14.1.10 (09) NAPIM Study

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Efflux CupReprint 142

By Jean S. Lavelle, NIPRI Staff, Lehigh UniversityReprinted with Permission from Flexo, June 1988

NAPIM Studies Show Zahn Is Least Accurate Efflux Cup

Efflux cups are important tools for adjusting and controlling theflow properties of gravure and flexographic inks. Ely [1980]stressed the economic importance of obtaining correct inkdilutions; his data indicated that a one second rise in drain time,18 instead of 17 seconds, can increase ink consumption on thepress by 18 percent using a #2 Zahn and 7.3 percent using a #3Shell. On the other hand, there are cases where two inks havingthe same Zahn cup reading had completely different printingcharacteristics [Bates, 1982].

The National Association of Printing Ink Manufacturers (NAPIM)has commissioned its research arm, the National Printing InkResearch Institute (NPIRI), to undertake a scientific study of theprintability of flexographic inks. A study of the flow properties ofthe inks by efflux cups and other appropriate instruments is anessential part of the program.

This article summarizes the results of the experiments in theNPIRI laboratories. It also encompasses a brief literature searchon the four major efflux cups — the Ford, Zahn, Shell and ISO.The major intent is to present the limitations of these deceptivelysimple devices and to give the reader an appreciation of thenumerous factors that influence their performance. Topics to bediscussed are:

A. The design of efflux cupsB. Laboratory experiments with Zahn and Shell cups

1. Calibration2. Influence of surface tension3. Influence of temperature4. Effect of shear rate

Design of Efflux CupsEfflux cups are variations of a capillaryviscometer, which is intended todetermine the viscosity of Newtonianfluids by measuring the time required forthe liquid to drain. The force pushing theliquid through the capillary and the draintime is related to a number of parameterswhich are described in detail in theaccompanying article.

For the purpose of this discussion, it isimportant to note that the basicequations assume a parabolic flowprofile, such as illustrated in figure 1. Thisrequirement can be met only with asufficiently long capillary. It is also

important to note that the drain time is particularly sensitive to theradius of the orifice.

Efflux cups were developed as inexpensive robust alternativesto glass capillary viscometers. The difference in features amongthe four major efflux cups will be discussed.

Ford CupThe Ford cup was developed in the 1920’s for thinningautomotive paints. As seen in the schematic in figure 2(a), itconsists of a hollow cylinder with a conical base, small orificeand a stubby capillary with a 100-degree conical entrance. It isnormally filled by pouring the liquid into the cup. Although theprecision of test measurements is reasonable (see table 1), it hasnot been widely adopted by the ink industry.

Zahn CupThe Zahn cup, which is filled by dipping into the liquid, wasdeveloped in the 1930’s for quality control of varnishes. Asshown in figure 2(b), the capillary length corresponds to thethickness of the wall, about 2 mils or 0.05 mm.

The short capillary coupled with the simple design makes theZahn cup not only easy to clean but also inexpensive. It isundoubtedly for these reasons that it has grown to be the mostpopular efflux cup in use not only throughout the paint andvarnish industries but also in the flexo and gravure industries.

These same features in the Zahn present serious flow problems.According to Owczarek [1968], the untapered entrance does notallow formation of a parabolic flow pattern. Instead, the fluidcontracts as it enters the short capillary and a portion splits offand forms eddies along the wall (see figure 3). Owczarek alsostates that the flow pattern is dependent upon the surfacetension of the liquid. Patton [1979] arrived at a similar conclusion.

In addition, the stream of fluid does not exhibit a sharp break asthe cup empties (see figure 4). This “dribbling” makes it difficultto time the endpoint and probably contributes to the poor

Figure 1. Parabolic flowprofile of Newtonian

fluid through capillary. Figure 2. Schematic diagram of Ford, Zahn, Shell, and ISO efflux cups.


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reproducibility of test results shown intable 1, obtained when one cup wascirculated.

Another problem is that since drain timeis inversely proportional to the fourthpower of the radius, minor variations inorifice size lead to poorer reproducibilitywhen different cups are used [Bagnall,1982; Knorps, 1980]. Moreover, cupcapacity, intended to be 44 mL, actuallyranges from 43-48 mL among cups fromseveral manufacturers.

Shell CupLike the Zahn, the Shell cup is a dip-type efflux cup. As seen infigure 2(c), it has a longer capillary than the Zahn (25 mm vx. 0.05mm) which improves the smoothness of flow [Mewis, 1980] andincreases the probability of obtaining a parabolic flow profile.However, the untapered entrance to the capillary can present thesame problems of turbulent flow and surface tensiondependency as with the Zahn cup.

As seen in figure 4, the endpoint is considerably sharper than onthe Zahn. In turn, the precision of test measurements is muchimproved (see table 1). There is only one manufacturer and thevolume is always 23 mL.

Because of the greater precision, the Gravure TechnicalAssociation [Vomacka, 1968] recommended that the Shell cupbe adopted as the industry standard. However, the change fromthe Zahn to the Shell has not been accomplished to any greatdegree. A similar situation exists in the flexo industry [Bagnall,1982].

ISO CupIn order to solve some of the problems which evolved fromattempts to use a variety of flow cups as viscometers forcomplex fluids, the International Standards Organization (ISO) in1965 authorized a task group to design an international flow cup.The rationale for the final design of the cup has been describedin detail by McKelvie [1970].

As seen in figure 2(d), key features of the ISO cup include the120-degree angle of the conical entrance and a 2 mm capillary.McKelvie also stressed the importance of smoothness of theinterior surface. Particularly germane is the fact that the ISO cuphas the best precision of the four cups (see table 1).

Experiments with Zahn and Shell Cups CalibrationThe reliability of test results can only be judged by cupperformance during calibration. The importance of calibrationhas been stressed by Euverard [1948, 1950], McKelvie [1970],and Patton [1979], and both the ASTM and ISO test methodsrequire this procedure.

[The Zahn cup]

has grown to be

the most

popular efflux

cup in use not

only throughout

the paint

and varnish

industries but

also in the flexo

and gravure

industries.

Figure 3. Flow in duct with suddencontraction of its cross-section.

Figure 4. High speed photographs ofendpoint on Zahn cup (top) and Shell cup

(bottom).

Cup Test Method OriginalYear

Single-operatorRepeatability(% relative)

InterlaboratoryReproducibility

(% 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

TABLE 1. PRECISION OF EFFLUX CUPS

* using identical cups.


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In addition to the better precision of theShell, illustrated by results in table 1,another indication of the superiority ofShell cups over Zahn cups came fromcalibration studies in the NPIRIlaboratories. The calibration wasconducted with standard Newtonian oilson a total of nine cups using theprocedure described in ASTM TestMethod D-4212.

Results indicated that essentially nocorrection was required for the Shellcups tested (#2, #3, and #4). Thecorrection factor for the Zahn cups (#2and #3) averaged about 1.25 with a 100cp oil and 1.45 with a 29 cp oil. Thecorrection factor for a #1 Zahnexceeded 2.0 with the latter oil.

Figure 5 illustrates, in addition, that thegood agreement between the viscositiescalculated from the Shell and the actualviscosities extended over temperaturesranging from 20 to 30°C. On the otherhand, the Zahn always gave calculatedviscosities considerably less than thetrue viscosities. Note also that theagreement between the Shell and actualviscosities was further improved whenthe sample was free of air bubbles.

The conversion from drain time toviscosity was calculated by Patton’sequations [1979], which assume that allcups of the same type and model havethe same dimensions. To take intoconsideration that there are likely

differences among cups, a calibration chart relating drain time tokinematic viscosity should be constructed for each cup.

Figure 6 illustrates that drain times of Newtonian oils in the Shellcup are much more sensitive than in the Zahn to changes insample viscosity. Note also that the plot line for the Zahn doesnot go through zero, indicating that a correction factor is neededto account for turbulent flow [Euverard, 1950].

It should be pointed out that the only available standard fluidsare oils, most of which have viscosities giving drain times beyondthe recommended range for a particular cup. A more seriousproblem is that their wetting characteristics are different fromthose of typical liquid inks. Therefore, the relationship betweendrain time and viscosity obtained with one type of fluid may notbe applicable to other types of fluids [McKelvie, 1970; GeneralElectric, 1981].

Even when the efflux cup is being used for quality control ofestablished formulations, a calibration procedure is necessary todetect differences in dimensions among cups, e.g. between thesupplier’s and the customer’s, and also to follow changes in cupperformance due to dents, scratches or wear with use.

Influence of Surface TensionIn order to determine the extent to which wetting characteristicsinfluence efflux cup results, experiments were conducted withaqueous isopropanol (IPA) solutions varying in surface tensionfrom 72 (pure water) to 21 (pure IPA) dynes per centimeter.Surface tension as a function of IPA concentration is plotted infigure 7(a). Figure 7(b) shows that as the IPA concentrationincreased the drain times on the Zahn decreased slightly whilethose on the Shell increased slightly.

Therefore,

the

relationship

between drain

time and

viscosity

obtained with

one type of

fluid may not

be applicable

to other types

of fluids.

Figure 5. Viscosity of Cannon standard oil S-20 on Zahn and Shell cupsas function of temperature.

Figu

re 6

. Ca

libra

tion

cur

ves

for

#3 Z

ahn

and

#4 S

hell

cups

usin

g Ca

nnon

sta

ndar

d oi

ls S

-20,

S-6

0, a

nd S

-200

.


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Conversion of drain time to viscosityusing Patton’s equations revealed thatthe Zahn, as seen in figure 7(c), gave aviscosity/IPA concentration plot verysimilar to that of the surface tension plotin figure 7(a). On the other hand, theShell curve showed a maximum inviscosity at about 50% IPA. Moreimportantly, the Shell curve shapematched that from the Brookfieldviscometer. The Brookfield data areidentical to those reported by Patton[1979].

The results in figure 7 suggest that thedrain times on the Zahn cup are highlysensitive to surface tension of the testfluid while those on the Shell are not. Inother words, the Shell should be theefflux cup of choice when attempting tocharacterize the flow properties of aseries of water-based inks or othersystems involving significant differencesin surface tension.

Influence of TemperatureASTM Test Method D-4212 requires that the sample temperatureeither be maintained at 25°C or be recorded to 0.1°C forcalibration and 1°C for general testing. The procedure suggestsconstruction of a temperature correction curve for each liquid byplotting drain time as a function of sample temperature over theexpected temperature range. The instructions also specifyimmersion of the cup in the sample for at least five minutes toreach sample temperature. For the more volatile inks,considerable evaporation and settling could occur during thisperiod.

In the following experiments, one solvent-based and two water-based commercial flexographic inks were diluted to a #2 Zahncup reading of 21 ± 0.5 at 25°C (78°F) and then equilibrated at 20(68°F) and 30°C (86°F). Drain times were measured on the #2Zahn and the #3 Shell at the three temperatures.

The results plotted in figure 8 indicate that, on both cups, thechange in drain time per degree Celsius varies widely from oneink to another. For a specific ink, the drop in drain time withincreasing sample temperature is much greater on the Shell thanon the Zahn. These results are not surprising, considering thatthe calibration curves in figure 6 had indicated a greatersensitivity of the Shell drain times to changes in viscosity.

In addition, data in figure 8 clearly illustrate the ability of the Shellto differentiate among inks that exhibited essentially the samedrain time on the Zahn at 25°C. These results confirm thosereported by Bagnall [1982] and may explain the previously

. . . 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.

Figure 7. Viscosity of aqueous isopropanolsolutions varying in surface tension

measured on Zahn #2 and Shell #2 cups andon Brookfield viscometer. Fi

gure

8.

Dra

in t

imes

for

thr

ee w

ater

or

solv

ent

base

d fl

exog

raph

icin

ks a

t 20

, 25

, 30

°C o

n Za

hn #

2 an

d Sh

ell #

3 cu

ps.


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Figure 9 shows that all of the water based inks tested decreasedin viscosity as shear rates increased, in this case from 10 to 1000sec-1. In limited studies at low shear rates, solvent-based inksexhibited much the same shear thinning properties as didaqueous inks.

Figure 9 also illustrates that some inks are more shear thinningthan others. Such tendencies can be detected only frommeasurements from at least two different shear rates. On effluxcups, shear rate varies across the diameter of the capillary. Anapproximate shear rate can be calculated for a Newtonian fluid[Rodriquez, 1982]. The calculated shear rate for a 25 cp fluid onthe #3 Shell is approximately 300 s-1. Estimated shear rates onoperating presses are well in excess of 1000 s-1.

Because of the shear thinning nature of liquid inks, the equationsrelating drain time to viscosity no longer apply [McKelvie, 1970;Patton, 1979; Mewis, 1980; Pierce, et al, 1982]. Therefore, testresults should be reported as drain times and not in terms ofkinematic viscosity, or if the density is measured, the dynamicviscosity.

Pigmented inks, besides having a complex rheology, presentunique measuring problems including evaporation, pigmentflocculation, settling of solids, foaming of water based inks,structure buildup with time and probably wetting differences.Results in our laboratory also indicate that ink viscoelasticityvaries with ink composition and degree of dilution and couldinfluence drain time.

Conclusions1. A literature search and laboratory results clearly illustrate the

complexity and limitations of efflux cup measurements andthe careful control required to obtain correct data even onsimple Newtonian fluids.

2. Of the four efflux cups studied, the ISO is most precise and theZahn is least precise.

3. The Shell cup is preferred over the Zahn cup because certaindesign features of the Shell make it more reproducible, lesssensitive to surface tension of the liquid, and better able todifferentiate among test fluids having different flow properties.

4. Construction of calibration curves with standard oils isnecessary to detect differences among cups of the same typeand model and changes that occur with use.

5. The reporting of drain times must include the sampletemperature and the cup type and model. Useful informationcan be derived by measuring drain times at room and at presstemperatures.

6. Liquid inks exhibit varying degrees of non-Newtonianism and,for these reasons, drain times cannot be converted toviscosity.

The Shell cup

is preferred

over the Zahn

cup because

certain design

features of

the Shell

make it more

reproducible,

less sensitive

to surface

tension of the

liquid, and

better able to

differentiate

among test

fluids having

different flow

properties.

Figure 9. Viscosity of four water basedflexographic inks at 25°C on the Brookfield

viscometer at 10 s-1 and the Bohlinrheometer at 100 s-1 and 1000 s-1.

mentioned comment by Bates [1982]that inks having the same Zahn cupreading performed differently on thepress.

Note also in figure 8 that the order inwhich the inks are ranked for drain timeis different at 30°C than at 25°C.According to Stevko [1984], operatingtemperatures on a gravure press mayreach as high as 50°C (122°F).Therefore, it may be advantageous tomake efflux cup measurements at presstemperatures and at those normallyrecommended in test methods.Irrespective, the sample temperatureshould always be reported along withthe test results.

Effect of Shear RateSince efflux cups are variations ofcapillary viscometers, they have a samebasic restriction, namely that drain timecan be converted to viscosity only if thetest fluid is Newtonian. (Newtonianrefers to a fluid whose viscosity does notchange with shear rate.)

Although liquid inks are low in viscosity,the fact that they are pigmented polymersolutions inherently indicates that theyare rarely Newtonian but are usuallyshear thinning. Confirming evidencewas provided by measurements at avariety of shear rates on the Brookfieldviscometer and the Bohlin rheometer,both of which are rotational viscometers.


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Rodriquez, R., Principles of Polymer Solutions, Second edition,McGraw-Hill Book Company, New York, 1982.

Schramm, G., Introduction to Practical Viscometry, Haake Mess-Technik GMBH-u.-CO, Karlsruhe, W. Germany, 1965.

Stevko, P., “The effect of temperature on ink fountain solutionviscosity,” Gravure Research Institute Report, No. M-273, NewYork, 1984.

VanWazer, J.R., J.W. Lyons, K.Y. Kim, and R.E. Colwell, Viscosityand Flow Measurement, Wiley-Interscience, New York, 1963.

Vomacka, F.N., “Shell and Zahn cups,” Gravure TechnicalAssociation Bulletin, Vol. XIX, No. 2, 1968, pp. 122, 123, NewYork.

Acknowledgement is made of the National Printing Ink ResearchInstitute for support of this work and permission to publishresults. Appreciation is also extended to F.J. Micale, J.M. FetskoandY.P. Lee for technical and editorial assistance; to Jo EvelynGallagher for her skillful rheological measurements; to BernadineDancho for preparing the figures; and to Arlene Toth for typingthe manuscript.

Equations Describing Capillary FlowThe Hagen-Poiseuille equation (equation 1) describing liquid flowin classical fine-bore glass capillary viscometers such as theOstwald or Ubbelohde is usually applied to efflux cups [Patton,1979]. The equation is based upon a parabolic flow profile ofliquid through the capillary.where:h = dynamic viscosity, centipoise (cp)d = density of fluid, µg/mm3

g = gravitational acceleration, 9800 mm/sec2

h = effective hydrostatic head of liquid, related to difference invertical height before and after the test, mm

r = radius of capillary, mmL = length of capillary, mmT = drain time, seconds (s)V = volume of flow during time t, mm3

If the density of the liquid is not known, the measurement yieldsthe kinematic viscosity (v). The dynamic viscosity can beobtained by multiplying the kinematic viscosity value by thedensity.

At the center of the capillary, the shear stress is zero, the shearrate is zero, and the velocity is at maximum. At the capillary wall,

�dghr4t

8LV= (1)�

ReferencesStandard Test Method D1200, “Viscosity of paints, varnishes andlacquers by Ford viscosity cup,” Annual Book of ASTMStandards, Vol. 06.01, American Society for Testing andMaterials, Philadelphia, 1952 (82).

Standard Test Method D4212, “Viscosity by dip-type cups,” Ibid.1982.

Bagnall, K., “Viscosity control of flexographic ink,” BoxboardContainers, June 1983.

Bates, J.B., “Printing ink research — a vital resource,” AmericanInk Maker, Vol. 60, No. 12, 1982, pp. 22, 24, 26, 30.

Ely, J.K., “Experiments to show ‘Seconds come first’ in waste-preventing controls,” American Ink Maker, Vol. 58, No. 10, 1980,pp. 46, 49, 50.

Euverard, M.R., “The efflux type viscosity cup,” Scientific Editionof National Pain, Varnish, and Lacquer Association, Washington,D.C., 1948.

“Evaluation of empirical viscosity measurements for varnishesand resin solutions,” ASTM Bulletin, No. 169, October, 1950, pp.67-70.

General Electric Company, “Instructions for Zahn viscometers,”Publication No. 198 4541K23-001A, Lynn, MA, 1981.

International Standard 2431, “Paint and varnishes —Determination of flow time by use of flow cups,” InternationalOrganization for Standardization, Geneva, 1980.

Knorps, L., “Standardizing Zahn cups,” American Ink Maker, Vo.58, No. 8, 1980, pp. 20, 21, 50.

McKelvie, A.N., “An international flow cup,” Journal of Oil andColor Chemists Assn., Vol. 53, 1970, pp. 92-120.

Mewis, J., “Paints and printing inks,” Chapter 6, Rheometry:Industrial Applications, edited by K. Walters, John Wiley & Sons,New York, 1980, pp. 281-338.

Owczarwek, J., Introduction to Fluid Dynamics, InternationalTextbook Company, Scranton, PA, 1968.

Patton, T.C., Paint Flow and Pigment Dispersion, Second edition,John Wiley & Sons, New York, 1979.

Pierce, P.E., and C.K. Schoff, “Rheological measurements,” Kirk-Othmer: Encyclopedia of Chemical Technology, Vol. 20, Thirdedition, John Wiley and Sons, New York, 1982, pp. 259-319.


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the shear stress and shear rate are at a maximum, and thevelocity is assumed to be zero. Because the shear rate variesacross the diameter of the capillary and the shear stress isundefined, these capillaries should be limited to testingNewtonian fluids. Non-Newtonian fluids do not produce aparabolic flow profile, which requires modification of the basicequation [Rodriquez, 1982].

Two corrections are required for processingdata from capillaryviscometers: a kinetic energy correction (K.E.) and a Couettecorrection (C). Energy is expended as the height of liquid in thecup decreases reducing the potential energy of the system. TheHagen-Poiseuille equation assumes that this energy is utilizedcompletely in overcoming viscous resistance to flow. A portion,however, is required to set the fluid into motion [Patton, 1979].This correction factor becomes extremely important for lowviscosity Newtonian fluids and approaches zero for high viscosityfluids.

Calculation of the actual viscosity requires inserting a kineticenergy correction term in the basic equation (equation 2).

The Couette correction relating to end effects is described byequation 3 in which NDE is the Deborah number of the liquid.The number is related to the ability of the liquid to recover afterbeing stressed [VanWazer, 1963]. NDE approaches zero forNewtonian fluids and is much greater for clastic fluids.

For very accurate results, corrections must also be made forincomplete drainage, turbulence, and possible heat and surfacetension effects [Pierce et al, 1982]. Corrections are minimized byusing a capillary with length at least 50 times the diameter[Schramm, 1965] and efflux times longer than 300 s [Pierce et al,1982].

The correction terms for kinetic energy and end effects areincorporated into the kinematic viscosity equation (equation 4)which is theoretically significant but usually shortened toequation 5.

The k and c values for each model Zahn, Shell, Ford and ISOcups appear in the literature [Patton, 1979; ISO, 1980; Pierce etal, 1982; ASTM, 1983]. The correct values for a specific cup canbe calculated from calibration curves obtained with standardNewtonian fluids [Euverard, 1950]

L + NDE r

L=C (3)

��dghr4t

8VL= – (2)

dV

8 � LT(K.E. term)

v = kt - c/t (4)

v = (t-c) (5)

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