law, which governs the flow of fluids through capillaries: υ = kinematic viscosity, stokes (cm 2 /sec) µ = absolute viscosity, poises (dyne-sec/cm 2 ) ρ = density of liquid, g/cm 3 g = acceleration due to gravity, cm/sec 2 h = vertical distance between ends of capillary, cm R = radius of capillary, cm L = length of capillary, cm V = volume of liquid flowing, cm 3, in time t, sec Intrinsic Viscosity µ π υ = = ghr 4 t ρ 8VL 8.62(3) To determine molecular weight of a polymer, the intrinsic viscosity or limiting viscosity must be determined (Figure 8.62b). Intrinsic viscosity [η] is defined by the relationship, η η η 0 [ η] = lim = lim c 0 η c c 0 c 0 η η η = 0 sp η 0 sp 8.62(4) 8.62(5) [η] X FIG. 8.62b Viscometer calibration relates intrinsic viscosity to molecular weight. η = viscosity of the solution η 0 = viscosity of the solvent c = solution concentration in grams per milliliter or grams per deciliter Another definition of intrinsic viscosity is 8.62(6) Intrinsic viscosity is related to molecular weight as expressed by the Mark Houwink equation, 8.62(7) K and a are constants for a given polymer-solvent system at the temperature of the viscosity measurement. Non-Newtonian Fluids log [η] = log K + a log M a = Y = X log (0.2) = log K log 10 4 ( 0.70) = log K (4) log K = K = Y MOLECULAR WEIGHT In ηη / 0 [ η] = lim c 0 c a [ η] = KM or log [ η] = log K + a log M The resistance to deformation (or viscosity) of Newtonian substances is constant as the shear rate (velocity gradient) changes, if other such variables as temperature and pressure are also constant. Their shear stress is a linear function of the shear rate they experience while undergoing continuous deformation. Non-Newtonian fluids do not have such a linear relationship between shear stress to shear rate, even under constant pressure and temperature. The viscosity of non-newtonian fluids varies as a function of shear rate and, in some cases, it also varies as a function of time. Therefore, one cannot speak of the viscosity of a non-newtonian fluid without specifying the shear stress or the velocity gradient (shear rate) at

3 1702 Analytical Instrumentation FORCE SHEAR STRESS (4) (6) (5) (1) (2) (3) FLOW SHEAR RATE (VELOCITY GRADIENT) NEWTONIAN FLUID-(I) (WATER, MOST OILS, SALT SOLUTIONS) (2) PSEUDOPLASTIC (SHEAR THINNING) (PAPER PULP, CATSUP) (3) DILATANT (SHEAR THICKENING) (STARCH, QUICK SAND) (4) PLASTIC SOLID (CHEWING GUM, TAR) (5) THIXOTROPIC (ASPHALTS, LARD, SILICA GEL) (6) RHEOPECTIC (SHEAR THICKENING) GYPSUM IN WATER VISCOSITY (3) (4) (1) (2) (5) FLOW SHEAR RATE (VELOCITY GRADIENT) (6) FIG. 8.62c The viscosity and shear stress of Newtonian and non-newtonian fluids when these fluids are deformed at various shear rates (velocity gradients). which the resistance to deformation is of interest. Consequently, the viscometers used to measure non-newtonian substances must be provided with accurate means of detecting the velocity gradient. Newtonian Fluids Figure 8.62c illustrates the behavior of newtonian and non-newtonian fluids. When a fluid is newtonian (curve 1 in Figure 8.62c), its viscosity is unaffected by share rate (flow velocity), and the relationship between force (stress) and resulting flow (velocity) is linear. Some of the newtonian fluids include gasoline, kerosene, mineral oils, water, and salt solutions in water. Pseudoplastics Pseudoplastics (curve 2) are shear-thinning materials whose apparent viscosity drops as flow (shear rate) rises. Some such substances exhibit a yield stress above which the apparent viscosity drops, so that a unit increase of driving force results in more and more flow. Pseudoplastic materials include catsup, paper pulp, and printer s ink. Dilatant Fluids Dilatant (curve 3) materials are shear-thickening substances. Their apparent viscosity increases as the flow (shear rate) rises, and more and more stress (force) is required to obtain the same increase in flow. Dilatant materials include quicksand, starch, peanut butter, and many candy compounds. Plastic Solids Plastic solids (curve 4) are true plastics in the sense that they normally behave like solids, but, when the shear stress (force) reaches their yield point, they start to behave as viscous fluids and start to cold flow. Most plastics, chewing gum, tar, and some oils exhibit this behavior. Thixotropic Materials Thixotropic materials (curve 5) are usually pseudoplastics (shear-thinning substances), but they exhibit hysteresis. They seem to remember their past history and, for example, when reagitated will require less horsepower than was required during the first agitation. Thixotropic substances include asphalt, lard, silica gel, most paints, glues, and fruit juice concentrates. Rheopectic Substances Rheopectic substances (curve 6) also display hysteresis, but, instead of a shear-thinning behavior, they display shear thickening. Their viscosity appears to increase, and some will set after some duration of agitation. Gypsum in water, for example, behaves in this manner. Apparent Viscosity Readings It is important to understand that the apparent viscosity of many different substances depends on the design of the viscometer that is measuring it. Each viscometer exposes the process sample to a different experience in terms of shear stress and shear velocity, so non- Newtonian substances will register different apparent viscosity readings. In process control, this is not a serious problem, because one is likely to use the same viscometer all the time, and we are not interested so much in the absolute viscosity of the product as in making the same product one day to the next. On the other hand, when viscosity specifications are passed on from one plant to another, it is essential that the viscometer used in making the measurement be specified. Conversion among Units of Viscosity Newton s hypothesis defines absolute viscosity of fluid as shear stress shear stress absolute viscosity = = shear rate velocity gradient FAg = ( / ) c, ( ul / ) poise 8.62(8)

4 8.62 ViscometersApplication and Selection 1703 TABLE 8.62d Viscosities of Different Materials in Different Units of Viscosity, Measured at Constant Temperature of 70 F (23 C)* Saybolt Universal (SSU) Centistokes (cst) Centipoise a (cp) Typical 70 F b Water Kerosene No. 2 fuel oil No. 4 fuel oil Transformer oil Hydraulic oil SAE 10W oil SAE 10 oil 1, SAE 20 oil 2, SAE 30 oil 5,000 1, SAE 50 oil 10,000 2,200 1,760 SAE oil 50,000 10,800 8,640 Molasses B a Centistokes specific gravity = centipoise. Specific gravity is assumed to be 0.8 except in the case of water. b Use actual specific gravity for liquid in question. * Courtesy of Cole-Parmer Instrument Co. TABLE 8.62e Conversion between Centipoise (cp) and Other Units of Absolute Viscosity Name (Definition) Abbreviation Value Equivalent to 1 cp kgf-sec/m kgm/m-hr 3.6 lbf-sec/ft lbf-sec/in lbm/ft-sec lbm/ft-hr 2.42 lbm/in.-sec Pascal-seconds (N-sec/m 2 ) Pas Poises Ps 0.01 Poiseuille (N-sec/m 2 ) PI F = total load force, gram force A = area of plate, cm 2 l = thickness of fluid between plates, cm u = velocity, cm/sec g c = Newton s acceleration caused by gravity, (gram mass) (cm)/(sec 2 ) (gram force) For the viscosity of common liquids in a variety of units, see Table 8.62d, and refer to Table 8.62e for conversion factors between centipoise (cp) and other units of absolute (dynamic) viscosity. For additional viscosity conversion tables and charts, refer to Tables A.2p, A.2q, and A.2r in Appendix A.2. Kinematic Viscosity The value of the kinematic viscosity (in cm 2 /sec units) can be obtained approximately from the indications of the following viscometers (which all give their readings in seconds) by the associated equations. Saybolt Universal, when 32 < t < 100, υ = t 1.95/t when t < 100, υ = t 1.35/t Saybolt Furol, when 25 < t < 40, υ = t 1.84/t when t > 40, υ = 0.216t 0.60/t Redwood No. 1 (English), when 34 < t < 100, υ = t 1.79/t when t > 100, υ = t 0.50/t Redwood Admiralty (English), υ = 0.027t 20/t Engler (German), υ = t 3.74/t While the kinematic viscosity unit of stokes are not much used anymore, one stoke is equivalent to 100 centistokes (cst), or ft 2 /sec, or m 2 /sec. VISCOMETER SELECTION AND APPLICATION Table 8.62f, which is an orientation table, lists all available viscometers and compares the features of the various designs to assist the reader in selecting the right one for the application at hand. When several choices appear to be acceptable for a particular application, the reader is advised to read about each in the following sections before making the final selection. Section 8.63 covers the laboratory-type viscometer designs, and Section 8.64 describes the industrial in-line detectors. Selection In selecting a viscometer for a specific task, the following should be determined: 1. Is this instrument for laboratory use or for continuous measurement in the plant for control? 2. What type of materials will this viscometer handle? a. Highly volatile? Closed system needed? b. Newtonian fluids, non-newtonian fluids, or both? c. Rheological characteristics of the materialplastic, thixotropic, dilatant, etc.

5 TABLE 8.62f Orientation Table for Industrial Viscometers Application Laboratory Industrial Features Provides Continuous Signal In-line Device Laboratory Device Local Readout Remote Readout Trans. Temp. Compensation Gas Fluids Newtonian Non-Newtonian Maximum Design Pressure, PSIG. (1 Bar = 14.2 PSI) Maximum Design Temperature, F ( C = [ F 32]/1.8) Inaccuarcy (±%) (1) Based on Full Scale (2) Based on Measurement Type of Design Bubble time Manual (2) 13 CC Capillary tube Manual timing (2) 20 CC Auto timing (2) 20 CC Capillary Influx efflux (2) 0.7 CC extrusion 5, (2) 30 CC Efflux cup Saybolt (2) 60 CC Ford cup (2) 150 CC Zahn cup (2) 44 CC Auto timing (2) Falling ball Falling needle Rotational Manual Automatic Manual Automatic Coaxial-cylinder 15,000 ATM 20, (2) 0.1 1(2) 0.5 1(2) 0.5 1(2) 1.0(2) 2.0(1) Minimum sample Size or Flow Rate 30 CC 70 CC 2 10 CC 2 10 CC CC Cone and plate (2) 0.1 CC Piston Travel time 10, (2) In-line Continuous capillary Falling element Float Oscillating Differential pressure Back pressure Ball or slug Piston Single float Two-float Concentric Blade Piston Torsional ,000 5, (1) 4.0(2) 2 4(2) 2 4(2) 2.0(2) 2.0(2) 1 4 GPH 1 GPH GPM GPM 2 GPM Up to 6.5 fps (2 m/s) Applicable Viscosity Ranges Centipoises Analytical Instrumentation Plastometer Cone and plate Kneader Capillary 100 5, (1) 2.0(1) 25 CC 80 CC 0.6 #/HR Arbitrary Units Are Used Mooney % Scale MI & CIL Points 0 1,000 Division and Rotational Cone disc sphere Agitator power Double cylinder 1, ~5.0(1) Vibrational Reed 3, Normal Range. With Special Modifications

6 8.62 ViscometersApplication and Selection 1705 d. Corrosiveness of the fluids e. Does the fluid contain solids? What are the special characteristics of this slurry or emulsion? Plastic, thixotropic, dilatant, etc.? f. What are the operating temperatures and pressures of the fluids? g. Do the sample composition and/or viscosity (due to reaction or time lag) change with time? Is a low lag time for manual sampling and testing sufficient, or is on-stream measurement essential? h. What is the relationship between viscosity and operating temperature? 3. Area classificationdoes the viscometer need to be explosion proof? 4. What are the viscosity ranges to be measured? 5. What levels of accuracy (maximum error allowable), sensitivity, and repeatability (for continuous process viscometer) are required? 6. What special features are needed? a. Remote indication or recording b. Automatic operation c. Automatic closed-loop control d. Temperature compensating system 7. What is the viscometer response time requirement? 8. What are the flow conditionslaminar or turbulent? Applications A viscosity measurement can be of value for one of the following two reasons: 1. It is very difficult to size a pump, pipeline, orifice meter, or agitator without knowing the viscosity of the process fluid. In any operation liquids are used (spraying, coating, or dipping processes), the viscosity of the fluid determines the effectiveness of the process and the quality of the finished product. In short, viscosity is one of the most important process properties. 2. Viscosity readings can vary as a function of other process variables. These include molecular weight and its distribution in polymers, lubricating oils, and other substances, as well as the concentration, specific gravity, color, size, shape, and distribution of solids in a slurry or in an emulsion. All of these can cause viscosity variations. Viscometers can be used for several purposes, primarily (1) to ensure that the finished product meets specifications, (2) to perform routine laboratory testing, (3) for scientific research, and (4) for in-line process control. Each is described briefly below. Finished Product Specification For such applications, the appropriate type of viscometer has been specified by industry standards for product testing. Test procedures should be carefully followed and test results correctly reported. Routine Laboratory Testing Simple-to-operate, easy-to-clean and direct-reading viscometers should be considered for this purpose. The coaxial-cylinder type viscometer is well suited, because it is inexpensive and meets most of the above requirements. The efflux-cup viscometer is recommended for field laboratory testing work. If the available sample size is small (less than 1 cc), then modified coaxial-cylinder or cone-andplate rotating viscometers should be considered. Scientific Research Study For scientific research purposes, accuracy and versatility should be the main selection considerations. Cone-and-plate rotational viscometers are the most versatile units but are also the most expensive. If extreme accuracy is desired, consider the automatic capillary-tube viscometer (See Figure 8.62g). If it is important to record the results to maintain a permanent record, both of the previously mentioned viscometers have the appropriate capability. For the measurement of gas and vapor viscosity, the falling-ball viscometer is the best option. In-Line Process Control In selecting an in-process viscometer, cost, repeatability, sensitivity, construction materials, reliability, response time, and ease of cleaning should all be considered. Vibrating-reed viscometers are successfully used in the polymer industry. Rotating-cone and agitator power viscometers have been successfully employed in the paper industry. Continuous capillary viscometers are widely applied in the petroleum industry. The manufacture of synthetic rubbers and certain plastics would be almost impossible without the plastometers. Continuous viscometers are reliable. Viscosity measurement need not be an expensive and time-consuming operation. Continuous in-line viscometers are available to satisfy most process needs. Even such unique applications as the measurement of the viscosity of molten steel can be handled. Viscometer signals can be readily sent over digital networks and be accepted by process computers, which can calculate other related fluid properties or perform closed-loop control. TERMINOLOGY Absolute (dynamic) viscosity (µ). Constant of proportionality between applied stress and resulting shear velocity (Newton s hypothesis). Apparent viscosity. Viscosity of a non-newtonian fluid under given conditions. Same as consistency. Consistency. Resistance of a substance to deformation. It is the same as viscosity for a newtonian fluid and the same as apparent viscosity for a non-newtonian fluid. Fluidity. Reciprocal of absolute viscosity; the unit in the cgs system is the rhe, which equals 1/poise.

7 1706 Analytical Instrumentation FIG. 8.62g A single process viscosity system can measure absolute (kinematic or dynamic), relative, reduced, and intrinsic viscosities as well as viscosity index. (Courtesy of Brinkmann Instruments Inc.) Hagen-Poiseuille law (flow through a capillary), Q= π R4 ( P P2 ) 8µL (9) Kinematic viscosity (υ). Dynamic viscosity/density = υ = µ/ρ. Pascal-second (Pas). Internationally accepted unit of 2 absolute (dynamic) viscosity. Pas = newton-sec/m = 10 poise = 1000 centipoise. Poise (µ). Unit of dynamic or absolute viscosity (dyne2 sec/cm ). Poiseuille (Pi). Suggested name for the new international standard unit of viscosity, the pascal-second. Relative viscosity. Ratio of absolute viscosity of a fluid at any temperature to that of water at 20 C (68 F). Because water at this temperature has a µ of cp, the relative viscosity of a fluid equals approximately its absolute viscosity in cp. Because the density of water is 1, the kinematic viscosity of water equals ctks at 20 C. Saybolt furol seconds (SFS). Time units referring to the Saybolt viscometer with a Furol capillary, which is larger than a universal capillary. Saybolt universal seconds (SUS). Time units referring to the Saybolt viscometer. Saybolt viscometer (universal, furol). Measures time for given volume of fluid to flow through standard orifice; units are seconds. Shear viscometer. Viscometer that measures viscosity of a non-newtonian fluid at several different shear rates. Viscosity is extrapolated to zero shear rate by connecting the measured points and extending curve to zero shear rate. Specific viscosity. Ratio of absolute viscosity of a fluid to that of a standard fluid, usually water, both at same temperature. 2 Stoke. Unit of kinematic viscosity υ (cm /sec). Stress. Force/area (F/A). Velocity gradient (shear). Rate for change of liquid velocity across the streamv/l for linear velocity profile and dv/dl for nonlinear velocity profile. 1 Units are V L = ft/sec/ft = sec. Bibliography Bandrup, J. and Immergut, E., Polymer Handbook, 3rd ed., John Wiley & Sons, New York, Basker, V. R. et al., Evaluation of an online torsional oscillatory viscometer for kraft black fluid, Paperi ja Puu/Pulp and Timber, 82(7), October Bourne, M. C., Food Texture and Viscosity Concept and Measurement, Academic Press, New York, Dealy, J. M., Viscometers for online measurement and control, Chem. Eng., October 1, Dutka, A. P. et al., Evaluation of a capillary-coriolis instrument for online viscosity and density measurement, Proc. TAPPI Process Control, Electrical and Instrumentation Conf. (ISA), March Hallikainen, K. E., Viscometry, Instrum. Control Sys., November Helle, H. et al., Comparing a 10 MHz thickness-shear mode quartz resonator with a commercial process viscometer, Sensors and Actuators B (Chem.), B81(2 3), January Krigman, A., Viscosity measurement: still sticky, but stepping ahead steadily, InTech, November Langer, G. and Werner, U., Measurements of viscosity of suspensions in different viscometer flows and stirring systems, Ger. Chem. Eng., August 1981.

8 8.62 ViscometersApplication and Selection 1707 Mansion, D., State of the art in transducers viscometer, Nouvel Automatisme (France), June Matuski, F. J. and Scarna, P.C., Instrument makes on-line viscosity control of slurries possible, Control Eng., 28(13), Mizier, M. O., The measurement of the viscosity of liquids, Mesures (France), March Rabinovich, V. A. et al., Viscosity and Thermal Conductivity of Individual Substances, Begell House, New York, Roussel, G. and du Parquet, J., Development of a fully automatic viscometer, Society of Automatic Engineers, Paper #82149, Warrendale, PA, October Sheble, N., How do you like your mashed potatoes? InTech, June Skeist, I., Handbook of Adhesives, 3rd ed., Van Nostrand Reinhold, New York, Spearot, J. A., Ed., Oil Viscosity: Measurement and Relationship to Engine Operation, ASTM, Steltzer, W. D. and Schulz, B., Theory and measurement of the viscosity of suspensions, High Temp.High Press., 15(3), , Viscometers, Meas. Control, June Walsh, L., Quality Management Handbook, Marcel Dekker, New York, Wunderlich, T., Ultrasound pulse doppler method as a viscometer for process monitoring, Flow Meas. Instrum., 10(4), Zhang, Z. et al., Viscosities of lead silicate slags, Miner. and Metall. Process., 19(1), February 2002.