Efflux Cup  Reprint 142  NAPIM Studies Show Zahn Is Least Accurate Efflux Cup      By Jean S. Lavelle, NIPRI Staff, Lehigh...
Efflux Cup  Reprint 142   [The Zahn cup]      reproducibility of test results shown in      Shell Cup                     ...
Efflux Cup  Reprint 142                            In addition to the better precision of the     differences among cups, ...
Efflux Cup  Reprint 142                     Conversion of drain time to viscosity         Influence of Temperature        ...
Efflux Cup  Reprint 142                    mentioned comment by Bates [1982]             Figure 9 shows that all of the wa...
Efflux Cup  Reprint 142  References                                                            Rodriquez, R., Principles o...
Efflux Cup  Reprint 142  the shear stress and shear rate are at a maximum, and the             For very accurate results, ...
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14.1.10 (09) NAPIM Study

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NAPIM studies show Zahn is the least accurate Efflux Cup, this is a study showing the Shell should be the Efflux Cup of choice when attempting to characterize the flow properties of a series of water based inks or other systems involving significant differences in surface tension.

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14.1.10 (09) NAPIM Study

  1. 1. Efflux Cup Reprint 142 NAPIM Studies Show Zahn Is Least Accurate Efflux Cup By Jean S. Lavelle, NIPRI Staff, Lehigh University Reprinted with Permission from Flexo, June 1988 Efflux cups are important tools for adjusting and controlling the important to note that the drain time is particularly sensitive to the flow properties of gravure and flexographic inks. Ely [1980] radius of the orifice. stressed the economic importance of obtaining correct ink dilutions; his data indicated that a one second rise in drain time, Efflux cups were developed as inexpensive robust alternatives 18 instead of 17 seconds, can increase ink consumption on the to glass capillary viscometers. The difference in features among press by 18 percent using a #2 Zahn and 7.3 percent using a #3 the four major efflux cups will be discussed. Shell. On the other hand, there are cases where two inks having the same Zahn cup reading had completely different printing Ford Cup characteristics [Bates, 1982]. The Ford cup was developed in the 1920’s for thinning automotive paints. As seen in the schematic in figure 2(a), it The National Association of Printing Ink Manufacturers (NAPIM) consists of a hollow cylinder with a conical base, small orifice has commissioned its research arm, the National Printing Ink and a stubby capillary with a 100-degree conical entrance. It is Research Institute (NPIRI), to undertake a scientific study of the normally filled by pouring the liquid into the cup. Although the printability of flexographic inks. A study of the flow properties of precision of test measurements is reasonable (see table 1), it has the inks by efflux cups and other appropriate instruments is an not been widely adopted by the ink industry. essential part of the program. Zahn Cup This article summarizes the results of the experiments in the The Zahn cup, which is filled by dipping into the liquid, was NPIRI laboratories. It also encompasses a brief literature search developed in the 1930’s for quality control of varnishes. As on the four major efflux cups — the Ford, Zahn, Shell and ISO. shown in figure 2(b), the capillary length corresponds to the The major intent is to present the limitations of these deceptively thickness of the wall, about 2 mils or 0.05 mm. simple devices and to give the reader an appreciation of the numerous factors that influence their performance. Topics to be The short capillary coupled with the simple design makes the discussed are: Zahn cup not only easy to clean but also inexpensive. It is A. The design of efflux cups undoubtedly for these reasons that it has grown to be the most B. Laboratory experiments with Zahn and Shell cups popular efflux cup in use not only throughout the paint and 1. Calibration varnish industries but also in the flexo and gravure industries. 2. Influence of surface tension 3. Influence of temperature These same features in the Zahn present serious flow problems. 4. Effect of shear rate According to Owczarek [1968], the untapered entrance does not allow formation of a parabolic flow pattern. Instead, the fluid Design of Efflux Cups contracts as it enters the short capillary and a portion splits off Efflux cups are variations of a capillary and forms eddies along the wall (see figure 3). Owczarek also viscometer, which is intended to states that the flow pattern is dependent upon the surface determine the viscosity of Newtonian tension of the liquid. Patton [1979] arrived at a similar conclusion. fluids by measuring the time required for the liquid to drain. The force pushing the In addition, the stream of fluid does not exhibit a sharp break as liquid through the capillary and the drain the cup empties (see figure 4). This “dribbling” makes it difficult time is related to a number of parameters to time the endpoint and probably contributes to the poor which are described in detail in the accompanying article. For the purpose of this discussion, it is important to note that the basic equations assume a parabolic flow profile, such as illustrated in figure 1. This requirement can be met only with a Figure 1. Parabolic flow sufficiently long capillary. It is also profile of Newtonian fluid through capillary. Figure 2. Schematic diagram of Ford, Zahn, Shell, and ISO efflux cups. RP142_Page1NORCROSS Corporation 255 Newtonville Avenue Newton, MA 02458 USA 14.1.10 (09)Telephone 617 969 7020 Fax 617 969 3260 Email sales@viscosity.com On the Internet www.viscosity.com
  2. 2. Efflux Cup Reprint 142 [The Zahn cup] reproducibility of test results shown in Shell Cup table 1, obtained when one cup was Like the Zahn, the Shell cup is a dip-type efflux cup. As seen in has grown to be circulated. figure 2(c), it has a longer capillary than the Zahn (25 mm vx. 0.05 mm) which improves the smoothness of flow [Mewis, 1980] and Another problem is that since drain time increases the probability of obtaining a parabolic flow profile. the most is inversely proportional to the fourth However, the untapered entrance to the capillary can present the power of the radius, minor variations in same problems of turbulent flow and surface tension popular efflux orifice size lead to poorer reproducibility dependency as with the Zahn cup. when different cups are used [Bagnall, cup in use not 1982; Knorps, 1980]. Moreover, cup As seen in figure 4, the endpoint is considerably sharper than on capacity, intended to be 44 mL, actually the Zahn. In turn, the precision of test measurements is much only throughout ranges from 43-48 mL among cups from improved (see table 1). There is only one manufacturer and the several manufacturers. volume is always 23 mL. the paint Because of the greater precision, the Gravure Technical and varnish Association [Vomacka, 1968] recommended that the Shell cup be adopted as the industry standard. However, the change from industries but the Zahn to the Shell has not been accomplished to any great degree. A similar situation exists in the flexo industry [Bagnall, also in the flexo 1982]. and gravure ISO Cup In order to solve some of the problems which evolved from industries. attempts to use a variety of flow cups as viscometers for complex fluids, the International Standards Organization (ISO) in 1965 authorized a task group to design an international flow cup. The rationale for the final design of the cup has been described in detail by McKelvie [1970]. As seen in figure 2(d), key features of the ISO cup include the 120-degree angle of the conical entrance and a 2 mm capillary. McKelvie also stressed the importance of smoothness of the interior surface. Particularly germane is the fact that the ISO cup Figure 3. Flow in duct with sudden has the best precision of the four cups (see table 1). contraction of its cross-section. Experiments with Zahn and Shell Cups Calibration The reliability of test results can only be judged by cup performance during calibration. The importance of calibration has been stressed by Euverard [1948, 1950], McKelvie [1970], and Patton [1979], and both the ASTM and ISO test methods require this procedure. TABLE 1. PRECISION OF EFFLUX CUPS Single-operator Interlaboratory Original Cup Test Method Repeatability Reproducibility Year (% relative) (% relative) Ford ASTM D1200 1952 8 20 Zahn ASTM D4212 1982 11* 33* Shell ASTM D4212 1982 9 18 ISO ISO 2431 1980 5 10 Figure 4. High speed photographs of * using identical cups. endpoint on Zahn cup (top) and Shell cup (bottom). RP142_Page2NORCROSS Corporation 255 Newtonville Avenue Newton, MA 02458 USA 14.1.10 (09)Telephone 617 969 7020 Fax 617 969 3260 Email sales@viscosity.com On the Internet www.viscosity.com
  3. 3. Efflux Cup Reprint 142 In addition to the better precision of the differences among cups, a calibration chart relating drain time to Shell, illustrated by results in table 1, kinematic viscosity should be constructed for each cup. another indication of the superiority of Shell cups over Zahn cups came from Figure 6 illustrates that drain times of Newtonian oils in the Shell calibration studies in the NPIRI cup are much more sensitive than in the Zahn to changes in Therefore, laboratories. The calibration was sample viscosity. Note also that the plot line for the Zahn does conducted with standard Newtonian oils not go through zero, indicating that a correction factor is needed the on a total of nine cups using the to account for turbulent flow [Euverard, 1950]. procedure described in ASTM Test relationship Method D-4212. It should be pointed out that the only available standard fluids are oils, most of which have viscosities giving drain times beyond between drain Results indicated that essentially no the recommended range for a particular cup. A more serious correction was required for the Shell problem is that their wetting characteristics are different from time and cups tested (#2, #3, and #4). The those of typical liquid inks. Therefore, the relationship between correction factor for the Zahn cups (#2 drain time and viscosity obtained with one type of fluid may not viscosity and #3) averaged about 1.25 with a 100 be applicable to other types of fluids [McKelvie, 1970; General cp oil and 1.45 with a 29 cp oil. The Electric, 1981]. obtained with correction factor for a #1 Zahn exceeded 2.0 with the latter oil. Even when the efflux cup is being used for quality control of one type of established formulations, a calibration procedure is necessary to Figure 5 illustrates, in addition, that the detect differences in dimensions among cups, e.g. between the fluid may not good agreement between the viscosities supplier’s and the customer’s, and also to follow changes in cup calculated from the Shell and the actual performance due to dents, scratches or wear with use. be applicable viscosities extended over temperatures ranging from 20 to 30°C. On the other Influence of Surface Tension to other types hand, the Zahn always gave calculated In order to determine the extent to which wetting characteristics viscosities considerably less than the influence efflux cup results, experiments were conducted with of fluids. true viscosities. Note also that the aqueous isopropanol (IPA) solutions varying in surface tension agreement between the Shell and actual from 72 (pure water) to 21 (pure IPA) dynes per centimeter. viscosities was further improved when Surface tension as a function of IPA concentration is plotted in the sample was free of air bubbles. figure 7(a). Figure 7(b) shows that as the IPA concentration increased the drain times on the Zahn decreased slightly while The conversion from drain time to those on the Shell increased slightly. viscosity was calculated by Patton’s equations [1979], which assume that all Figure 6. Calibration curves for #3 Zahn and #4 Shell cups cups of the same type and model have the same dimensions. To take into using Cannon standard oils S-20, S-60, and S-200. consideration that there are likely Figure 5. Viscosity of Cannon standard oil S-20 on Zahn and Shell cups as function of temperature. RP142_Page3NORCROSS Corporation 255 Newtonville Avenue Newton, MA 02458 USA 14.1.10 (09)Telephone 617 969 7020 Fax 617 969 3260 Email sales@viscosity.com On the Internet www.viscosity.com
  4. 4. Efflux Cup Reprint 142 Conversion of drain time to viscosity Influence of Temperature using Patton’s equations revealed that ASTM Test Method D-4212 requires that the sample temperature the Zahn, as seen in figure 7(c), gave a either be maintained at 25°C or be recorded to 0.1°C for viscosity/IPA concentration plot very calibration and 1°C for general testing. The procedure suggests similar to that of the surface tension plot construction of a temperature correction curve for each liquid by . . . the Shell in figure 7(a). On the other hand, the plotting drain time as a function of sample temperature over the Shell curve showed a maximum in expected temperature range. The instructions also specify should be the viscosity at about 50% IPA. More immersion of the cup in the sample for at least five minutes to importantly, the Shell curve shape reach sample temperature. For the more volatile inks, efflux cup of matched that from the Brookfield considerable evaporation and settling could occur during this viscometer. The Brookfield data are period. choice when identical to those reported by Patton [1979]. In the following experiments, one solvent-based and two water- attempting to based commercial flexographic inks were diluted to a #2 Zahn The results in figure 7 suggest that the cup reading of 21 ± 0.5 at 25°C (78°F) and then equilibrated at 20 characterize drain times on the Zahn cup are highly (68°F) and 30°C (86°F). Drain times were measured on the #2 sensitive to surface tension of the test Zahn and the #3 Shell at the three temperatures. the flow fluid while those on the Shell are not. In other words, the Shell should be the The results plotted in figure 8 indicate that, on both cups, the properties of efflux cup of choice when attempting to change in drain time per degree Celsius varies widely from one characterize the flow properties of a ink to another. For a specific ink, the drop in drain time with a series of series of water-based inks or other increasing sample temperature is much greater on the Shell than systems involving significant differences on the Zahn. These results are not surprising, considering that water based in surface tension. the calibration curves in figure 6 had indicated a greater sensitivity of the Shell drain times to changes in viscosity. inks or other In addition, data in figure 8 clearly illustrate the ability of the Shell systems to differentiate among inks that exhibited essentially the same drain time on the Zahn at 25°C. These results confirm those involving reported by Bagnall [1982] and may explain the previously significant Figure 8. Drain times for three water or solvent based flexographic differences in inks at 20, 25, 30°C on Zahn #2 and Shell #3 cups. surface tension. Figure 7. Viscosity of aqueous isopropanol solutions varying in surface tension measured on Zahn #2 and Shell #2 cups and on Brookfield viscometer. RP142_Page4NORCROSS Corporation 255 Newtonville Avenue Newton, MA 02458 USA 14.1.10 (09)Telephone 617 969 7020 Fax 617 969 3260 Email sales@viscosity.com On the Internet www.viscosity.com
  5. 5. Efflux Cup Reprint 142 mentioned comment by Bates [1982] Figure 9 shows that all of the water based inks tested decreased that inks having the same Zahn cup in viscosity as shear rates increased, in this case from 10 to 1000 reading performed differently on the sec-1. In limited studies at low shear rates, solvent-based inks press. exhibited much the same shear thinning properties as did The Shell cup aqueous inks. Note also in figure 8 that the order in is preferred which the inks are ranked for drain time Figure 9 also illustrates that some inks are more shear thinning is different at 30°C than at 25°C. than others. Such tendencies can be detected only from over the Zahn According to Stevko [1984], operating measurements from at least two different shear rates. On efflux temperatures on a gravure press may cups, shear rate varies across the diameter of the capillary. An cup because reach as high as 50°C (122°F). approximate shear rate can be calculated for a Newtonian fluid Therefore, it may be advantageous to [Rodriquez, 1982]. The calculated shear rate for a 25 cp fluid on certain design make efflux cup measurements at press the #3 Shell is approximately 300 s-1. Estimated shear rates on temperatures and at those normally operating presses are well in excess of 1000 s-1. features of recommended in test methods. Irrespective, the sample temperature Because of the shear thinning nature of liquid inks, the equations the Shell should always be reported along with relating drain time to viscosity no longer apply [McKelvie, 1970; the test results. Patton, 1979; Mewis, 1980; Pierce, et al, 1982]. Therefore, test results should be reported as drain times and not in terms of make it more Effect of Shear Rate kinematic viscosity, or if the density is measured, the dynamic Since efflux cups are variations of viscosity. reproducible, capillary viscometers, they have a same basic restriction, namely that drain time Pigmented inks, besides having a complex rheology, present less sensitive can be converted to viscosity only if the unique measuring problems including evaporation, pigment test fluid is Newtonian. (Newtonian flocculation, settling of solids, foaming of water based inks, to surface refers to a fluid whose viscosity does not structure buildup with time and probably wetting differences. change with shear rate.) Results in our laboratory also indicate that ink viscoelasticity tension of the varies with ink composition and degree of dilution and could Although liquid inks are low in viscosity, influence drain time. liquid, and the fact that they are pigmented polymer solutions inherently indicates that they Conclusions better able to are rarely Newtonian but are usually 1. A literature search and laboratory results clearly illustrate the shear thinning. Confirming evidence complexity and limitations of efflux cup measurements and differentiate was provided by measurements at a the careful control required to obtain correct data even on variety of shear rates on the Brookfield simple Newtonian fluids. among test viscometer and the Bohlin rheometer, 2. Of the four efflux cups studied, the ISO is most precise and the both of which are rotational viscometers. Zahn is least precise. fluids having 3. The Shell cup is preferred over the Zahn cup because certain design features of the Shell make it more reproducible, less different flow sensitive to surface tension of the liquid, and better able to differentiate among test fluids having different flow properties. properties. 4. Construction of calibration curves with standard oils is necessary to detect differences among cups of the same type and model and changes that occur with use. 5. The reporting of drain times must include the sample temperature and the cup type and model. Useful information can be derived by measuring drain times at room and at press temperatures. 6. Liquid inks exhibit varying degrees of non-Newtonianism and, for these reasons, drain times cannot be converted to viscosity. Figure 9. Viscosity of four water based flexographic inks at 25°C on the Brookfield viscometer at 10 s-1 and the Bohlin rheometer at 100 s-1 and 1000 s-1. RP142_Page5NORCROSS Corporation 255 Newtonville Avenue Newton, MA 02458 USA 14.1.10 (09)Telephone 617 969 7020 Fax 617 969 3260 Email sales@viscosity.com On the Internet www.viscosity.com
  6. 6. Efflux Cup Reprint 142 References Rodriquez, R., Principles of Polymer Solutions, Second edition, Standard Test Method D1200, “Viscosity of paints, varnishes and McGraw-Hill Book Company, New York, 1982. lacquers by Ford viscosity cup,” Annual Book of ASTM Standards, Vol. 06.01, American Society for Testing and Schramm, G., Introduction to Practical Viscometry, Haake Mess- Materials, Philadelphia, 1952 (82). Technik GMBH-u.-CO, Karlsruhe, W. Germany, 1965. Standard Test Method D4212, “Viscosity by dip-type cups,” Ibid. Stevko, P., “The effect of temperature on ink fountain solution 1982. viscosity,” Gravure Research Institute Report, No. M-273, New York, 1984. Bagnall, K., “Viscosity control of flexographic ink,” Boxboard Containers, June 1983. VanWazer, J.R., J.W. Lyons, K.Y. Kim, and R.E. Colwell, Viscosity and Flow Measurement, Wiley-Interscience, New York, 1963. Bates, J.B., “Printing ink research — a vital resource,” American Ink Maker, Vol. 60, No. 12, 1982, pp. 22, 24, 26, 30. Vomacka, F.N., “Shell and Zahn cups,” Gravure Technical Association Bulletin, Vol. XIX, No. 2, 1968, pp. 122, 123, New Ely, J.K., “Experiments to show ‘Seconds come first’ in waste- York. preventing controls,” American Ink Maker, Vol. 58, No. 10, 1980, pp. 46, 49, 50. Acknowledgement is made of the National Printing Ink Research Institute for support of this work and permission to publish Euverard, M.R., “The efflux type viscosity cup,” Scientific Edition results. Appreciation is also extended to F.J. Micale, J.M. Fetsko of National Pain, Varnish, and Lacquer Association, Washington, andY.P. Lee for technical and editorial assistance; to Jo Evelyn D.C., 1948. Gallagher for her skillful rheological measurements; to Bernadine Dancho for preparing the figures; and to Arlene Toth for typing “Evaluation of empirical viscosity measurements for varnishes the manuscript. and resin solutions,” ASTM Bulletin, No. 169, October, 1950, pp. ␲ dghr 4 t 67-70. ␩ = (1) 8LV General Electric Company, “Instructions for Zahn viscometers,” Publication No. 198 4541K23-001A, Lynn, MA, 1981. Equations Describing Capillary Flow International Standard 2431, “Paint and varnishes — The Hagen-Poiseuille equation (equation 1) describing liquid flow Determination of flow time by use of flow cups,” International in classical fine-bore glass capillary viscometers such as the Organization for Standardization, Geneva, 1980. Ostwald or Ubbelohde is usually applied to efflux cups [Patton, 1979]. The equation is based upon a parabolic flow profile of Knorps, L., “Standardizing Zahn cups,” American Ink Maker, Vo. liquid through the capillary. 58, No. 8, 1980, pp. 20, 21, 50. where: h = dynamic viscosity, centipoise (cp) McKelvie, A.N., “An international flow cup,” Journal of Oil and d = density of fluid, µg/mm3 Color Chemists Assn., Vol. 53, 1970, pp. 92-120. g = gravitational acceleration, 9800 mm/sec2 h = effective hydrostatic head of liquid, related to difference in Mewis, J., “Paints and printing inks,” Chapter 6, Rheometry: vertical height before and after the test, mm Industrial Applications, edited by K. Walters, John Wiley & Sons, r = radius of capillary, mm New York, 1980, pp. 281-338. L = length of capillary, mm T = drain time, seconds (s) Owczarwek, J., Introduction to Fluid Dynamics, International V = volume of flow during time t, mm3 Textbook Company, Scranton, PA, 1968. Patton, T.C., Paint Flow and Pigment Dispersion, Second edition, If the density of the liquid is not known, the measurement yields John Wiley & Sons, New York, 1979. the kinematic viscosity (v). The dynamic viscosity can be obtained by multiplying the kinematic viscosity value by the Pierce, P.E., and C.K. Schoff, “Rheological measurements,” Kirk- density. Othmer: Encyclopedia of Chemical Technology, Vol. 20, Third edition, John Wiley and Sons, New York, 1982, pp. 259-319. At the center of the capillary, the shear stress is zero, the shear rate is zero, and the velocity is at maximum. At the capillary wall, RP142_Page6NORCROSS Corporation 255 Newtonville Avenue Newton, MA 02458 USA 14.1.10 (09)Telephone 617 969 7020 Fax 617 969 3260 Email sales@viscosity.com On the Internet www.viscosity.com
  7. 7. Efflux Cup Reprint 142 the shear stress and shear rate are at a maximum, and the For very accurate results, corrections must also be made for velocity is assumed to be zero. Because the shear rate varies incomplete drainage, turbulence, and possible heat and surface across the diameter of the capillary and the shear stress is tension effects [Pierce et al, 1982]. Corrections are minimized by undefined, these capillaries should be limited to testing using a capillary with length at least 50 times the diameter Newtonian fluids. Non-Newtonian fluids do not produce a [Schramm, 1965] and efflux times longer than 300 s [Pierce et al, parabolic flow profile, which requires modification of the basic 1982]. equation [Rodriquez, 1982]. The correction terms for kinetic energy and end effects are Two corrections are required for processingdata from capillary incorporated into the kinematic viscosity equation (equation 4) viscometers: a kinetic energy correction (K.E.) and a Couette which is theoretically significant but usually shortened to correction (C). Energy is expended as the height of liquid in the equation 5. cup decreases reducing the potential energy of the system. The Hagen-Poiseuille equation assumes that this energy is utilized v = kt - c/t (4) completely in overcoming viscous resistance to flow. A portion, however, is required to set the fluid into motion [Patton, 1979]. v = (t-c) (5) This correction factor becomes extremely important for low viscosity Newtonian fluids and approaches zero for high viscosity fluids. The k and c values for each model Zahn, Shell, Ford and ISO cups appear in the literature [Patton, 1979; ISO, 1980; Pierce et Calculation of the actual viscosity requires inserting a kinetic al, 1982; ASTM, 1983]. The correct values for a specific cup can energy correction term in the basic equation (equation 2). be calculated from calibration curves obtained with standard Newtonian fluids [Euverard, 1950] ␲dghr4 t dV ␩= – 8 ␲ LT (2) 8VL (K.E. term) The Couette correction relating to end effects is described by equation 3 in which NDE is the Deborah number of the liquid. The number is related to the ability of the liquid to recover after being stressed [VanWazer, 1963]. NDE approaches zero for Newtonian fluids and is much greater for clastic fluids. L + N DE r C = (3) L RP142_Page7NORCROSS Corporation 255 Newtonville Avenue Newton, MA 02458 USA 14.1.10 (09)Telephone 617 969 7020 Fax 617 969 3260 Email sales@viscosity.com On the Internet www.viscosity.com

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