Ribbing instability in rigid and deformable forward roll coating flows

Transcription

1 Korea-Australia Rheology Journal Vol. 22, No. 1, March 2010 pp Ribbing instability in rigid and deformable forward roll coating flows Je Hoon Lee 1, Sang Kwon Han 2, Joo Sung Lee 3, Hyun Wook Jung 1, * and Jae Chun Hyun 1 1 Department of Chemical and Biological Engineering, Korea University, Seoul , Korea 2 POSCO, Surface Technology Research Group, Gwangyang , Korea 3 LG Chem/Research Park, Daejeon , 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 rigid and deformable forward roll coating flows. Especially, the role of viscoelasticity of coating liquids and roll deformability or hardness on the coating flow has been scrutinized. Coating thickness at steady uniform states and wavelength and severity at unstable ribbing states have been measured, incorporating thickness measurement device and two-roll coating equipment. Relationship between wavelength and severity in ribbing instability strongly depends on the viscoelasticity as well as other operating conditions such as capillary number, coating gap, and roll deformability. Coating windows demarcating uniform and ribbing instability are considerably reduced by increasing viscoelasticity and decreasing roll deformability. In other words, ribbing is aggravated as the viscoelasticity of coating liquids that can generate the extensional property in film splitting region rises or roll deformability decreases, leading to higher severity and narrower wavelength. Keywords : ribbing, forward roll coating, wavelength, severity, viscoelasticity, roll deformability, coating window 1. Introduction *Corresponding author: hwjung@grtrkr.korea.ac.kr 2010 by The Korean Society of Rheology Various coating processes have currently been involved in many industries manufacturing flat panel displays, secondary batteries, multi-purpose films, Cr-free steel products, solar cells and fuel cells. The main purpose of the coating technology is to produce continuous or intermittently patterned coating layers of desired uniform thickness by optimally controlling stability and dynamics in coating flow regimes (Cohen and Gutoff, 1992; Kistler and Schweizer, 1997; Weinstein and Ruschak, 2004). It is actually difficult task to maintain uniform coatings at high speeds because coating processes are inevitably subject to unexpected disturbances, affecting the productivity of coating products and processability. Many kinds of flow instabilities or defects such as leaking, air entrainment, ribbing, cascade, rivulet, barring, etc. are frequently observed in coating flows (Gutoff and Cohen, 1995). Numerous important 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, complicated 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 indispensable 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 forward roll coatings. Many researchers experimentally and theoretically exploited flow dynamics and ribbing instability 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) Korea-Australia Rheology Journal March 2010 Vol. 22, No. 1 75

2 Je Hoon Lee, Sang Kwon Han, Joo Sung Lee, Hyun Wook Jung and Jae Chun Hyun Fig. 1. Schematic diagrams of two-roll coating process with (a) rigid rolls and (b) rigid and deformable rolls. systematically solved roll coating dynamics using twodimensional 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 coatings have been investigated, focusing effects of the viscoelasticity 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 visualization 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 considered in the forward roll coating experiments. Rheological 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 filament 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 coating 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 minimum thicknesses at unstable ribbing state for estimating the severity have been more carefully recorded, since a ribbing 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, proving that the averaged wavelength taken from over 5 pictures at a given experiment are reliable within 5% tolerance 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 states Wet coating thickness on the roll surface in downstream flow regime under stable conditions is measured using IFD in real-time. Fig. 2 displays wet film thickness profile of Newtonian and viscoelastic coating liquids depending on Capillary number ( Ca ηv σ, 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 penetrating film splitting region (i.e., converging-diverging gap region). As depicted in Fig. 2a, the roll deformability significantly affects wet film thickness under small gap condition. Coating liquid can easily pass through the film splitting region with large gap (e.g., 400 µm here), regardless 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 penetrating the film splitting region is of course running down with decreasing coating gap. In this case, the wet film thickness by more deformable roll operation is larger than that 76 Korea-Australia Rheology Journal

3 Ribbing instability in rigid and deformable forward roll coating flows Fig. 2. (a) Effect of roll deformability on wet thickness in Newtonian 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 Newtonian case and (b) effect of viscoelasticity on the stability using deformable roll with 60 roll hardness. 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 thinner, resulting from elastic or extensional stress in film splitting region. Reduction of film thickness (or flow rate) by viscoelastic nature might be due to the significant extensional viscosity by a small amount of polymer in coating liquids in upstream film splitting region (i.e., converging flow domain) Coating windows Operability coating windows for both Newtonian and viscoelastic coating flows have been established with gapto-diameter ratio (H 0 /D, H 0 : 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; Dontula 1999; Chong et al., 2007). Fig. 3a displays that the system 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 Korea-Australia Rheology Journal March 2010 Vol. 22, No. 1 77

4 Je Hoon Lee, Sang Kwon Han, Joo Sung Lee, Hyun Wook Jung and Jae Chun Hyun 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). 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, comparing with Newtonian case. From the theoretical ribbing criterion 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 downstream more positive (Hao and Haber, 1999; Gaskell., 2001; Benkreira., 2002; Zevallos., 2005). Fig. 4 shows examples of ribbing instability under various operating conditions. et al et al et al 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 Newtonian 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 win78 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. dows, it has been revealed that the system with shorter Korea-Australia Rheology Journal

5 Ribbing instability in rigid and deformable forward roll coating flows To predict reliable severity of ribbing, we tried to measure maximum and minimum thickness along with roll width direction during ribbing state using thickness measurement device. Severity data, defined as 2(T max T min )/ (T max +T min ), 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 wavelength, 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 Newtonian case. 4. Conclusion Forward rigid and deformable roll coating experiments have been performed employing Newtonian and viscoelastic polymeric liquids. Based on fundamental results by Han et al (2009), more refined information on ribbing instability has been further elucidated in this study, focusing the role of roll deformability and viscoelasticity of coating liquids 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 conditions 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. Especially, 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 coating window, leading to larger severity and smaller wavelength in comparison with Newtonian case. Acknowledgements Fig. 6. 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 severity of ribbing instability. wavelength is more unstable, although the wavelength of ribbing does not change so much at high Ca regime. This study was supported by research grants from the Seoul R&BD program and POSCO company. Also, the support of the KOSEF (R ) is gratefully acknowledged. References Benjamin, D.F., 1994, Roll Coating Flows and Multiple Roll Systems, Ph.D. thesis, University of Minnesota. Benkreira, H., M.F. Edwards and W.L. Wilkinson, 2002, Korea-Australia Rheology Journal March 2010 Vol. 22, No. 1 79

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