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.

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_Page1
NORCROSS 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. 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_Page2
NORCROSS 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. 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_Page3
NORCROSS 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. 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_Page4
NORCROSS 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. 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_Page5
NORCROSS 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. 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_Page6
NORCROSS 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. 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_Page7
NORCROSS 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