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Improved Coating Window for Slot Coating Chih-Ping Chin,† Ho-Shing Wu,*,† and Shaw S. Wang†,‡ Department of Chemical Engineering and Materials Science, Yuan Ze UniVersity, 32003 Taiwan, Republic of China, and Department of Chemical and Biochemical Engineering, Rutgers UniVersity, The State UniVersity of New Jersey, New Brunswick, New Jersey 08901-8554
Slot die is a premetered coating operation in which the coating solution is extruded from a feed slot onto the surface of a substrate passing through. The defect-free region of operation is known as the “coating window”, and the wider it is, the more versatile the operation will be. The slot-coating experiments reported here were carried out with two types of coating solutions, a hard coating solution with low viscosity and a polysilica solution with high viscosity. The coating windows were measured as flow rates q versus minimum and maximum coating speeds, Vmin and Vmax, respectively. Therefore, at a given flow rate of the coating solution, there exists a minimum speed and a maximum speed that border the corresponding coating window, outside which coating defects occur. Also, in our experiments, the coating windows shifted to higher coating speed and obtained thinner coating film thicknesses through different settings of the die angle to the substrate and different geometries of die lips. The data showed that the coating windows shifted to higher speed and thinner film thicknesses when the die angle and the geometry of the die lips were varied appropriately. These results have important practical implications. The fundamental principles involved here are also applicable to other premetered coating processes. 1. Introduction The slot-die coating process is one of the premetered coating methods in which the coating thickness can be predetermined before the operation. The advantages of premetered coating processes include excellent uniformity in lateral coating, high coating speed, and coating in a closed environment, which is essential to minimize contamination and pollution. It is commonly used in the manufacturing of many products, including coated paper, paints, photographic films, etc. The coating process studied here can produce protective sheets for optical applications. These protective sheets are used to prevent dust, debris, stains, and scratches on the surface of image display devices such as plasma displays, cathode ray tubes, and liquid-crystal displays. In a slot-die coating process, the coating solution is pumped to a coating die in which there is an elongated chamber and distributed across the width of a narrow slot, through which the flow rate per unit width at the slot exit is made uniform. As it exits the slot, the coating solution fills the gap between the die and the moving substrate or web. The coating solution in the gap, bounded upstream and downstream by gas-liquid interfaces or menisci, forms the coating bead. The coating beads are carried away from the downstream meniscus by the substrate moving past the die, and the coated layer is formed on the surface of the substrate. Like other coating processes, the slotdie coating process should be carefully operated in applicable conditions to prevent coating defects and produce a uniform coating layer. The common defects observed in a slot-die coating process are dripping, air entrainment, ribbing, and barring. The occurrence of these defects depends on the design of the die coater, the operating conditions, and the physical properties of coating solutions.1–5 The slot-die coating process was invented by Begiun,6 but it was Ruschak7 who first developed a theory to predict the coating * To whom correspondence should be addressed. Tel: +88634638800 ext 2564. Fax: +886-3-4559373. E-mail: cehswu@saturn. yzu.edu.tw. † Yuan Ze University. ‡ Rutgers University.
ability of the slot coating and introduced the concept of a coating window. Ruschak observed that coating defects occur when either the upstream or downstream interface does not bridge the gap and showed that an ambient pressure difference across the coating bead that satisfies Pup - Pdown < 0 is required to coat thin and fast. Ruschak also established a correlation linking the minimum wet thickness with the capillary number, gap, and dynamic contact angle. Higgins and Scriven8 extended Ruschak’s work to include the viscous effect in the coating bead. O’Brien9 proposed a coating die with a beveled draw-down surface to impose boundary forces on the downstream side of the coating bead and to reduce the amount of vacuum necessary to maintain the bead stability. Kageyama and Yoshida10 proposed a coating die with a closed passage to circulate the coating liquid and to form a uniform coating layer on the substrate while at the same time keeping the composition and viscosity of the coating liquid stable. Sartor,11 Kistler and Schweizer,12 and Gates13 proved that a slight vacuum applied at the upstream meniscus region stabilizes the coating beads. Lee and Liu14 experimentally verified that the predictions of Ruschak6 were valid at low capillary numbers and found that extrusion slot coating was similar to blade coating at high capillary numbers. Brown and Maier15 proposed a slot-die coating process using an apparatus including the combination of a sharp-edge downstream die lip and a land-edge upstream die lip. They proved that coating performances were improved and thinner coating layers were obtained by having specific height differences between the upstream and downstream die lips. Ning et al.16 and Cai17 found experimentally that a small amount of polymer added to the coating solution extends the maximum coating speed of the slot-die coating. This stabilizing effect of polymer additives can be attributed to the extended polymer chain at high coating speeds. Romero et al.18,19 examined the low-flow limit in the slot coating of dilute solutions of a high-molecular-weight polymer, poly(ethylene glycol), with a vacuum applied on the upstream meniscus. They also proved that a slight suction on the upstream meniscus can expand the coating window and increase the low-flow limit
10.1021/ie801900t 2010 American Chemical Society Published on Web 03/17/2010
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Table 1. Operating Coating Conditions in the Industry Coating Process and Laboratory Coater Module industrial coating process
laboratory coater module
setting in the clean room with temperature and humidity control working with various polymer coatings
setting in ambient environment only working in a Newtonian fluid (glycerol solution) and with a simple polymer coating without any other process module without a machine limit thickness of the coating film calculated from the flow rate and coating velocity should be unity
with other process modules such as a drying oven, UV lamp, etc. within a machine limit thickness and precision of the coating film measured after curing
speed, but the effect depended on the rheological properties of coating solutions. Lin et al.20 examined the coating window for a combination of slide and slot coating, revealing that changing the flow direction in the coating die leads to a more stable coating flow and much thinner layer. Weinstein and Gros21 determined the steady-state operating window for extrusion slot coating in the presence of applied pressures. They explored the shape of the two-dimensional, thin viscous sheet between the slot and the substrate for a power-law liquid. They provided the theoretical analysis of the coating configuration to determine the shape of the liquid sheet and the extrusion coating window. The studies on slot-die coating process reviewed above presented the fluid mechanics of coating solutions and the effect
of die designs on the expansion of coating windows. As for related coating studies, Cohu and Benkreira22 examined the coating windows in angled dip coating, in which a substrate entered a pool of liquid with a laterally inclined angle from the vertical so that the dynamic wetting line is not perpendicular to the direction of motion. They observed experimentally that air entrainment was delayed to higher speeds, thus expanding the coating window. They also confirmed that having the dynamic wetting line not perpendicular to the substrate motion was an effective way to delay air entrainment in slide coating flows. Benkreira23 examined the dynamic wetting in forward roll coating and found that, as forward roll coating switches from metered to premetered with changes in the operation conditions, the dynamic wetting line moves near to the minimum gap position, just as in reverse roll coating. Ikin et al.24 studied the coating windows in the slide coating process and found that increasing the slide angle maintains the direction of flow down the slide normal to the web at the dynamic wetting line. Therefore, the dynamic wetting line, which can be adjusted by the contact angle of coating liquids to substrates and the geometry of die blocks, also affects the coating ability. Nam et al.25 found that vortices in flow can cause undesired effects on the coating layer by tracking the birth of vortices with computeraided analysis and design. They also proposed that the acceptable coating quality must be operated in “vortex-free windows”. In their study, they also proved that the acceptable operating ranges broaden with changes in the die-lip geometry. The literatures reviewed so far are those from laboratory studies that do not use industrial substrates and coating solutions. The coating formulas used in industry are more complicated than those applied in laboratory tests, with a mixture of monomers, surfactants, and solvents. The coating system applied for industrial coating processes is more complicated and is composed of a coater (die and rollers) and unwinding, rewinding, and curing modules (ovens and UV lamps) in an industrial coating line. Therefore, the operational parameters in an industrial coating line are not only those from the fluid mechanics of coating solutions in laboratory coating experiments but also the limitation of machines, design of the die coater, and operation (see Table 1). This study presents the influence of the contact angle of coating flow and the design of die geometry for retarding coating defects in a slot-die coating process. Thus, the coating window can be shifted or extended by changing the height of the slot die between upstream and downstream die lips with shim and inclination of the slot exit angle or the angle of the die to the substrate. Table 2. Physical Properties of the Coating Liquids Used in This Study
coating liquid Figure 1. Viscosity data of coatings measured by a rheometer. (a) polysilica solution; (b) hard coating solution.
polysilica solution hard coating solution
viscosity (mPa · s)
surface tension (dyn/cm)
density (kg/m 3)
150 10
23 16
840 740
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Figure 2. Schematic of the pilot coating line.
2. Experimental Section A polysilica solution [SYL-OFF(R) 7362 Coating; Dow Corning Corp.] and a hard coating solution (HC-6149; Pufeng Industral Co., Taiwan) were used as coating liquids in this study. The viscosities of the coating liquids (Figure 1) were measured to an accuracy of (5% with a rheometer (TA-Ares; TA Instruments Co.), and the surface tensions were measured by using the pendent drop method to an accuracy of (5%. These measurements were carried out at a temperature of 25 ( 2 °C, and the data are displayed in Table 2. A poly(ethylene terephthalate) film was used as the web substrate, with an average thickness of 23 ( 2 µm (G121; Shinkong Co., Taiwan). The experimental apparatus used in this study was an industrial pilot coating line (manufacturer: Inokin Inc., Japan.), as shown in Figure 2, which consists of an unwinding unit, a floating die coater (as shown in Figure 3), drying modules, a UV lamp unit, and a rewinding unit. The maximum substrate translating speed of this pilot coating line is 20 m/min. The drying modules were constructed with air floating nozzles (AG204, CA type) having five sections with temperature control, and heating is done by a medium-heat boiler with a maximum temperature capacity of 225 °C. The web tension was controlled by dancing rollers monitored by sensors. The whole coating line was set in a clean room with specification class 1000, where the ambient temperature and relative humidity were controlled at 25 °C and 50%, respectively. The coating liquid flow transferring system consisted of a microgear pump (Micropump Inc. model type 200), a Carioles flowmeter, a polyethylene (PE) tube (Φ ) 9.6 mm), a stainless steel tank, and a filter. The backing roller was made of a hollow stainless steel cylinder coated with a chrome layer and with a diameter of 200 mm and a length of 720 mm. A single-cavity T-die made of stainless steel was used to feed the coating liquid onto the coating roller, and the slot gap was adjusted by inserting stainless steel shims between the die pieces to obtain any desired feed gap. The feeding angle of the die was adjusted by inclining forward or backward for a maximum of 5° from the vertical position of the substrate. The rotational mode and the speed of the roller were controlled independently by a separate motor/speed control device. In our experiments, the surface film thickness was measured with an online spectrometer (STEAG ETA-Optic). The die coater, constructed with high precision, can generate a 450-mm-wide thin liquid film, which is quite uniform on the substrate without slipping problems. Under normal coating conditions, no serious edge effects were observed. The important parameters of this study such as the coating gap L, inclining angle θ, and distance T between the upstream and downstream die lips are shown in
Figure 3. (a) Schematic of the die coating system. (b) Definition for the coating flow and die geometry system.
Figure 3. In addition to variation of the coating solutions, the flow rates and the coating speed of the substrate Vs were also varied with operating parameters during the experiment, but the settings of the coating and slot gaps were fixed at L ) 150 µm and D ) 1 mm, respectively. The values of the substrate speeds, Vmax, and Vmin, were measured based on visual observation of the boundary of the no defect zone, using procedures identical with those used by Lee and Liu.14 3. Results and Discussion Several types of coating defects (dripping, ribbing, and air entrainment) were observed during the experiment. The “dripping” defect implies that the coating beads are not stable in the gap between the substrate and die lips, and so gravity will pull the liquid down from the coating bead. The formation of regular waves of coating layers on the surface of the substrate is called “ribbing”.
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Figure 4. Effect of the viscoelasiticity at various coating solutions in the plot of the volumetric rate versus the coating speed at D ) 1 mm, H ) 0.15 mm, and inclining angle ) 0° and flat die geometry for (b, O) a polysilica solution (150 mPa · s) and (1, 4) a hard coating solution (10 mPa · s). Black symbol: dripping. White symbol: air entrainment.
Figure 6. Effect of the die-lip geometry at D ) 1 mm and H ) 0.15 mm including coating windows of (a) a polysilica solution and of (b) a hard coating solution for (9, 0) front, (1, 4) flat, and (b, O) rear. Black symbol: dripping. White symbol: air entrainment. Figure 5. Effect of the viscoelasiticity at various coating solutions in the plot of the thickness of the coating layer versus the coating speed at D ) 1 mm, H ) 0.15 mm, and inclining angle ) 0° and flat die geometry for (b) a polysilica solution and (O) a hard coating solution.
“Air entrainment” is caused by air bubbles trapped between the coating film and the substrate and forms blank bubble traces. 3.1. Effect of the Viscoelasticity. Figures 4 and 5 show that increments of the viscosity of the coating solution can not only increase the minimum wet thickness but also reduce the maximum coating speed. This finding agrees with the data of Lee and Liu14 that reducing the viscosity of the coating solution can reduce the minimum thickness and increase the maximum coating speed. Increasing the viscosity of the coating solution is a destabilizing factor because the coating defects such as air entrainment and ribbing would appear at a lower coating speed under high viscosity. It also indicates that both the film thickness and coating window relate strongly to the viscosity of the coating solution and substrate speed Vs. The coating window of a highviscosity coating solution is formed in lower coating viscosity than a coating solution with low viscosity. The film thickness for a polysilica coating solution is thicker than that for a hard coating liquid at each location. 3.2. Effect of the Die-Lip Geometry. Figure 6 indicates that the coating window varie with changes in the die geometry for
Figure 7. Effect of die-lip geometries in a plot of the thickness of the coating layer versus the coating speed at D ) 1 mm and H ) 0.15 mm with a hard coating solution: (1) front; (b) flat; (O) rear.
both a polysilica liquid and a hard coating liquid. The rearneck geometry of the die lips can delay the coating defects to
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Figure 8. Effect of the inclining angles of a flat die-lip geometry at D ) 1 mm and H ) 0.15 mm for coating windows of a polysilica solution with (a) inclining backward angles [θ ) (b, O) 0°, (1, 4) 2°, and (9, 0) 4°] and (b) inclining forward angles [θ ) (b, O) 0°, (1, 4) -2°, and (9, 0) -4°] and of a hard coating solution with (c) inclining backward angles [θ ) (b, O) 0°, (1, 4) 2°, and (9, 0) 4°] and (d) inclining forward angles [θ ) (b, O) 0°, (1, 4) -2°, and (9, 0) -4°]. Black symbol: dripping. White symbol: air entrainment.
higher speed and make the coating window shift to higher substrate speed and a thicker coating layer. In our experiments, we found that the rear-neck geometry of the die lips became a barrier in the upstream die block and allowed the upstream meniscus to be pinned in a fixed position and away from the feed slot, the so-called “bead vacuum effect”. A bead vacuum formed in the upstream die block can produce the same effect on the meniscus as reported by Sartor,11 Romero et al.,18,19 and Nam et al.25 As shown in Figure 7, with the rear-neck geometry at a fixed substrate speed, a larger coating flow rate produced thicker film thicknesses because of more stable coating beads. Thus, the coating window can be expanded to larger flow rates than those of the regular flat die geometry. In the front-neck die geometry, the coating window becomes smaller than other die-lip geometries, but the minimum film thickness becomes thinner because of a barrier that is formed by the higher downstream die block as a blade effect. When the blade effect is formed, the thickness of the coating layer is uniform in both lateral and longitudinal distributions. Through variation of the die geometry, the coating windows can be extended because of the advancement of pressure drops between the upstream and downstream menisci, as reported by Nam et al.25 Therefore, the proper selection of die-lip geometries can stabilize coating
beads and expand the coating windows. One specific advantage of using the front-neck die-lip geometry is that a thinner uniform coating can be obtained without additional accessories. This result also demonstrates that variation of the die-lip geometries can overcome the physical property limitation of coating liquids, retard coating defects, and shift the coating window to higher coating speeds and/or larger volumetric flow rates in the coating process with various coating solutions. 3.3. Effect of the Inclining Angles. Figure 8 shows the results of the coating experiments with polysilica and hard coating solutions at three different inclining angles θ of 0°, 2°, and 4° in either the forward or backward direction with a flat die-lip geometry. According to the experimental results of the effect of an increase in the backward inclining angle, as shown in Figure 8a,c, increasing the backward inclining angle of the die coater causes a decrease in the minimum film thickness and shifts the coating window to higher coating speeds. The experimental results also reveal that an increase in the backward incline angle θ causes a thinner coating layer with acceptable coating quality obtained because of a relative decrease of the gap between the downstream die block and the substrate. Furthermore, the said decreased gap also acts like a blade formed in the downstream die block and
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Figure 9. Effect of the inclining angles of rear-neck die-lip geometry at D ) 1 mm and H ) 0.15 mm for coating windows of a polysilica solution with (a) inclining backward angles [θ ) (b, O) 0°, (1, 4) 2°, and (9, 0) 4°] and (b) inclining forward angles [θ ) (b, O) 0°, (1, 4) -2°, and (9, 0) -4°] and of a hard coating solution with (c) inclining backward angles [θ ) (b, O) 0°, (1, 4) 2°, and (9, 0) 4°] and (d) inclining forward angles [θ ) (b, O) 0°, (1, 4) -2°, and (9, 0) -4°]. Black symbol: dripping. White symbol: air entrainment.
creates a uniform coating layer. The experimental results of the effect of an increase in the forward inclining angle are shown in Figure 8b,d. Increasing the forward incline angle of the die coater increases the minimum film thickness, and instead of shifting the window, it expands the coating window to larger coating flow rates. This is most likely due to the fact that, as the angle θ increases, the gap between the downstream die block and the substrate also increases. In the meantime, the gap between the upstream die block and the substrate decreases with an increase in angle θ and becomes a barrier to retard air entrainment formation during the coating process. Thus, the coating window is expanded, and thicker coating layers are also obtainable. The deviation of the coating thickness is also increased as the forward inclining angle increases. On the other hand, as the backward inclining angle increases, the gap between the upstream die block and the substrate also increases and so makes more space for the coating solution, which is needed for operating coating processes at higher coating speeds. Thus, the coating window is shifted toward higher coating speeds. 3.4. Combined Effects of the Die-Lip Geometry and Inclining Angles. As shown in Figure 9a,c, the rear-neck die-lip geometry with a backward inclined angle can maintain the uniformity of coating layer because of the blade effect formed by the smaller gap in the downstream die block. In this combination, the capacity of the gap in between is limited by the higher die lip
of the upstream and the smaller gap in the downstream caused by a backward inclined angle. Therefore, the thickness of the coating layer and the coating windows are also limited. Even though the expansion of the coating windows in a backward inclined angle is limited, the coating beads are more stable and suitable for an industrial coating process with a low-viscosity coating solution and producing larger amounts of uniformly coated products than can be obtained under other conditions. The experimental results as shown in Figure 9b,d indicate that coating windows are expanded to larger volumetric flow rates and higher coating speeds in both polysilica and hard coating solutions by using the rear-neck dielip geometry with a forward inclined angle. It is due to the barrier formed by the upstream die block that prevents air entrainment from forming; thus, the coating windows is expanded to a higher coating speed than that described before in the bead vacuum effect. As the die coater is inclined forward, the gap between the upstream die block and the substrate decreases relatively and allows the barrier in the upstream die block to work more effectively. This condition can expand the coating windows to larger flow rates and cause the minimum thickness of the coating layer to become thicker. However, it is difficult to maintain the uniform thickness of the coating layer in this setting because of gravity on the coating beads in larger coating flow rates.
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Figure 10. Effect of the inclining angles of the front-neck die-lip geometry at D ) 1 mm and H ) 0.15 mm for coating windows of a polysilica solution with (a) inclining backward angles [θ ) (b, O) 0°, (1, 4) 2°, and (9, 0) 4°] and (b) inclining forward angles [θ ) (b, O) 0°, (1, 4) -2°, and (9, 0) -4°] and of a hard coating solution with (c) inclining backward angles [θ ) (b, O) 0°, (1, 4) 2°, and (9, 0) 4°] and (d) inclining forward angles [θ ) (b, O) 0°, (1, 4) -2°, and (9, 0) -4°]. Black symbol: dripping. White symbol: air entrainment. Table 3. Comparison of Original and Optimum Operating Conditions in the Quality of the Coated Product
coating polysilica solution hard coating solution
required thickness of product (µm) 15 ( 2 5 ( 0.5
operating condition
die construction
inclining angle (deg)
coating velocity (m/min)
film thickness (µm)
productivity (m2/day)
original optimum original optimum
flat plane rear neck flat plane front neck
0 +1 0 +4
8 12 3 10
15 ( 1.8 15 ( 1.0 5 ( 0.8 5 ( 0.3
6240 9360 2340 7800
Parts a and c of Figure 10 show that the increment of the backward inclined angle in the front-neck die-lip geometry shifts the coating windows to higher coating speeds and also makes the thickness of the coating layer much thinner than other conditions. Therefore, the coating windows contrarily dwindle to low flow rates in this condition as the backward inclined angle increases. This is because, as the gap of the downstream die block increases, the blade effect is enhanced and thus blocks the larger flows of coating solutions. The experimental results shown in Figure 10b,d indicate that combining the front-neck die-lip geometry with the forward inclined angle also expands the coating windows to higher coating flow rates as the inclined angle increases. This condition cannot make a uniform coated product because the blade effect formed by the higher downstream die block becomes invalid when the forward inclined angle increases beyond -4°. It is interesting that the inclining backward angle with front-neck die-lip geometry gives
the thinnest thickness of the coating layer at high coating speeds. So, this is the best way to produce a thin uniform film product with high speed during a precise coating process without any additional equipment. 3.5. Uniformity of the Coating Layer. Industrial coating processes are influenced by fluid mechanics of coating solutions, die geometry, limitations of machines, process design, and operation. In general, the uniformity of the coating layer on the substrate (appearance of products) is an important factor in defining an optimized process, although it is not found in the diagrams of the coating window obtained from coating studies in the laboratory. The key difference between this study and laboratory works is that this work was conducted on an industrial coating line and the coating layer was cured after coating on the substrate so that the thickness could be measured by an instrument on line. The
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thickness of the sample was measured every 5 cm in lateral distribution by a spectrometer and a thickness gauge after each operating condition was stabilized, and then values were calculated and averaged for standard deviation for each operational condition using various inclination angles and different die geometries. Standard deviation values of the coating thickness can be used to indicate the uniformity of the coated product. Hence, plotting them in various inclined angles versus available maximum coating velocities in different die geometries can obtain the optimum operational coating conditions for a specific coating solution. In coating window studies, we found that both the backward inclined angle and the front-neck die geometry can enhance the uniformity of the coating layer and obtain a thinner precise coated product. On the contrary, with an increase in the forward inclined angle, the standard deviation value of the thickness becomes larger and so the uniformity of the coating layer decreases. However, when the backward inclined angle increases, the coating widows of a hard coating solution is dwarfed because of the low viscoelasticity of the coating solution and gravity acting on the coating beads. These results are consistent with those reported by Lee and Liu.8 Afterall, optimization of the industrial coating process should be decided by low production cost and high quality. A comparison of the results of the original condition (flat die lips and no inclined angle) and the modified optimum operating conditions is given in Table 3. These could be reached by a high productivity and a high precision coating process, yielding products that meet the specifications of the clients. 4. Conclusion In reported coating studies, most of them discuss the fluid mechanics of the coating solution and how the properties of the coating solution affect their own coating windows. However, the results of those studies are difficult to apply to industrial coating processes. This is because the formulation of the coating solution used in industries is more complicated than that in the laboratory and has its own purpose. Industrial coating solutions are mixtures of several kinds of polymers, surfactants, and additives, not the single polymer solution usually used in laboratory. In this study, we have proven that the coating ability can be improved by changing the die-lip geometry and inclining contact angle in the slot-die coating in an industrial process without additional accessories or modification of the design. Even when the composition of the coating solution is fixed, the high-quality coated products and high productivities are still available as reported in this study. These results have important practical implications and suggest that the fundamental principles involved are also applicable to other coating solutions. Using this result, a simple and efficient way has been proposed to retard the occurrence of coating defects to higher coating speeds and so increase the precision of the process. Acknowledgment The authors thank the Yu-Shan Precise Coating Co. for their support with the coating apparatus and financing. Appendix Notations d ) coating thickness D ) slot gap L ) gap spacing between the slot and substrate Pdown ) ambient air pressure applied on the downstream interface Pup ) ambient air pressure applied on the upstream interface q ) volumetric flow rate per unit width minute
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Q ) volumetric flow rate per unit width R ) radius of the roller T ) difference of height between the die blocks Vmax ) maximum optimum coating speed Vmin ) minimum optimum coating speed Vs ) dimensionless substrate speed; equivalent to the thickness ratio D/d Vs ) substrate speed Greek Letters Φ ) internal diameter of the PE tube θ ) inclining angle of the die coater
Literature Cited (1) Benkreira, H. Thin film coating; The Royal Society of Chemistry: London, 1993. (2) Gutoff, E. B.; Cohen, E. D.; Kheboian, G. I. Coating and drying defects; Wiley-Interscience: New York, 1995. (3) Matsumoto, K. Basic guide to laminating technology; Converting Technical Institute: Tokyo, 1999. (4) Satas, D.; Tracton, A. A. Coating Technology Handbook; Marcel Dekker Inc.: New York, 2001. (5) Weiss, H. L. Coating and Laminating Machines; Converting Technology Co.: Elk Grove Village, IL, 1977. (6) Begiun, A. E. Method of coating strip material. U.S. Patent 2,681,694, 1954. (7) Ruschak, K. J. Limiting flow in a pre-metered coating device. Chem. Eng. Sci. 1976, 31, 1057–1060. (8) Higgins, B. G.; Scriven, L. E. Capillary pressure and viscous pressure drop set bounds on coating bead operability. Chem. Eng. Sci. 1980, 35, 673–682. (9) O’Brien, W. G. Beveled edge metered bead extrusion coating apparatus. U.S. Patent 4,445,458, 1984. (10) Kageyama, T.; Yoshida, M. Coating method and apparatus. U.S. Patent 4,675,208, 1987. (11) Sartor, L. Slot Coating: Fluid Mechanics and Die Design. Ph.D. Thesis, University of Minnesota, Minneapolis, MN, 1992. (12) Kistler, S.; Schweizer, P. M. Liquid Film Coating; Chapman & Hall: London, 1997. (13) Gates, I. A. Slot coating flows: Feasibility, Quality. Ph.D. Thesis, University of Minnesota, Minneapolis, MN, 1999. (14) Lee, K. Y.; Liu, T. J. Minimum web thickness in extrusion slot coating. Chem. Eng. Sci. 1992, 47, 1703–1713. (15) Brown, O. D.; Maier, G. W. Die coating method and apparatus. U.S. Patent 5,639,305, 1997. (16) Ning, C. Y.; Tsai, C. C.; Liu, T. J. The effect of polymer additives on extrusion slot coating. Chem. Eng. Sci. 1996, 51, 3289–3297. (17) Cai, J. J. The analysis for pre-metering coating of low viscosity Newtonian fluid and poly(vinyl-alcohol). M.S. Thesis, National Tsing Hua University, Hsinchu, Taiwan, 1998. (18) Romero, O. J.; Scriven, L. E.; Carvalho, M. S. Slot coating of mildly viscoelastic liquids. J. Non-Newtonian Fluid Mech. 2006, 138, 63–75. (19) Romero, O. J.; Suszynsky, W. J.; Scriven, L. E.; Carvalho, M. S. Low-flow limit in slot coating of dilute solutions of high molecular weight polymer. J. Non-Newtonian Fluid Mech. 2004, 118, 137–156. (20) Lin, Y. N.; Liu, T. J.; Hwang, S. J. Minimum wet thickness for double-layer slide-slot coating of poly(vinyl-alcohol) solutions. Polym. Eng. Sci. 2005, 45, 1590–1599. (21) Weinstein, S. J.; Gros, A. Viscous liquid sheets and operability bounds in extrusion coating. Chem. Eng. Sci. 2005, 60, 5499–5512. (22) Cohu, O.; Benkreira, H. Air entrainment in angled dip coating. Chem. Eng. Sci. 1998, 53, 533–540. (23) Benkreira, H. Dynamic wetting in metering and pre-metering forward roll coating. Chem. Eng. Sci. 2002, 57, 3025–3032. (24) Ikin, J. B.; Gaskell, P. H.; Noakes, C. J.; Thompson, H. M. An Experimental Study of Instability Phenomena and Coating Limits in Industrial Carrier Layer Flows. 4th European Coating Symposium, AdVances in Coating Processes, Belgium, October 1-4, 2001; pp 277-282. (25) Nam, J.; Scriven, L. E.; Carvalho, M. S. Tracking birth of vortex in flows. J. Comput. Phys. 2009, 228, 4549–4567.
ReceiVed for reView December 10, 2008 ReVised manuscript receiVed January 13, 2010 Accepted March 4, 2010 IE801900T
