Korea-Australia Rheology Journal March 2010 Vol. 22, No. 1 75

Korea-Australia Rheology JournalVol. 22, No. 1, March 2010 pp. 75-80

Ribbing instability in rigid and deformable forward roll coating flows

Je Hoon Lee1, Sang Kwon Han

2, Joo Sung Lee

3, Hyun Wook Jung

1,* and Jae Chun Hyun1

1Department of Chemical and Biological Engineering, Korea University, Seoul 136-713, Korea2POSCO, Surface Technology Research Group, Gwangyang 545-090, Korea

3LG Chem/Research Park, Daejeon 305-380, Korea

(Received December 2, 2009; final version received February 2, 2010)

Abstract

Dynamics and ribbing instability for Newtonian and viscoelastic liquids have been investigated in both rigidand deformable forward roll coating flows. Especially, the role of viscoelasticity of coating liquids and rolldeformability or hardness on the coating flow has been scrutinized. Coating thickness at steady uniformstates and wavelength and severity at unstable ribbing states have been measured, incorporating thicknessmeasurement device and two-roll coating equipment. Relationship between wavelength and severity in rib-bing instability strongly depends on the viscoelasticity as well as other operating conditions such as cap-illary number, coating gap, and roll deformability. Coating windows demarcating uniform and ribbinginstability are considerably reduced by increasing viscoelasticity and decreasing roll deformability. In otherwords, ribbing is aggravated as the viscoelasticity of coating liquids that can generate the extensional prop-erty in film splitting region rises or roll deformability decreases, leading to higher severity and narrowerwavelength.

Keywords : ribbing, forward roll coating, wavelength, severity, viscoelasticity, roll deformability, coating

window

1. Introduction

Various coating processes have currently been involved

in many industries manufacturing flat panel displays, sec-

ondary batteries, multi-purpose films, Cr-free steel prod-

ucts, solar cells and fuel cells. The main purpose of the

coating technology is to produce continuous or intermit-

tently patterned coating layers of desired uniform thickness

by optimally controlling stability and dynamics in coating

flow regimes (Cohen and Gutoff, 1992; Kistler and Sch-

weizer, 1997; Weinstein and Ruschak, 2004). It is actually

difficult task to maintain uniform coatings at high speeds

because coating processes are inevitably subject to unex-

pected disturbances, affecting the productivity of coating

products and processability. Many kinds of flow instabil-

ities or defects such as leaking, air entrainment, ribbing,

cascade, rivulet, barring, etc. are frequently observed in

coating flows (Gutoff and Cohen, 1995). Numerous impor-

tant theoretical and experimental facts on flow behaviors

and instabilities in coating flows have been explored by

many researchers in both industry and academia, however,

there exist many unresolved issues in this area, for

instance, role of viscoelasticity on coating flows, compli-

cated flow dynamics in multilayer coatings, high-speed

coating technology for productivity enhancement, etc

(Coyle, 1984; Kistler and Scriven, 1984; Benjamin, 1994;

Gutoff and Cohen, 1995; Carvalho, 1996; Dontula et al.,

1997; Dontula, 1999, Gaskell et al., 2001; Benkreira et al.,

2002). As polymeric liquids or suspensions or slurries to be

coated are being diversified and specified, it is indispens-

able to elucidate the rheological aspects of coating liquids

for the environment-friendly drying process to efficiently

evaporate solvent and for enhancement of the product

quality (Dontula, 1999).

In this study, forward roll coating processes, which have

been conventionally used for quite a long time, have been

revisited, among many possible coatings to be employed in

industries such as slot, slide, curtain, air-knife, and roll

coatings. Roll coating is characterized by the use of one or

more gaps or nips between rotating rolls to meter and apply

a coating liquid to web or substrates. Fig. 1 exhibits a basic

schematic diagram of two-roll rigid and deformable for-

ward roll coatings. Many researchers experimentally and

theoretically exploited flow dynamics and ribbing insta-

bility in forward roll coating processes (Mill and South,

1967; Middleman, 1977; Fall, 1978; Greener et al., 1980;

Gokhale, 1981; Savage, 1984; Castillo and Patera, 1997;

Carvalho and Scriven, 1997, 1999; Hao and Haber, 1999;

Benkreira et al., 2002; Chong et al., 2007). Coyle (1984)*Corresponding author: hwjung@grtrkr.korea.ac.kr© 2010 by The Korean Society of Rheology

Je Hoon Lee, Sang Kwon Han, Joo Sung Lee, Hyun Wook Jung and Jae Chun Hyun

76 Korea-Australia Rheology Journal

systematically solved roll coating dynamics using two-

dimensional Navier-Stokes equation. Carvalho and Scriven

(1997, 1999, 2003) eloquently developed novel simulation

for deformable roll coating flow. Also, ribbing instability,

which is a regular cross-web variation, for various coating

liquids has been experimentally elucidated in the literature

(Hasegawa and Sorimachi, 1993; Varela Lopez et al.,

2002; Chong et al., 2007; Han et al., 2009).

Albeit important aspects on the forward roll coating flow

have been established, the role of viscoelastic nature of

coating liquids on flow behavior and instability has not

been fully understood yet. In this study, based on preceding

results by Han et al. (2009), steady and unsteady flow

behaviors in both rigid and deformable forward roll coat-

ings have been investigated, focusing effects of the vis-

coelasticity of several coating liquids and roll deformability

or hardness. Considering rheological properties of coating

liquids, final wet coating thickness at steady states and

wavelength and severity for ribbing information at unstable

states have been correlated with the use of flow visual-

ization apparatus.

2. Experiments

Newtonian (a mixture of 90 wt% glycerin and 10 wt%

water (N)) and two viscoelastic liquids (addition of

200 ppm (P1) and 500 ppm (P2) of Polyacrylamide

(PAAm, 5,000,000 Mw) in the Newtonian liquid) are con-

sidered in the forward roll coating experiments. Rheolog-

ical properties for these liquids are fully reported in Han et

al. (2009), exhibiting that they give the same constant

shear viscosity (0.163 Pa.s) and surface tension (about

65 mN/m), and viscoelastic liquids as Boger fluids possess

elastic property by a small amount of PAAm. From fil-

ament breakup time data of coating liquids via the CaBER

experiment (Han et al., 2009), it has been found that strain

hardening extensional property in polymer solutions is

larger than Newtonian case.

Cr-coated rigid roll and deformable rolls with hardness

35 and 60 specified by Shore durometer (e.g., deformable

roll with hardness 35 is softer than 60 one.) have been

implemented for two-roll forward coating experiments

shown in Fig. 1. Their diameter is 136 mm. The wet coat-

ing thickness is measured by a thickness sensor (IFD-2401,

Micro-Epsilon Co.) with submicron accuracy (0.04 µm

resolution) which uses a confocal measurement principle.

Because the polychromatic light source of this device is

only focused on a spot of roll surface, wet thickness under

stable conditions has been averaged within 3% tolerance

error from data measured for 30 seconds at different roll

positions. It should be also noted that maximum and min-

imum thicknesses at unstable ribbing state for estimating

the severity have been more carefully recorded, since a rib-

bing pattern slightly moves from side to side, keeping

nearly constant amplitude and wavelength. Wavelength of

ribbing is captured using Camscope or DSLR Camera.

Distance between peaks (or troughs) of a regular ribbing

are also calculated from pixels of digital image data, prov-

ing that the averaged wavelength taken from over

5 pictures at a given experiment are reliable within 5% tol-

erance error. Steady and unsteady flows have been

observed by changing coating gap between two rolls from

100 to 400 µm and roll speed from 0 to 40 m/min.

3. Results and discussion

3.1. Coating thickness profile at steady statesWet coating thickness on the roll surface in downstream

flow regime under stable conditions is measured using IFD-

2401 in real-time. Fig. 2 displays wet film thickness profile

of Newtonian and viscoelastic coating liquids depending on

Capillary number ( , η: shear viscosity, V: roll

speed, σ: surface tension, Ca is defined as ratio between

viscous and surface tension forces.), minimum gap between

rolls, roll deformability, and viscoelasticity. As Ca (e.g., roll

speed) and coating gap increases, wet thickness is raised

due to the increase of flow rate of coating liquids pene-

trating film splitting region (i.e., converging-diverging gap

region). As depicted in Fig. 2a, the roll deformability sig-

nificantly affects wet film thickness under small gap con-

dition. Coating liquid can easily pass through the film

splitting region with large gap (e.g., 400 µm here), regard-

less of roll deformability or hardness, resulting in the same

wet film thickness (i.e., same flow rate) at different roll

deformability cases. The flow rate of coating liquid pen-

etrating the film splitting region is of course running down

with decreasing coating gap. In this case, the wet film thick-

ness by more deformable roll operation is larger than that

Ca ηV σ⁄≡

Fig. 1. Schematic diagrams of two-roll coating process with (a)

rigid rolls and (b) rigid and deformable rolls.

Ribbing instability in rigid and deformable forward roll coating flows

Korea-Australia Rheology Journal March 2010 Vol. 22, No. 1 77

by less deformable or rigid one. It is also worthwhile to note

that the reason why the range of Ca to measure wet film

thickness is different with the coating gap is closely related

with the occurrence of unstable ribbing instability, which is

featured by cross-web variation.

Fig. 2b substantiates that a small portion of viscoelastic

polymer in coating liquids can dramatically changes flow

behavior, albeit coating liquids to be adopted here gives the

same shear viscosity. From the results, it has been found

that the viscoelasticity makes the wet film thickness thin-

ner, resulting from elastic or extensional stress in film split-

ting region. Reduction of film thickness (or flow rate) by

viscoelastic nature might be due to the significant exten-

sional viscosity by a small amount of polymer in coating

liquids in upstream film splitting region (i.e., converging

flow domain).

3.2. Coating windowsOperability coating windows for both Newtonian and

viscoelastic coating flows have been established with gap-

to-diameter ratio (H0/D, H0: minimum gap between two

rolls, D: diameter of roll) and capillary number (Fig. 3).

Neutral curve for the Newtonian liquid for two-roll rigid

case, demarcating uniform state and ribbing instability, is

almost in agreement with those introduced in the previous

reports (Gokhale, 1981; Carvalho and Scriven, 1999; Don-

tula 1999; Chong et al., 2007). Fig. 3a displays that the sys-

tem is more stable with increasing gap-to-diameter ratio and

decreasing Ca and also more deformable roll expands the

stable uniform regime. This stability tendency might be

related to flow rate data under same conditions. In other

words, as described in the previous section, deformable roll

increases flow rate of coating liquids penetrating the narrow

converging-diverging film splitting regions under the same

operating conditions, leading to stabilizing the system.

As illustrated in Fig. 3b, the viscoelasticity makes the

system more unstable, aggravating the ribbing instability.

The destabilizing effect of the polymer solution might be

Fig. 2. (a) Effect of roll deformability on wet thickness in New-

tonian case and (b) effect of viscoelasticity on the wet

thickness using deformable roll with 60 roll hardness.

Fig. 3. (a) Effect of roll deformability on the stability in New-

tonian case and (b) effect of viscoelasticity on the stability

using deformable roll with 60 roll hardness.

Je Hoon Lee, Sang Kwon Han, Joo Sung Lee, Hyun Wook Jung and Jae Chun Hyun

78 Korea-Australia Rheology Journal

caused by the reduction of flow rate due to the high elastic/

extensional property of polymer coating liquids in

upstream and downstream film splitting regimes, compar-

ing with Newtonian case. From the theoretical ribbing cri-

terion introduced in the literature (Gokhale, 1981; Castillo

and Patera, 1997; Carvalho and Scriven, 1997), ribbing

instability inevitably occurs in forward roll coating systems

due to the always positive pressure gradient at downstream

meniscus. Ribbing can be readily seen under the condition

inducing the large positive pressure gradient. It is also

believed that from the experimental facts of this study, the

viscoelasticity makes the pressure gradient in the down-

stream more positive (Hao and Haber, 1999; Gaskell et al.,

2001; Benkreira et al., 2002; Zevallos et al., 2005). Fig. 4

shows examples of ribbing instability under various oper-

ating conditions.

3.3. Wavelength and severity of ribbing To further clarify the ribbing instability, its wavelength

and severity have been scrutinized as delineated in Figs. 5

and 6. The wavelength decreases by increasing Ca and

decreasing roll deformability and coating gap for New-

tonian liquid from Figs. 5a and 5b. Also, the viscoelasticity

of polymer solutions leads to the decrease of wavelength

(Fig. 5c) in comparison with Newtonian case under the

same conditions. Considering the operability coating win- dows, it has been revealed that the system with shorter

Fig. 4. Examples of ribbing for liquid P2 at (a) Ca=0.33 in 400 m

coating gap and (b) Ca=1.2 in 100 m coating gap (60 roll

hardness).

Fig. 5. Effects of (a) coating gap for Newtonian liquid (60 roll

hardness), (b) roll deformability for Newtonian liquid, and

(c) viscoelasticity of coating liquids (60 roll hardness) on

the wavelength of ribbing instability.

Ribbing instability in rigid and deformable forward roll coating flows

Korea-Australia Rheology Journal March 2010 Vol. 22, No. 1 79

wavelength is more unstable, although the wavelength of

ribbing does not change so much at high Ca regime.

To predict reliable severity of ribbing, we tried to mea-

sure maximum and minimum thickness along with roll

width direction during ribbing state using thickness mea-

surement device. Severity data, defined as 2(Tmax−Tmin)/

(Tmax+Tmin), will decisively represent the intensiveness of

ribbing instability or non-uniformity of coating layer. From

Figs. 6a and 6b in the Newtonian case, the increase of the

coating gap and roll deformability makes the severity

lower. It is noted that there is no dependence on the roll

deformability of the severity for large coating gap (e.g.,

400 µm here), indicating that the role of roll deformability

is meaningful only in small positive or squeezing negative

gaps. Above severity and wavelength data are well

matched with each other, implying that the shorter wave-

length, the larger severity. Furthermore, the increase of the

viscoelasticity gives rise to the larger severity due to the

aggravation of the ribbing instability in contrast to New-

tonian case.

4. Conclusion

Forward rigid and deformable roll coating experiments

have been performed employing Newtonian and viscoelas-

tic polymeric liquids. Based on fundamental results by Han

et al (2009), more refined information on ribbing insta-

bility has been further elucidated in this study, focusing the

role of roll deformability and viscoelasticity of coating liq-

uids on dynamics and stability in roll coating systems. Wet

film thickness at steady states and wavelength and severity

at ribbing states have been connected with process con-

ditions such as capillary number (or roll speed), coating

gap, roll deformability (or hardness), and viscoelasticity.

Wet coating thickness decreases as coating gap or softness

of the roll decreases and the viscoelastic nature rises. Espe-

cially, a small amount of polymer in coating liquids with

same shear viscosity plays a key role in reducing the wet

film thickness, generating the higher elastic or extensional

property in film splitting region. Also, the viscoelasticity

aggravates the ribbing instability and then curtails the coat-

ing window, leading to larger severity and smaller wave-

length in comparison with Newtonian case.

Acknowledgements

This study was supported by research grants from the

Seoul R&BD program and POSCO company. Also, the

support of the KOSEF (R01-2008-000-11701-0) is grate-

fully acknowledged.

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