Latex Carpet Compound Rheology

Abstract

This is a study of three-phase foam rheology to qualify penetration in to backing webs during frothed carpet compounds applications. Transient viscosity as a function of shear rate under a short time period is proposed to characterize flow of these compounds in response to a rapidly changing shear field during their application. We developed a fluid dynamic model that predicts the shear and pressure distributions in the compound during its processing in a metering nip based on process parameters and rheological results. We tested frothed compound formulations that are empirically known to be "penetrating" and "non-penetrating" based on the choice of soap (frothing surfactant). Formulated at the same froth density, penetrating to carpet backing compounds had large froth bubbles, relatively low transient shear viscosity and showed increasing foam breakdown due to shear when compared to non-penetrating compounds. Such frothed compounds readily collapse under shear and have relatively low dynamic stability, so the transition from a three-phased (air/aqueous/solid) to a two-phased (water/solid) system occurs much easier and faster during application. The model predicts the shear rate development and a small difference in the pressure distributions in the applicator nip between these formulations, but reduction in drainage for the non-penetrating formulation.

Full text

64250-1 Applied Rheology
Volume 18 · Issue 6
Abstract:
This is a study of three-phase foam rheology to qualify penetration in to backing webs during frothed carpet com-
pounds applications. Transient viscosity as a function of shear rate under a short time period is proposed to char-
acterize flow of these compounds in response to a rapidly changing shear field during their application. We devel-
oped a fluid dynamic model that predicts the shear and pressure distributions in the compound during its processing
in a metering nip based on process parameters and rheological results. We tested frothed compound formulations
that are empirically known to be “penetrating” and “non-penetrating” based on the choice of soap (frothing sur-
factant). Formulated at the same froth density, penetrating to carpet backing compounds had large froth bubbles,
relatively low transient shear viscosity and showed increasing foam breakdown due to shear when compared to
non-penetrating compounds. Such frothed compounds readily collapse under shear and have relatively low dynam-
ic stability, so the transition from a three-phased (air/aqueous/solid) to a two-phased (water/solid) system occurs
much easier and faster during application. The model predicts the shear rate development and a small difference
in the pressure distributions in the applicator nip between these formulations, but reduction in drainage for the
non-penetrating formulation.
Zusammenfassung:
Die vorliegende Arbeit befasst sich mit der Rheologie von Dreiphasen-Schaumklebstoffen, um deren Eindringen in
die Trägerbahn während der Herstellung von Teppichbahnen zu bewerten. Die zeitliche Änderung der Viskosität
als Funktion der Scherrate während einer kurzen Zeitdauer wird als Maß zur Charakterisierung der Strömung die-
ser Komponenten, als Antwort auf ein sich rasch änderndes Scherfeld während der Verarbeitung, vorgeschlagen.
Die Autoren haben ein fluiddynamisches Modell entwickelt, das die Scherkraft- und Druckverteilung im Verbund-
werkstoff während seiner Herstellung in einem Dosierspalt einer Rollenbeschichtungsanlage in Abhängigkeit von
den Prozessparametern und der Klebstoffrheologie vorhersagt. Es wurden Rezepturen untersucht, die empirisch
als „penetrierend“ oder „nicht-penetrierend“ auf der Grundlage der verwendeten Tenside bekannt sind. Es stellte
sich heraus, dass bei gleicher Dichte die in den Träger penetrierenden Klebstoffe größere Blasen aufweisen, eine
relativ niedrige transiente Scherviskosität besitzen und eine zunehmende Tendenz zu Schaumzerfall durch Scher-
kräfte zeigen, verglichen mit nicht-penetrierenden Klebstoffen. Solche geschäumten Komponenten kollabieren
leicht unter Scherbelastung und haben eine relativ niedrige dynamische Stabilität, so dass der Übergang von einem
Dreiphasen-System (Luft/Wasser/Feststoff) zu einem Zweiphasen-System (Wasser/Feststoff) während der Verar-
beitung viel leichter und rascher auftritt. Das Modell sagt die Entwicklung der Scherrate sowie einen kleinen Unter-
schied in der Druckverteilung im Auftragsspalt zwischen diesen Formulierungen voraus, darüber hinaus eine Redu-
zierung der Entwässerung für die nicht-penetrierende Formulierung.
Résumé:
C'est une étude rhéologique sur une mousse à 3 phases dont le but est de caractériser la pénétration des composés
au verso des tissus (tapis) pendant les applications de colle sous forme de mousse. Le changement temporel de la
viscosité en fonction du taux de cisaillement pendant une période de temps court est proposé pour caractériser le
flux de ces composés en réponse à un domaine de contraintes changeant rapidement pendant leur application.
Nous avons développé un modèle dynamique de fluide qui prédit les distributions de cisaillement et de pression
dans le composé pendant son passage dans le nip du metering basé sur des paramètres de process et des résultats
rhéologiques. Nous avons testé des formulations de composé sous forme de mousse, qui sont connus d'expérience
pour être “pénétrant” et “non-pénétrant:, en rapport avec le choix du savon (surfactant moussant). Formulés à la
même densité de mousse, les composés “pénétrant” le dos des tapis présentaient de larges bulles de mousse, avec
un faible changement temporel de viscosité, et montraient une rupture de mousse croissante due au cisaillement,
quand comparés à des composés “non pénétrants”. De tels composés mousseux s'effondrent facilement sous
cisaillement et ont une stabilité dynamique basse, de telle sorte que la transition d'un système 3 phases
(air/eau/solide) à 1 système 2 phases (eau/solide) arrive plus facilement et plus vite pendant l'application. Le mod-
èle prédit, pour ces formulations, le développement du taux de cisaillement et une petite différence dans les dis-
tributions de pression dans le nip de l'applicateur, et par ailleurs une réduction de drainage pour la formulation
“non pénétrante”.
Latex Carpet Compound Rheology
Nick Triantafillopoulos*, Bruce Schreiner, James Vaughn,
and Douglas Bousfield1
OMNOVA Solutions Inc., Akron, OH 44305, USA
1Department of Chemical Engineering, University of Maine, Orono, ME 04469, USA
*Email: nick.triantafillopoulos@omnova.com
Fax: x1.330.794.6239
Received: 3.10.2007, Final version: 2.9.2008
© Appl. Rheol. 18 (2008) 64250-1 – 64250-9
DOI: 10.1515/arh-2008-0023

final processing stage, hot air drying ensures
annealing of the latex to develop film formation
and binding strength.
Upon application, compounds may either
stay at the surface of the carpet backing or pen-
etrate into the loomed backing. Too little pene-
tration causes the latex to stay only at the sur-
face and consequently provides poor coverage,
and therefore binding, of looped carpet fibers.
The result is poor tuft bind and delaminating
strength, key properties of the final product.
Excessive penetration into the substrate does
not allow adhesive to reinforce the fiber-sub-
strate interface or the adhesion of the primary to
the secondary backing, causing poor binding.
Flow properties, more specifically rheological
properties of a compound under carpet coating
conditions are critical. They greatly depend on
the discrete microstructure, arising from filler
particles and air bubbles that determine the
global behavior of the compound.
Rheological tests of frothed carpet com-
pounds are currently performed in the carpet
industry. It is common to measure and report vis-
cosity of a compound using a spindle viscometer.
However, this single-point viscosity measure-
ment technique reports a single viscosity value
by digging a hole in a viscous material, such as
frothed carpet compounds. Since frothed com-
pounds require an initial force before they start
flowing (i.e. they have a 'yield stress'), a rotating
spindle in a beaker shears the material next to it,
without causing all of the material across the
beaker's width to flow. Spindle-based viscosity
measurements do not give the variable viscosity
of the material over a range of shear rates repre-
sentative of the shearing that occurs in a roll
coater. Therefore, it is not expected to help pre-
dict product performance.
In some cases, practioners generate viscosi-
ty data of frothed carpet compounds over a range
of shear rates with concentric cylinders or cone
and plate geometries [5]. In these measure-
ments, typically the shear rate increases first to
a maximum rotational speed of the moving ele-
ment and then decreases. This test method gen-
erates a loop of increasing and decreasing shear
64250-2
Applied Rheology
Volume 18 · Issue 6
1 INTRODUCTION
Tufted carpet, commonly used for residential and
commercial floor covering, is comprised of tufts
of yarn needled through fabrics. A compilation of
layers keeps piles of fibers in place and provides
dimensional stability, resiliency, and other desir-
able properties [1]. While the primary backing of
a carpet pile holds the tufts of yarn, secondary
backing is commonly used to provide dimen-
sional stability and resiliency. Both backings are
made from polyolefin or polyester woven or non-
woven materials. Compounded with inorganic
pigments and organic thickeners, emulsion latex
is used as an adhesive in the backing to hold the
tufted piles of fibers together and to bond the pri-
mary and secondary backings used to form the
final pile of a carpet.
The frothed compounds including latexes are
most common materials to bind tufted carpet.
Compounds are typically comprised of filler, emul-
sion latex, surfactant and a thickener. Frothing of
compounds helps control the weight applied onto
the carpet, yielding the same add-on level at three
times the solids level of water diluted binder,
thereby reducing the water removal load and
energy requirements to about one third [2]. We
use the terms foam and frothed compounds inter-
changeably here to identify stable combinations
of three-phase (gas-liquid-solid) systems. They
represent true foams, exhibiting closed bubbles
with no gas filled channels connecting a given
bubble with any of its neighbors [3]. Additionally,
they are wet foams in the sense that liquid with
dispersed inorganic filler particles comprise the
meniscus (Plateau border) regions of the foam.
Frothed compounds persist for a measurable peri-
od of time – or at least until their application and
drying. Foam life depends on: (a) repulsion of elec-
trical double layers, high surface and liquid vis-
cosities and the (thermal) Marangoni effect [2, 4].
In carper manufacturing, compounds are applied
using roll coaters which spread material evenly
across the moving backside of a carpet's primary
and secondary backings. After application, the
three-phase compound breaks down to a two-
phase system (aqueous solution, and dispersed
solid filler and binder emulsion particles). At the
Key words: foam rheology, bubble formation, shear viscosity, carpet compounding

rates, called a rheogram. The time to reach the
maximum shear rate condition is called the ramp
time. Practice in the field is to use predetermined
ramp times supplied by the manufacturer of the
measuring instrument. However, these times are
too long to adequately represent the actual
increase in shear rate experienced by the com-
pound during compound application at typical
line speeds of industrial coaters. Because frothed
carpet compounds are non-Newtonian vis-
coelastic materials, the ramp time influences the
viscosity values at a certain shear rate and the
form of the rheogram. Non-Newtonian vis-
coelastic materials have shear viscosity which
depends on the rate with which shear rates are
applied on them, reaching higher viscosity values
when the time to attain a certain shear rate, or
ramp time, decreases.
Typically, one could empirically determine
how a frothed compound behaves during its
application after it has been formulated and run
onto a carpet mill coater. Newly developed car-
pet compounds and adhesives must be run by
carpet mills to determine how effectively they
penetrate into carpet backings. It is therefore
highly desirable to develop laboratory methods
which predict the potential behavior and pene-
tration or lack of penetration of frothed carpet
backing compounds and adhesives for industrial
conditions.
Here we describe viscosity tests that char-
acterize the deformation of frothed compounds
during their application. They are based on the
response of a freshly prepared frothed com-
pound to variable shear rates over a short period
of time. A model of the frothed compound appli-
cation is proposed that uses these results to pre-
dict the depth of penetration of compounds into
the web. Selected frothed compounds that have
empirically been determined to be “penetrating”
and “non-penetrating” were considered to quan-
tify their rheological differences. The compounds
were qualitatively associated with variable air
bubble sizes, which yielded differences in rheo-
logical properties.
2 EXPERIMENTAL
2.1 FROTHED COMPOUND PREPARATION
Typical compound ingredients comprise inor-
ganic filler, synthetic latex emulsion, a synthetic
thickener and surfactant (soap or frothing aid).
They are dispersed in water and mixed well to
create a homogeneous mixture. The mixture
then is processed with an air generating device,
such as a Kitchen Aid® mixer, to introduce air and
form a frothed compound. Frothing continues
until a certain amount of air has been introduced
into the compounds, measured by the weight of
the frothed compound inside a certain size cup.
The finally formed frothed compound is stable,
or “immobile”, resembling shaving cream foam.
If a frothed carpet compound has been
standing for more than several hours, significant
settling may occur, depending on foam's stabili-
ty. Compounds should be stirred slowly for 45
seconds with a large spatula prior to sampling. In
a 4-quart stainless steel bowl, 200 g of the com-
pound are frothed with a mixer using a wire
attachment and at a speed of “8” until the result-
ing froth has the selected “3-ounce” cup weight
(density). Normally a 3-ounce cup weight of 50 or
60 g is desired. The wires of the mixing attach-
ment must be centered and the stainless steel
bowl must be clamped to prevent rocking. Best
cup weight repeatability is obtained this way.
After frothing, the attachment is removed from
the bowl and froth on it is shaken into the center
of the bowl. Froth is gently transferred from the
top center of the bowl into a 30-mL beaker using
a 150x19-mm wooden applicator stick. The froth
must be handled as carefully as possible because
it is fragile and can be damaged. The beaker is
filled level and then weighed. The weight of the
froth in the beaker multiplied by a factor of 2.2 is
the 3-ounce cup weight. Air pockets in the froth
should be taken into consideration when calcu-
lating the weight of the froth.
Focus in our work was on determining the
stability of frothed carpet compounds from
macroscopic viscosity measurements. Dynamic
stability affects the shear flow and drainage of
the frothed compounds into a carpet backing
during processing and, consequently, compound
penetration. Although stability has been shown
to increase with reduced particle size and filler
concentration [6], we have chosen to keep the
filler and its concentration the same and vary the
soap (surfactant) type to influence stability.
Specific carpet compounds were prepared in
the laboratory using different froth aids. Carpet
Compound 1 contained surfactant Stanfax® 238
(Parachem, USA), a penetrating froth aid. Carpet
64250-3 Applied Rheology
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Compound 3 contained a non-penetrating froth
aid (Stanfax® 167M). The compounds were the
same in other respects; they contained calcium
carbonate filler, styrene butadiene latex, and a
thickener. The “load” amount of filler was 550
and the compounds were frothed in the lab using
a mixer to 63 g in a 3-ounce cup.
Another series of tests involved using dif-
ferent surfactants as froth aids. The frothed com-
pounds were made in the laboratory using the
standard recipe from above with the exception
of the froth aid. The compounds contained thick-
ener SKA-111-D (Parachem, USA) and were for-
mulated and frothed the same way for 3-ounce
cup weights close to 60 g. The froth aides were
surfactants A, B, and C, corresponding to trade
names SCT-180-A, SCT-182-B, and SCT-194-A,
respectively (Southern Chemicals & Textiles, Dal-
ton, GA, USA). From practical experience in tuft-
ed carpet manufacturing, surfactant B causes a
compound to be most penetrating.
2.2 VISCOSITY MEASUREMENT
An advantage of the viscosity test described here
is that it is completed in a short period of time or
short ramp time. A rheogram displaying the vis-
cosity of a compound as a function of shear rate
is completed within five seconds. The test mea-
sures deformation and shear rate response of a
carpet compound under subsequent increasing
and decreasing shear rates similar to processing
in metering rolling nips. The short-time testing
selection more accurately represents actual time
periods involved in processing compounds on a
roll carpet coater at realistic machine line speeds.
Flow through rolling nips is a major process
condition during compound application in a car-
pet mill. At this processing step, mechanical per-
turbations and external stresses induce (a)
breaking of the stabilizing thin film between
froth bubbles, causing them to collapse, and (b)
structure rearrangement of the dispersed filler
particles. This is typically shown by shear thin-
ning in a rheogram. Martin et al. [7] have shown
that, for ice cream foams, viscous behaviour
dominates at high shear stresses, like those man-
ifested in rolling nips. Furthermore, Barigou and
Deshpande [8] demonstrated that power-law
fluid models describe well the flow of wet foams
in vertical pipes. Because of the three-phase com-
position of frothed compounds, the magnitude
of shear thinning depends on the test ramp time,
which here we tried to minimize in order to more
accurately represent the transient time period to
reach high shear under the operating conditions
of a carpet mill coater.
We used the AR-2000 rheometer made by
TA Instruments with the coaxial cylinders geom-
etry. This geometry allows for containing the
frothed sample without letting contained air to
escape. Enough froth was transferred into the
cup to fill it to a height of 23 mm. This was done
carefully using a 114 · 9 mm wooden applicator
stick. The bob was lowered manually to a point
just above the froth, subsequently lowered very
slowly by a computer command to a gap of 5.9
mm. Lowering the bob rapidly can cause consid-
erable damage to the froth and testing will not
be representative of the compound. Froth above
the bob was then smoothed with a wooden appli-
cator stick, making sure that the bob was covered
completely. The cup was covered with a solvent
trap to prevent evaporation of water. The bob-
cup gap was 1.1 mm. Testing normally was done
at 21°C, but it can be also done at higher temper-
atures. The sample was equilibrated for 30 sec-
onds by leaving the instrument idle. Then shear
rate was ramped up to 1600 s-1 over a period of 5
seconds, then back down from 1600 to 0.5 s-1 over
a period of 5 seconds.
2.3 PHYSICS OF CARPET BACKING APPLICATION
The web treatment during frothed compound
application in carpet manufacturing is applied
with a rolling nip, conceptually shown in Figure 1.
In zone 1, excess frothed compound is fed into a
64250-4
Applied Rheology
Volume 18 · Issue 6
Figure 1:
Conceptual model of appli-
cation, pressing, and drying
of carpet compounds.

flooded puddle and metered to a controlled
amount applied onto the moving backing
through a rolling nip formed between two
rollers. The coater operating parameters and the
viscosity of the compound, as well as the pattern
of the backing, determine the pick up weight.
Progressively increasing shear is applied to the
compound in this region, while metering takes
place through the process of lubrication. Hydro-
static pressure developed at the rolling nip per-
pendicularly to the web movement direction
forces penetration and compound enters the
porous moving web. This pressure induces
drainage of the frothed compound into the back-
ing and rearrangement of the filler structure.
Upon exiting the metering nip in zone 2, mater-
ial settles under atmospheric conditions,
drainage occurring due to gravity, followed by
pressure penetration at the “marriage rollers.”
Relaxation of material and capillary drainage
dominate in zone 2. At the dryer oven section,
zone 3, water evaporates, causing the film-form-
ing latex to set the frothed compound.
Flow properties, described by rheology, play
a key role in frothed compound application. The
critical step in zone 1 depends on the effective vis-
cosity at the corresponding shear rates at the nip
formed in Fig. 1 between the two rollers. Com-
pounds are shear-thinning thixotropic, decreas-
ing viscosity with shear over time. This flow
behavior under shear arises from collapsing of
the fragile structure of entrained air bubbles in
the froth and reversible destruction of the filler
structure in suspension. Air bubble stability and
association of filler-latex and thickener con-
tribute to the strength of the structure in sus-
pension. Soaps, used as frothing surfactants,
influence bubble stability.
We considered the geometry in the applica-
tion zone 1 to analytically study it with computer
simulations. Mathematical details of the model
are given in Appendix A. Lubrication approxima-
tion was used to describe the relevant momentum
balance; an approximation commonly used to
successfully describe flow in rolling nips [9].
Dynamic drainage or penetration into the moving
web was resolved simultaneously with the pres-
sure field in the film between the rolls. The shear-
thinning rheology of compounds was taken into
account using the power-law model. Figure 2
shows the geometry of interest. As frothed com-
pound is pulled into the nip from the flooded pond
upstream, pressure builds up and compound is
pushed through the nip and into the web. The web
is considered porous and the penetration depth
into the web is denoted as L(x).
A series of calculations were done to under-
stand the amount of compression of stable
foams during the pressure buildup through the
rolling nip. Results indicated that foam com-
pression was not large for typical processing and
operating conditions in carpet mills, such as line
64250-5 Applied Rheology
Volume 18 · Issue 6
Figure 2 (above):
Enlargement of the nip
geometry of interest with
the web following the bot-
tom roll and the coating
material coming in to the
nip on the top roll from left
to right. A puddle of the
coating material exists
upstream (denoted h(X)), on
the left, and a thin film is
applied onto the moving
web after film split.
Figure 3 (below):
Model predictions of
(a) pressure, (b) shear rate,
and (c) penetration for a
Newtonian fluid and two
shear thinnig compounds
Table 1 (above):
Process parameters used in
the working model.
Table 2:
Power-law parameters for
experimental compounds
(a) (b) (c)

speed, top roller rotation and shear viscosity of
the foam. The simulation model was adjusted for
the constant-viscosity Newtonian case by using
the shear rate calculated in the Appendix. The
pressure gradient from the upstream position
assumed to be close enough to use to calculate a
shear viscosity value for the power-law model.
The power-law equation to describe the frothed
compound rheology was:
(1)
Table 1 describes processing conditions and Table
2 shows typical values of the power-law para-
meters in the model. The latter were calculated
from actual rheograms, where the power-law
approximation was fitted to the experimental
data to estimate its coefficients. Figure 3 com-
pares the model predictions for pressure, shear
rates, and penetration for a Newtonian fluid and
a power law fluid. Pressure builds as material is
pulled into the nip from region upstream. Near
the region of the thinnest gap, the pressure falls
quickly to a sub-ambient value. The profile is sim-
ilar to experimental measurements and previous
analytical works [10 – 12]. Accounting for pene-
tration in the flow field is a unique aspect of our
work, as bubbles in the frothed compound can
collapse under pressure. Though the non-pene-
trating compound generated high pressures in
the nip, the amount of penetration into the web
reduces because of higher viscosity, compared
with the penetrating case. Unless the penetra-
tion volume is close to the magnitude of the gap,
the pressure pulse changes by only a small
amount through penetration. As result, the pres-
sure pulse is controlled by foam rheology, not by
the amount of penetration.
3 RESULTS
We obtained low magnification micrographs of
the state of foams formed with the different
frothed compound at approximately the same
aging after preparation and frothing. We corre-
lated the photographs with the corresponding
flow curves obtained with rheological measure-
ments of viscosity as a function of shear rate. Fig-
ure 4 shows the microscopic photographs of the
frothed compounds taken at the same magnifi-
cation and showing the relative formation of air
bubbles in each compound.
64250-6
Applied Rheology
Volume 18 · Issue 6
Compound 1 Compound 3 Surfactant A Surfactant B Surfactant C
10.00
100.0 1000 10000
shear rate (1/s)
0.01000
0.1000
Compound 1
Penetrating
Non-penetrating
Compound 3
Inc. shear rate
Dec. shear rate
Dec. shear rate
Inc. shear rate
1.000
viscosity (Pa .s)
100.0 1000 10000
shear rate (1/s)
0.01000
0.1000
1.000
10.00
viscosity ( Pa.s)
Surfactant A
Non-penetrating
Surfactant B
Penetrating
Surfactant C
Non-penetrating
Inc. shear rate
Dec. shear rate
Figure 4 (above):
Appearance of bubbles in
the Compounds 1 and 3 and
with different surfactants.
Figure 5 (middle):
The viscosity measured with
a bob and cup geometry for
compounds 1 and 3. Test
conducted at 21°C initial
froth temperature.
Figure 6 (below):
The increasing and decreas-
ing shear rate rheograms
associated with the three
compounds A, B, and C.
Data for A and C overlap.
At a constant filler loading level, bubble size
influences the rheology of frothed compounds
(Figures 5 – 6). Transient viscosity vs. shear rate
results accurately followed the power-law mod-
el to describe frothed compound rheology using
the increasing shear rate curve (Table 2). The
additive to make Compound 1, a penetrating
froth aid, contained large bubbles with a wide
size distribution, while other frothed compounds
contained small bubbles with a narrow size dis-
tribution. The same was true for the case of Sur-
factant B, which also yielded a penetrating for-
mulation. All penetrating compounds had low
viscosities and were not stable to shear. Large
bubbles having a wide size distribution bubbles

in frothed compound gave lower viscosity, and
had more thixotropy (shear thinning over time);
they were characteristic of empirically penetrat-
ing compounds. Small bubbles having a narrow
size distribution gave high viscosity and little
thixotropy; they were characteristic of empiri-
cally (from carpet mill operations) non-penetrat-
ing compounds.
The pressure pulse and penetration predict-
ed by the model are given in Figures 3 and 7. Sur-
prisingly, the pressure profiles are quite close to
each other. Differences in rheology between
compounds did not change the pressure distrib-
ution inside the nip, but influenced the amount
of penetration (draining). The non-penetrating
formulations actually generate a higher pressure
pulse in the nip which potentially could drive
more fluid into the web, but these formulations
also have a higher viscosity that slows down pen-
etration.
Quantitative determination of penetration
with these exact frothed compounds in the indus-
trial process was not possible to obtain. However,
identification of formulations that are non-pene-
trating or penetrating are empirically known from
practical experience. The actual penetration of
frothed compounds may differ even more. This is
because the power-law rheological model does
not account for the thixotropic nature and the
compound stability under shear must be a key fac-
tor to consider. The model proposed here is only
intended to be an approximation for estimating
behavior in a precise industrial situation. Further
refinement is possible when accurate penetration
data are obtained for a number of compounds,
backings, and operating conditions.
4 CONCLUSIONS
We correlated results from viscosity versus shear
rate rheological tests with the size and distribu-
tion of bubbles in frothed carpet compounds.
Rheological tests characterize the time response
to shear of frothed compounds and accurately
determine the flow behavior arising from small
or large bubbles at constant filler loading and
froth density (or weight). Penetrating com-
pounds are found to have larger bubble sizes, are
more shear thinning and, therefore, are sensitive
to shear. This is critical because compounds with
small bubbles create stable froths, having rheo-
grams with a thixotropic loop between increas-
ing and decreasing shear rate curves, and do not
penetrate as much as froths with large bubbles.
Subsequently, frothed compounds with uni-
formly formed small bubbles increase the delam-
inating strength of carpet backing.
Analysis of the physics involved in manufac-
turing of carpet with roll coaters accounts for the
shear-thinning nature of compounds and pene-
tration of frothed material into the moving back-
ing web. It predicts the pressure distribution and
the amount of penetration after the rolling nip of
application. Model predictions qualitatively fol-
low known industrial trends. Results agree with
past empirical observations where stable, non-
penetrating compounds have fine bubbles and
higher viscosity than penetrating compounds.
However, high viscosity does not change the pres-
sure distribution in the rolling nip, but seems to
act as the viscosity that resists penetration.
ACKNOWLEDGEMENT
We would like to thank Southern Chemicals &
Textiles Co. for their co-operation to providing
materials for these studies.
APPENDIX: ANALYTICAL MODEL DEVEL-
OPMENT
The rolling nip applicator shears and forces the
froth into the backing. This general flow field is sim-
ilar to forward roll coating that has been described
by a number of other researchers, such as Coyle et
al. and Carvalho et al. [11 - 15]. However, the physics
are different from past analyses in two ways: (a) the
fluid is able to penetrate into one of the boundaries,
and (b) the fluid is shear thinning. The lubrication
approximation for the momentum equation
describes the foam motion assuming, at first, a con-
stant-viscosity Newtonian fluid:
64250-7 Applied Rheology
Volume 18 · Issue 6
Figure 7:
Pressure profiles prediction
of the model for shear thin-
ning parameters that repre-
sent compounds 1 and 3.

(A1)
Where Pis pressure, mis the viscosity, and vxis
the velocity in the x-direction defined in Figure 2.
The boundary conditions for velocity are at y= 0,
the top surface of the porous web, the velocity is
U2, and at the surface of the top roll, y= h(x), the
velocity is U1. The velocity profile, between the
web and the roll surface is then:
(A2)
The shear rate is the derivative of the velocity pro-
file. At the web surface, it is:
(A3)
The first term in Eq. A3 is from the simple veloc-
ity differences between the roll surface and the
second term comes from pressure driven flow. A
mass balance in any slice forces the total flow
rate through the nip, including what has been
forced into the porous web, to be constant. Mass
balance generates the equation:
(A4)
Where Qis the total flow into the nip, that must
equal the inlet thickness of the fluid, hi, multi-
plied by the top roll surface speed U1. This total
flow must also match the net flow rate in the flu-
id between the web and the top roll plus the flu-
id carried along in the pores, U2L(x)e, where L(x)
is the depth of penetration of fluid into the pores
and eis the void fraction of the porous media.
Inserting Eq. A2 in to Eq. A4, integrating, and
arranging in terms of the pressure gradient, we
obtain the differential equation for pressure:
(A5)
The top roll can be any speed relative to the web.
Eq. A5 represents the mass and momentum bal-
ance for this situation for a Newtonian fluid. An
approximate method to account for shear thin-
ning is to use an appropriate viscosity in Eq. A5
that relates to a relevant shear rate at that vicin-
ity of the flow field. Eq. A3 in combination with
the power-law model given in Eq. 1 is one way to
do this. A complete analysis would lead to finite
element analyses. Darcy’s law links penetration
rate into the web with the local pressure field.
Assuming that the air pressure in the porous web
is atmospheric, the penetration rate would be:
(A6)
Where Kpis the Darcy permeability coefficients
of the web, and vy= 0 is the penetration veloci-
ty. The velocity above is the rate of change of pen-
etration volume per unit area into the web:
(A7)
Where Vis volume per unit area of the fluid that
penetrates the web. From a mass balance, the
volume is related to the depth of penetration:
(A8)
The geometry between the two surfaces is well
defined and follows the expression:
(A9)
Where Ris the roll radius and ho is the minimum
gap between the rolls at x= 0. Carvalho and Scriv-
en [11, 15] suggested a boundary condition for the
film split location:
(A10)
Where Rmis the radius of curvature of the film-
split meniscus, and sis the fluid surface tension.
The radius of curvature is then:
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Applied Rheology
Volume 18 · Issue 6

(A11)
With Qebeing the volumetric flow rate per unit
length at the exit and Ca the capillary number Ca
= mU/s. The meniscus location is found by match-
ing the circular meniscus to the asymptotic solu-
tion of the flow on a flat plate being withdrawn
from a pool of liquid. For a speed ratio of unity,
the film-split height at the exit he is:
(A12)
The inlet pressure is assumed to be atmospher-
ic. However, the inlet location is not known a pri-
ori. Therefore, a trial-and-error method was
employed to find the inlet location, where the
fluid first contacts the web; this location was esti-
mated and the pressure field was integrated. The
exit pressure must match the pressure given in
Eq. A10. If not, the entrance location was modi-
fied. The details of the exit location and pressure
condition are not critical to the predictions of the
model.
Numerical integration of the coupled differ-
ential equations, Eqs. A5 and A7, along with Eqs.
A6, A8 and A9 gives the pressure distribution in
the rolling nip and the depth of fluid penetration
in to the web. Shear thinning is taken into
account through an approximate method by
modifying the viscosity value used in Eqs. A5 and
A6 with the power-law expression, using the
shear rate at the surface of the porous web.
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