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Experimental Study on Air Entrainment in Slot Die Coating of High-Viscosity, Shear-Thinning Fluids
Chemical Engineering Science 80 (2012) 195–204
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Experimental Study on Air Entrainment in Slot Die Coating of High-Viscosity, Shear-Thinning Fluids Kanthi Bhamidipati, Sima Didari, Tequila A.L. Harris n George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, 813 Ferst Dr. Atlanta, Georgia, 30332, USA
H I G H L I G H T S c c c c c
Two distinct mechanisms are identified by which air bubble breakup occurs in slot die coating of shear-thinning solutions. Mechanism I is assisted by the solution in coating gap, while Mechanism II is facilitated by solution exiting slot die. Slot gap has no impact on air entrainment velocity, but smaller slot gaps produce smaller air bubbles. Smaller coating gaps delay air entrainment and generate smaller air bubbles. Bubble break up shifts from a predominant Mechanism I to Mechanism II as the slot gap or coating gap increases.
a r t i c l e i n f o
abstract
Article history: Received 29 December 2011 Received in revised form 16 June 2012 Accepted 18 June 2012 Available online 26 June 2012
The effects of slot die geometry, substrate geometry, and fluid properties on air entrainment in coatings have been extensively investigated by several researchers in the past. However, no studies exist to explain the bubble breakup mechanisms during slot die coating of highly viscous, shear- thinning solutions. An experimental study is performed to understand the bubble breakup mechanisms and the qualitative impact of geometric conditions and viscosity of the coating solution on the sizes of the air bubbles. Blackstrap molasses and dilute blackstrap molasses are used as the primary test solutions in this study. Two bubble breakup mechanisms were identified based on the shape of the sawteeth formed prior to air entrainment. In addition, smaller slot and coating gaps and high viscosity solutions were found to produce smaller bubble sizes. For example, reducing slot gap by 41% resulted in a 58% reduction in the effective bubble diameter. It was also found that as the dynamic contact angle approaches 1801 with increasing velocity, the behavior follows that of the interface formation model. & 2012 Elsevier Ltd. All rights reserved.
Keywords: Slot die High viscosity Shear-thinning Air entrainment Bubble breakup mechanisms Sawteeth structures
1. Introduction Many industrial processes involve applying coatings to a moving substrate for manufacturing thin films such as photographic, optical and energy functional films. Several coating processes exist for manufacturing thin films among which the slot die coating process is commonly used process (Harris and Walczyk, 2006). Slot-die coating is a common manufacturing method for producing plastics and polymer films (Krebs, 2009) with thicknesses ranging from few to several microns (Chin et al., 2010; Lin et al., 2008; Nam and Carvalho, 2010). There is a constant demand to increase the processing speed for thin films while simultaneously decreasing the film thickness. However, the film quality will not necessarily be maintained. Film quality is based on the type (e.g., pin holes, bubbles, etc.) and quantity of defects present and can be drastically altered depending upon the
n
Corresponding author. Tel.: þ11 404 385 6335; fax: þ 11 404 894 9342. E-mail address: [email protected] (T.A.L. Harris).
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material properties of the solution, the fabrication process and the processing conditions (Benkreira and Khan, 2008; Burley and Kennedy, 1976; Cohu and Benkreira, 1998a, 1998b; Gutoff and Kendrick, 1982; Veverka, 1995). The maximum speeds at which defect-free coated films can be produced are limited by the inception of air entrainment (Ablett, 1923; Deryagin and Levi, 1959; Higgins and Scriven, 1980; Ruschak, 1976). Air entrainment during thin-film coating occurs at the microscopic (up to a micron) and the macroscopic (a few tens to hundreds of microns) scales. Miyamoto and Scriven (Miyamoto and Scriven, 1982) found that conjoining pressure instabilities are responsible for the bubble breakup occurring during microscopic air entrainment. Microscopic air entrainment is less of a concern due to the ability of the relatively smaller bubbles to dissolve fast (Miyamoto and Scriven, 1982) compared to the bubbles that are formed during macroscopic entrainment. On the other hand, air entrainment at the macroscopic level is the more commonly observed form of bubble entrainment, due to the large size of air bubbles entrained in the film. There is an ambiguity in literature regarding the conditions at which air entrainment
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occurs; Carvalho et al. and Romero et al. (Carvalho and Kheshgi, 2000; Romero et al., 2006; Romero et al., 2004) determined the onset of air entrainment while vacuum was applied to the upstream meniscus as the application of vacuum delays the air entrainment. On the other hand, Chang et al., Lin et al., and Ning et al. (Chang et al., 2007a, 2007b; Lin et al., 2010; Ning et al., 1996) considers no upstream vacuum conditions but consider air entrainment as the point at which a critical velocity is reached and air is entrained in the material as bubbles. Burley and Kennedy, and Chang et al. (Burley and Kennedy, 1976; Chang et al., 2007a) performed a series of experiments to analyze the effects of viscosity and surface tension forces on air entrainment, using a continuously moving tape in a fluid bath, which is analogous to dip coating. The studies were limited to a low dynamic viscosity range, between 0.0059–1.9335 Pa-s. They observed that smaller air bubbles get entrained while coating high viscosity solutions versus low viscosity solutions. They also noticed that the velocity at which air entrainment occurred is lowered with decreasing surface tension. However, a study performed by Veverka (Veverka, 1995) for a side driven free surface cavity setup showed that for high viscosity, Newtonian solutions, lowering the surface tension increased the velocity at which air entrainment occurred. Gutoff and Kendrick (Gutoff and Kendrick, 1982) developed an empirical relationship between the air entrainment velocity and the viscosity of the coating solution for Newtonian solutions. A study performed by Cohu and Benkreira (Cohu and Benkreira, 1998a, 1998b) showed that the air entrainment velocity for non-Newtonian solutions obtained by dissolving a polymer in a solvent, was mostly a function of the solvent rheology and independent of bulk rheology. Benkreira and Khan (Benkreira and Khan, 2008) performed dip coating experiments under reduced air pressures to find the effects of air viscosity on air entrainment. They found that as the air viscosity reduced due to decreasing air pressures, the air entrainment velocity increased. It was also found that the size of the sawteeth structures reduced while the total number of sawteeth increased, resulting in delayed air entrainment. Bhamidipati et al. (Bhamidipati et al., 2011) found that relatively low processing speeds must be used when processing relatively high viscosity, shear thinning solutions compared to the low viscosity counterparts. In addition to the viscosity of the solution being coated, the viscosity of surrounding air or gas was found to impact the air entrainment phenomenon and sawteeth sizes. Effect of air viscosity on air entrainment is demonstrated by Benkreira and Khan (Benkreira and Khan, 2008) using dip coating experiments. They found that the air entrainment velocity nearly doubled as the ambient pressure was reduced from atmospheric value to around 2000 Pa. A reduction in the viscosity of air resulting from a reduced pressure condition caused the sawteeth structures to shrink in size while increasing the total number of sawteeth formed. Similar observations were made by Benkreira and Ikin (Benkreira and Ikin, 2010a, 2010b) when other gases like CO2 and helium were used in the study. Contrary to observations at atmospheric conditions, low-viscosity solutions experienced smaller air entrainment velocities than high-viscosity solutions. Benkreira and Ikin (Benkreira and Ikin, 2010a) did not observe breaking of entrained thin gas film into bubbles prior to dynamic wetting failure, which is contrary to the observations made by Miyamoto and Scriven (Miyamoto and Scriven, 1982) during curtain coating at atmospheric pressure. While performing dip-coating experiments, Ablett (Ablett, 1923) recognized that the apparent dynamic contact angle (the angle between the film and substrate) approaches 1801 during air entrainment. Later, Deryagin and Levi (Deryagin and Levi, 1959) conducted several experiments using a flexible substrate moving under a roller immersed in a coating hopper and captured the phenomena along the dynamic contact line (DCL) by observing the contrast in the illumination. They found that as the coating
speed increases, the apparent dynamic contact angle moved from 01 to approximately 1801, and the originally straight contact line broke into ‘‘vee’’ structures (also termed as sawteeth), which directly leads to air entrainment. They used mixtures of water and gelatin, which produced mildly shear-thinning solutions. However, they found that air entrainment occurred regardless of the coating solution used, however, the length and width of the sawteeth varied. Blake and Ruschak (Blake and Ruschak, 1979) performed experiments with a plunging tape, i.e., dip coating. They found that at low substrate speeds, the DCL remained straight, but when the substrate speed increased, the DCL split into multiple straight lines, forming angle j with the horizontal plane, which is perpendicular to the direction of substrate motion. Blake and Ruschak found that the magnitude of j adjusted such that at any location along the DCL, the perpendicular velocity would not exceed a maximum wetting speed, the speed at which air entrainment ensues. However, the mechanism by which the bubbles pinched off from the sawteeth was not investigated by Ablett or Deryagin and Levi, or Blake and Ruschak. Geometric considerations of the processing tool or equipment on air entrainment have been studied (Chang et al., 2007a; Lee et al., 1992). Lee et al. (Lee et al., 1992) showed using Newtonian solutions that smaller coating gaps facilitated higher velocities before air entrainment ensue, for slot die coating. Chang et al. (Chang et al., 2007a) observed similar trends for solutions with viscosities of 0.075 Pa-s and 0.2 Pa-s. On the other hand, the effect of slot gap on the air entrainment speed is inconclusive due to the contradicting findings between Lee et al. (Lee et al., 1992) and Chang et al. (Chang et al., 2007a). While Lee et al. (Lee et al., 1992) found that the slot gap had no influence on the air entrainment speed, Chang et al. (Chang et al., 2007a) noticed that the air entrainment speed was lowered for low viscosity solutions (0.003 Pa-s) when smaller slot gaps were used. However, neither of these studies focused on the effect of geometric conditions on the sawteeth and the bubble sizes. The inception of air entrainment has been extensively studied, as previously discussed. However, very few studies (Severtson and Aidun, 1996; Veverka and Aidun, 1991a, 1991b) focused on the mechanism that causes a bubble (entrained pocket of air) to break from the DCL. Veverka and Aidun (Veverka and Aidun, 1991a, 1991b) investigated the air entrainment mechanism at the macroscopic scale while coating a Newtonian solution on a rotating roll and concluded that air bubbles nucleated from the side of a sawtooth and broke off from the tip of that sawtooth. Severtson and Aidun (Severtson and Aidun, 1996) used long-wave stability analysis to explain the air entrainment mechanism in thin film coating of Newtonian solutions onto inclined channels. They found that the flow is unstable at the side of a sawtooth air pocket causing nucleation of air bubbles, while the flow in the middle was stable. However, none of these studies (Severtson and Aidun, 1996; Veverka and Aidun, 1991a, 1991b) focused on the bubble breakup mechanisms in pre-metered coating processes, e.g., slot die extrusion. The focus of the current study is to investigate the bubble breakup mechanisms and understand the impact of geometric parameters and viscosity on the sizes of the sawteeth and bubbles during slot die coating of relatively high-viscosity ( Z1 Pa-s), shear-thinning solutions. A custom designed experimental apparatus is used to capture the bubble break up mechanism, the location of the DCL, and the sawtooth formation. The effect of the slot die geometry on the sawtooth and entrained bubble sizes is investigated. Vacuum is not applied in this study.
2. Material properties Two shear-thinning, non-Newtonian, relatively high viscous fluids were used to conduct the experiments in this study;
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blackstrap molasses (BSM) and dilute blackstrap molasses (DBSM). BSM was used as purchased. DBSM solution was obtained by mixing 10 parts BSM with 1 part water, by volume. Silicone oil was used as a Newtonian solution for comparison. The viscosity of the solutions was measured using an ARES rheometer. The tests were conducted by employing a steady shear rate sweep between 1 to 100 s 1, using a parallel plate configuration. As shown in Fig. 1, the apparent viscosity of the non-Newtonian solutions Zapp, are functions of shear rate and can be defined by power-law model. The power-law model for the isothermal condition is:
Zapp ¼ kg_ n1
ð1Þ
where k is the consistency index and n is the power law index (k and n are listed for BSM and DBSM in Table 1). The consistency and power law indices are derived by fitting a curve through the data points. The curve fit predicted the viscosities within 710% of experimentally measured viscosities. From these measurements, it is evident that the solutions are non-Newtonian, shear-thinning solutions. The slot-die is made of stainless steel 316 and the moving substrate is polyterephthalate (PET). The contact angles (with respect to stainless steel 316 and PET) and surface tensions were measured using a Rame´-hart Goniometer Model 250. Sessile drop and pendant drop methods were used to measure contact angles and surface tensions, respectively, for both solutions. The densities of the solutions were obtained by dividing the weight of the fluid by its volume. The volume and weight measurements were obtained by using a standard methodology: The solution was poured into a graduated beaker, to a desired volume. The weight of the empty jar and the weight of the fluid filled jar were recorded. Then the total weight of the empty jar was subtracted from the fluid filled jar to obtain the fluid weight. All of these fluid properties are given in Table 1.
10
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3. Experimental set-up and procedure A custom designed and built roll-feed imaging system (RFIS) (Johnson and Harris, 2010), was used to monitor the dynamics of the solutions0 behavior as they were being deposited onto a moving substrate to investigate the air entrainment mechanism, shape and location of DCL, and formation of sawteeth. A schematic of the experimental set up (RFIS) is shown in Fig. 2. The RFIS is equipped with a temperature controlled pressured tank, a temperature controlled roll-to-roll feed system with adjustable speed and tensioning, a temperature controlled fabrication tool (slot die) and feedback control vision system. The feedback control vision system consists of a microscope with camera (Olympus Zoom Stereo Microscope-model SZ61TR and Olympus SIS-UC30 digital camera, 14 frames per second at 1040 772 resolution or a 2-megapixel Phantom V9.1 high-speed camera, 1,016 frames per second at 1632 1200 resolution). As illustrated in Fig. 2, a transparent plate is nestled below the slot die to allow for image capture as the solution is cast onto the substrate. Nitrogen supplied from a pressurized tank forces the solution through the slot die onto the moving substrate/web. A schematic detailing the parameters of the lower section of the slot die and the substrate is illustrated in Fig. 3. The slot die has an upstream and a downstream half, which is offset by a shim to control the slot gap, W, the distance between the two plates. The solution (coating fluid) is pumped through the die in the y-direction at a flow rate, Qin, and is caused to impact onto a moving web/substrate traveling at a speed, uw, in the x-direction. The flow rate is more conveniently defined by using volumetric flow rate per unit width, Q0 , which is obtained by dividing the volumetric flow rate, Qin, by the width of the slot die. The suspended fluid displaces the air that was originally in contact with the substrate forming the upstream and downstream menisci with the bottom surface of the slot die walls. The DCL is formed between the substrate and solution along the z-direction or the slot die width. The distance between the slot die and the substrate is referred to as the coating gap or stand-off height, H. The coating gap is adjusted
BSM Apparent Viscosity, Pa-s
DBSM Curve Fit
Nitrogen Tank
Pressure Gauge Pressure Vessel Ball Valve
1 0.1
1
10 Strain Rate, 1/s
100
1000
Fig. 1. Apparent viscosity of BSM and DBSM.
Slot Die Light Platen
Platen
Plate
Computer Camera & microscope
Table 1 Fluid properties of test solutions and silicone oil. Parameter
BSM
DBSM
Silicone Oil
Contact angle on stainless steel (deg.) Contact angle on PET (deg.) Surface tension, s (N/m) Density, r (kg/m3) Power-law index, n Consistency index, k (Pa-sn) Viscosity (Pa-s)
69 62 0.047 1452 0.83 8.07 –
68 74 0.049 1411 0.63 6.47 –
– – – 971 1 9.7 9.7
Feed Roller
Take-up roller Motorized roller
Roller with load cells Fig. 2. Illustration of experimental set up, RFIS (Bhamidipati et al., 2011).
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(2) Simultaneously, as the dynamic contact line cannot move beyond a critical speed (maximum coating speed) perpendicular to itself, sawtooth structures form (Blake and Ruschak, 1979). (3) Due to the three-dimensional nature of the sawtooth, a layer of coating solution exists above the layer of air. Interfacial instabilities between the air and fluid films cause bubble breakup (Severtson and Aidun, 1996). Four forces are primarily found (Chang et al., 2007a; Romero et al., 2006) to influence the stability of the coating bead in the slot die coating process; viscous forces, surface tension forces, inertia forces and gravity.
Fig. 3. Schematic of slot die coating.
with a vertical rail system equipped with worm gears. When the slot die engages a feeler gauge of a certain thickness, the coating gap is set. The distance between the menisci is the coating bead length, L. The final thickness of the coated film is the minimum wet thickness, h. The angle made by the upstream meniscus with the substrate is the apparent dynamic contact angle, yad. The angles made by the upstream and downstream menisci with the bottom surface of the slot die are the static contact angles,ys,a and ys,d, respectively. The point of air entrainment is a function of the substrate speed, as described by the coating window (Chang et al., 2007a; Higgins and Scriven, 1980; Ruschak, 1976). For a given pressure exerted by the Nitrogen tank on the coating solution in the slot die, there exists a maximum substrate speed beyond which air entrainment ensues. This is identified as the air entrainment velocity, uw,max. 3.1. Calculation of Q0 Because the coated solution does not solidify, measuring the film thickness is not practical without causing some film distortion. In order to analyze the results independently of geometry, the volumetric flow rate per unit width (across the die), Q0 , is calculated corresponding to the pressure, P exerted by the Nitrogen tank on the coating solution. Q0 is calculated by setting the pressure, P, and the substrate speed, uw, to the desired values. A known length, Lf, of the coated PET is weighed and the weight, mf, recorded. The mass of dry PET, mPET, is then recorded after it is cleaned and dried. The total time, tf, required to coat the known length of PET, Lf, is obtained by dividing Lf by uw. The volumetric flow rate per unit width, Q0 , is then obtained by Eq. (2). Q0 ¼
ðmf mPET Þ wf t f rcs
ð2Þ
where the casting solution density is given by rcs and wf is the width of the film.
4. Results and discussion Combining the observations made by past researchers, the steps involved in the air entrainment mechanism can be summarized in three steps: (1) When the pressure drop across the coating bead that is required to produce a stable bead is not maintained due to an imbalance with the externally imposed pressure gradient causing flow through the slot die, the bead becomes unstable (Higgins and Scriven, 1980) and the originally two-dimensional flow-field becomes three-dimensional.
The viscous forces, Fm, arise due to the viscous nature of the solution coated on the moving substrate. These forces are dominant in the coating gap region and influenced by the coating gap, H, viscosity parameters of the shear-thinning solution; consistency index, k and power-law index, n, and the substrate speed, uw. In terms of these parameters, viscous forces, Fm, are defined by Eq. (3): m n F m pk w ð3Þ H The surface tension, Fs, forces play an important role in determining the shape of the upstream meniscus formed by the coating bead, which in-turn dictate the stability of the coating bead (Chang et al., 2007b). Surface tension forces, Fs, can be described by Eq. (4): Fsp
s H
ð4Þ
where s is the surface tension of the shear-thinning solution in air. The inertia forces, Fi, arise due to the momentum of the fluid exiting the slot die. As presented by Chang et al. (Chang et al., 2007a), these are determined by the velocity of the fluid exiting the slot die, vin, and the density of the fluid, r, as given by Eq. (5): F i pru2in
ð5Þ
Finally, as observed by Chang et al. (Chang et al., 2007a), the orientation of the slot die and the substrate with respect to the direction of gravity is found to influence the air entrainment velocity. In this study, the coating solution flows in the direction of gravity (vertical coating). Eq. (6) describes the force due to gravity, Fg: F g prgH
ð6Þ
where g is gravity. A depiction of the four forces acting on the coating solution (in the region near the bottom portion of the slot die) is shown in Fig. 4: It can be seen from Fig. 4 that the horizontal component of surface tension force acts in the direction opposite to the substrate motion. Two important non-dimensional numbers derived from the forces that are applicable to this study are the capillary number (ratio of viscous to surface tension forces) and the Reynolds number (ratio of inertia to viscous forces). The capillary number, Ca, for shear-thinning solutions is presented in terms of Eq. (7): Ca ¼
Fm kðmw =HÞn1 mw ¼ Fs s
ð7Þ
K. Bhamidipati et al. / Chemical Engineering Science 80 (2012) 195–204
Downstream Die
Upstream Die
Fig. 4. Depiction of forces acting on the coating solution.
VL SHL SVL
HL
Fig. 5. Dimensional features of (a) sawtooth and (b) bubble.
Reynolds number, Re, defined by Eq. (8) as: Re ¼
ru2in Hn Fi ¼ Fm kmnw
ð8Þ
4.1. Bubble pinch-off Mechanisms The bubble entrainment mechanisms were captured using the microscope and high-speed camera, using the aforementioned approach. ImageGrab version 5.0.6En (Glagla software was used to create still shots of the video feed correlating to the data of interest. The sawteeth and bubbles were quantified using ImageJ 1.45 (Rasband image processing and analysis software. The features of the sawtooth and bubble are illustrated in Fig. 5. The sawtooth length is denoted by SVL, while the sawtooth width is represented by SHL. Parameters HL and VL denote the horizontal and vertical lengths of the bubble at pinch-off. Two distinct mechanisms that cause bubble pinch-off resulting in air entrainment were noticed for both shear-thinning and Newtonian solutions, and are subsequently discussed. Mechanism I: Pinch-off of an entrained bubble by Mechanism I occurs when the length of the sawtooth (SVL) is equal to or greater than its width (SHL). In this mechanism, bubble pinch-off is assisted by the solution present in the coating gap. As the substrate reaches the air entrainment speed, sawteeth or air pockets form. At this juncture, the viscous forces acting on the coating solution, which causes it to be pulled in the direction of substrate motion, as shown in Fig. 4, become dominant over the surface tension forces acting in the opposite direction because the upstream contact angle approaches 1801. This results in an interfacial instability causing the coating solution already present in the coating gap to entrain the air film from all sides. Air bubble pinch-off occurs when the solution fully surrounds the sawtooth. Then surface tension acts on the bubble causing it to shrink, after which the bubble moves
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downstream and becomes entrained in the coated film. In other words, Mechanism I is dictated by the capillary number as described by Eq. (7). As the length of the sawtooth approaches a value equal to its width, the pinch-off location shifts closer to the base as shown in Fig. 6(a). When the sawtooth length is greater than its width, the pinch-off is observed to occur closer to the tip of the sawtooth as shown in Fig. 6(b). The line X0 Y0 -X0 Y0 marked on the top view denotes the location of the side (sectional) view. Fig. 6(c) shows the experimental images of bubble pinch-off by Mechanism I. Mechanism II: In this mechanism, the broken dynamic contact line is displaced by a new wave of fluid. Hence, Mechanism II only occurs in pre-metered coating processes like slot die coating, where there is a continuous supply of coating solution at a given flow rate. When the width of the sawtooth (SHL) is much greater than its length (SVL), the bubble pinch-off occurs by Mechanism II. Due to the presence of a wider sawtooth, it becomes difficult for the solution upstream of the sawtooth to enclose the larger air pocket. Instead, the bubble pinchoff mechanism is aided by fresh solution exiting the slot die, which encloses the air pockets formed by the broken dynamic contact line. Therefore, a combination of pre-metering and the presence of a larger air pocket spread over a wide area are required for Mechanism II to occur. The absence of an upstream solution feed source would cause the air pocket to expand over a wider area, thereby making it impossible for the solution on the substrate to bind the pocket. Since the contact line is spread over a wider area, the new fluid coming out of the slot displaces a large part of the contact line, as illustrated in Fig. 7(a). The line X0 Y0 -X0 Y0 marked on the top view denotes the location of the side (sectional) view. In the bubble formation by Mechanism II, the pinch-off could extend over a larger area. The extent to which the sawtooth spreads before pinch-off occurs depends on the relative strength of inertia to viscous forces as determined by the Reynolds number. If inertia forces are dominant, then the sawtooth has less time to spread before pinch-off occurs and vice-versa. Since the bubble sizes are generally proportional to the sawtooth sizes, the bubble might look elongated in the direction perpendicular to the substrate motion. Subsequently, the elongated bubble can either remain intact or split into smaller bubbles. Experimental images demonstrating bubble pinch-off by Mechanism II is shown in Fig. 7(b). 4.2. Effect of geometric parameters and viscosity on air entrainment The effects of slot gap, coating gap and viscosity on sawtooth and bubble sizes are captured using the microscope and digital camera described previously. Digital images are presented to show the comparison between various cases. The average sizes of sawteeth and bubbles are presented in terms of sawtooth width (SHL), sawtooth length (SVL), and effective bubble diameter at pinch-off (approximated qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi as H2L þ V 2L . Because of the difficulty associated with capturing the thickness of the sawteeth and air bubbles, the sizes presented in the study only correspond to 2D projections of the sawteeth and air bubble as viewed from the camera placed under the substrate. 4.2.1. Effect of slot gap The impact of slot gap on the sawtooth geometry for BSM is illustrated in Fig. 8, Three slot gaps were tested W¼0.178 mm, 0.25 mm and 0.30 mm for H¼0.30 mm and Q0 ¼0.53 mm3/mm-s. Four images taken at different time intervals of the coating process are illustrated in Fig. 8(a) through (c) for W¼0.178 mm, 0.25 mm and 0.30 mm, respectively. A comparison between the sawtooth geometry from the pictures show that the width of the sawtooth increases with increasing slot gap, while the difference in the sawtooth0 s length are relatively small. The air entrainment speed is found to be approximately 3.50 mm/s in each case, which corresponds to a capillary number of
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Fig. 6. Pinch-off of air bubbles by Mechanism I (a) illustration of air bubble pinch-off closer to the sawtooth base), (b) illustration of air bubble pinch-off closer to the sawtooth tip), and (c) images from experiment demonstrating bubble pinch-off by Mechanism I.
Fig. 7. Pinch-off of air bubbles while slot die coating of silicone oil (a) images from experiment demonstrating bubble pinch-off by Mechanism I, (b) images from experiment demonstrating bubble pinch-off by Mechanism II.
0.40. Therefore, the differences in the viscous forces experienced by the solution due to the substrate motion are negligible. Since the flow rate per unit width is maintained constant, the velocity (vin) of
the coating solution through the slot die increases as the slot gap decreases. Therefore, the inertia forces are more dominant when the slot gap is smaller resulting in a smaller sawtooth.
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Contact Line
10
Sawtooth
W = 0.178 mm
201
W = 0.250 mm
W = 0.300 mm
Average Length (mm)
9 8 7 6 5 4 3 2 1.3
1.5
1 0
Fig. 9. Quantitative representation of the impact of slot gap, W, on the sawtooth and air bubble sizes at the air entrainment boundary for BSM solution, H¼ 0.30 mm and Q0 ¼0.53 mm3/mm-s.
Contact Line
Fig. 8. Qualitative representation of the impact of slot gap, W, on the sawtooth sizes at the air entrainment boundary for BSM solution, H ¼0.30 mm and Q0 ¼ 0.53 mm3/mm-s, dashed lines represent boundaries of die lips for (a) uw,max ¼ 3.54 mm/s (Ca¼0.41) for W¼ 0.178 mm, (b) uw,max ¼ 3.5 mm/s (Ca¼ 0.40) for W ¼0.25 mm and (c) uw,max ¼ 3.48 mm/s (Ca ¼0.40) for W ¼0.30 mm.
1.3
Sawtooth
1.5
The average sawtooth and air bubble sizes for the three cases specified in Fig. 8 are presented in Fig. 9. It is evident that the sawtooth and the bubble sizes increase with increasing slot gap. Even though bubble pinch-off occurs by both mechanisms in most of the cases, the pinch-off occurs predominantly by Mechanism I in the case of smaller slot gaps, while Mechanism II becomes dominant as the slot gap increases. This is evident in Fig. 9, where the increase in the width of the sawtooth is significant compared to the increase in its length as the slot gap increases. When the slot gap increases by 41%, from 178 mm to 300 mm, the sawtooth width, length and the effective bubble diameter increased by approximately 67%, 31%, and 58%, respectively. It is therefore advantageous to work with smaller slot gaps as they produce smaller sawteeth, which produces smaller bubbles. In addition, smaller bubbles would be expected to dissolve faster than larger bubbles, as shown by Miyamoto and Scriven (Miyamoto and Scriven, 1982).
4.2.2. Effect of coating gap The effect of coating gap on the sawtooth structures at the air entrainment boundary is illustrated in Fig. 10. DBSM is used as a solution. Three coating gaps were tested, H¼0.178 mm, 0.25 mm and 0.30 mm for slot gap, W¼ 0.178 mm. The air entrainment velocities corresponding to a flow rate per unit width, Q0 ¼0.62 mm3/m-s are 7.5 mm/s (Ca¼0.26), 5.5 mm/s, (Ca¼0.25) and 4.5 mm/s (Ca¼0.23) for H¼ 0.178 mm, 0.25 mm and 0.30 mm, respectively. From Fig. 10,
Fig. 10. Qualitative representation of the impact of coating gap, H, on the sawtooth sizes at the air entrainment boundary for DBSM solution, W ¼ 0.178 mm and Q0 ¼ 0.62 mm3/mm-s, dashed lines represent boundaries of die lips for (a) uw,max ¼7.50 mm/s (Ca¼ 0.26) for H¼0.178 mm, (b) uw,max ¼ 5.50 mm/s (Ca¼0.25) for H¼0.25 mm and (c) uw,max ¼ 4.50 mm/s (Ca¼0.23) for H¼0.30 mm.
it is observed that both the length and width of the sawtooth increase as the coating gap increases. However the increase in the sawtooth width is greater than the increase in its length. The increase in
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sawtooth geometry is due to two primary reasons. The air entrainment velocity decreases as the coating gap increase. As shown in Eq. (3), since the stresses experienced by the solution are proportional to the ratio of air entrainment velocity, uw,max to the coating gap, H, raised to power-law index, n, ([mw,max/H])n, the stresses decrease as the coating gap increases. Therefore, the stresses take longer to propagate upstream causing the sawtooth to spread over a larger area before pinch-off occurs. The larger area results in a larger air pocket, which makes it difficult for the solution in the coating gap to fill the void. This gives additional time for the sawtooth to spread. However, the presence of opposing forces (surface tension) that prevent the sawtooth from stretching in the direction of the substrate motion limits the length of the sawtooth from becoming too large. This can be explained by Eq. (4), which shows that surface tension forces, which pull the coating solution in the opposite direction (opposite to the direction of substrate motion), are proportional to (1/H), implying that surface tension forces are also lowered as the coating gap increases. But, as long as the surface tension forces are finite, they limit the extent to which the sawtooth extends lengthwise. Instead, the sawtooth spreads over a wider area causing the width of the sawtooth to increase more significantly. The relative differences in the sawtooth and bubble sizes pertaining to the conditions specified in Fig. 10 for the three coating gaps are depicted in Fig. 11. When the coating gap increases by 41%, from 178 mm to 300 mm, the sawtooth width, length and the effective bubble diameter increased by approximately 55%, 27%, and 51%, respectively. Due to the higher sawtooth0 s width compared to its length, it is observed that the bubble pinch-off mechanism shifts from a significant Mechanism I to a significant Mechanism II, for the larger coating gap. Larger sawteeth generated at higher coating gaps produces bigger bubbles, which is undesirable. Hence, in addition to obtaining larger coating speeds, smaller coating gaps are also advantageous because of the smaller bubble sizes. Another interesting observation is that when the coating gap is above 250 mm the sawtooth length is significantly lower than the sawtooth width, by approximately 40%, however this effect seems to be less dominant when the coating gap is 178 mm, having a percent difference of only 2%. Thus, as the coating gap decreases, the percent difference between the sawtooth width and length becomes less significant. When considering the sawtooth length and width of the coating gap to that of the slot gap a similar trend is observed, as seen in Fig. 9. At a slot gap below 250 mm the percent difference is
6
H = 0.178 mm
H = 0.250 mm
approximately 44%. However, the percent difference increases to approximately 73% when the slot gap is 300 mm. The significant increase in the sawtooth width compared to its length explains the shift in bubble breakup from Mechanism I to Mechanism II at larger slot gaps and coating gaps. 4.2.3. Effect of viscosity The effect of viscosity on the sawtooth structures is illustrated in Fig. 12(a) and (b) for DBSM and BSM, respectively, at W¼0.178 mm and H¼0.25 mm. For a volumetric flow rate per unit width, Q0 ¼0.55 mm3/mm-s, the air entrainment speeds were found to be 5.6 mm/s (Ca¼0.25) for DBSM, and 4.3 mm/s (Ca ¼0.46) for BSM. The inverse relationship between the viscosity and the air entrainment speeds was demonstrated by several researchers (Burley and Jolly, 1984; Chang et al., 2007a, 2007b; Gutoff and Kendrick, 1982; Lee et al., 1992). It can be observed that both the sawtooth length and width are larger for DBSM solution, which is a relatively low-viscosity solution compared to BSM. These results are consistent with the observations made by Burley and Kennedy (Burley and Kennedy, 1976). The reason for the differences in the sawtooth sizes is because the stresses experienced by the coating solution are proportional to the viscosity (consistency-index in the case of shear-thinning solutions) of the solution as presented by Eq. (3). Thus, higher viscosity solutions are expected to experience higher stresses. However, since high-viscosity solutions experience air entrainment at lower coating speeds, there would be a reduction in the stresses. Veverka (Veverka, 1995) showed that the effect of viscosity is dominant compared to the effect of air entrainment speed on the stresses. Thus, the slope of the air entrainment speed versus viscosity curve (air entrainment speed plotted on the vertical axis and viscosity plotted on the horizontal axis) is less than 1. In addition, for shear-thinning fluids the stresses are proportional to ðuw,max Þn , (the air entrainment speed raised to the power-law index -which is less than one) which further reduces
Contact Line
Sawtooth
H = 0.300 mm
Average Length (mm)
5 4 1.3
1.5
3 2 1 0
Fig. 11. Quantitative representation of the impact of coating gap, H, on the sawtooth and air bubble sizes at the air entrainment boundary for DBSM solution, W ¼0.178 mm and Q0 ¼0.62 mm3/mm-s.
Fig. 12. Qualitative representation of the impact of solution viscosity on the sizes of the sawtooth at the air entrainment boundary for W ¼0.178 mm, H¼ 0.25 mm and Q0 ¼ 0.55 mm3/mm-s, dashed lines represent boundaries of die lips for (a) uw,max ¼5.6 mm/s (Ca¼ 0.25) for DBSM and (b) uw,max ¼ 4.3 mm/s (Ca¼ 0.46) for BSM.
K. Bhamidipati et al. / Chemical Engineering Science 80 (2012) 195–204
the effect of the air entrainment speed on the stresses. Combining all the effects on the stresses, it can be concluded that the stresses follow the same trend as the viscosity. Since the stresses experienced by the low-viscosity solution are smaller (Fm,DBMS/Fm,BSM)o1, the sawtooth extends over a larger area before the bubble pinch-off occurs as shown in Fig. 12. The average sawtooth and bubble sizes corresponding to the conditions specified in Fig. 12 for the two solutions are presented in Fig. 13. As seen in Fig. 13, the presence of a larger sawtooth for DBSM compared to BSM confirms the assumption presented in the previous paragraph that the smaller viscous stresses experienced by the relatively low-viscosity solution causes the sawtooth to spread over a larger area. The sawtooth lengths, widths and the effective bubble diameters of the DBSM were found to be approximately 24%, 52%, and 7% larger than those for BSM. It was found that HL is 40% and 60% larger than VL for DBSM and BSM, respectively. This is consistent with the observations that BSM experienced a higher chance of bubble breakup by Mechanism II compared to DBSM. The change in the apparent dynamic contact angle of BSM with respect to the substrate speed has been captured by a monitoring system installed at the set up. The variation of dynamic contact angle versus the capillary number is show in Fig. 14. The measurements were done at the constant flow rate and geometrical configuration, while changing the substrate speed from the dripping to the threshold of air entrainment. As illustrated in the figure the values of the contact angle increased continuously until approaching a value close to 1601 at the point of air entrainment. The experimental data are compared by the interface formation theory proposed by Shikhmurzaev (Shikhmurzaev, 2008), which is based on Newtonian fluids. As
Average Length (mm)
5
DBSM
BSM
4 3 2
5. Conclusions A study is performed to explain the mechanisms by which air bubble pinch-off occurs prior to bubble entrainment in a coated film, for relatively high viscosity, shear thinning solutions. In addition, the effects of the geometric parameters and the viscosity of the coating solution on the sawtooth and air bubble sizes are analyzed. It has been found that there are two mechanisms that cause air bubble pinch-off. In the first mechanism, the bubble pinch-off is aided by the solution present in the coating gap, while in the second mechanism, the bubble pinch-off is assisted by the new solution coming out of the slot die. The comparative studies between the geometric parameters revealed that Mechanism I is dominant in smaller slot gaps, smaller coating gaps and low viscosity solutions. Mechanism II was found to be dominant when wider sawteeth are present. Bubble sizes were found to vary proportionally with the sawteeth sizes. Slot gap did not have any impact on the air entrainment speed, while smaller slot gaps have the advantage of producing smaller sawtooth and bubble sizes. Smaller coating gaps produce higher air entrainment speeds and smaller sawtooth/bubble sizes. Further, solutions can be processed at higher maximum coating speeds as the viscosity decreases, however, the sawtooth and air bubble sizes are larger at the air entrainment boundary. As Miyamoto and Scriven (Miyamoto and Scriven, 1982) have shown, smaller air bubbles tend to dissolve faster, which might nullify the impact of smaller bubbles on the properties of the coated film. This work can be useful in increasing the air entrainment velocity by determining the optimum slot and coating gaps for a given system when the limits of bubble sizes are known.
Nomenclature
Fig. 13. Quantitative representation of the impact of solution viscosity on the sawtooth and the air bubbles sizes at the air entrainment boundary for W ¼0.178 mm, H¼ 0.25 mm and Q0 ¼ 0.55 mm3/mm-s.
Experimental data
Dynamic Contact Angle (º)
shown in the Fig. 14 the presented experiential data follows the same trend of the model, although some discrepancy between them can be observed, which can be attributed to the uncertainty the experimental measurement.
1 0
Interface formation model (Shikhmurzaev 2008)
170 150
Fg Fi Fm Fs g h H HL k L mf mPET n P Q Q0
130
rcs
110
SHL SVL tf W
90 0.15
203
0.2
0.25
0.3 Ca
0.35
0.4
0.45
Fig. 14. The variation of apparent contact angle of BSM with respect to the substrate speed and comparison with the interface formation theory (Shikhmurzaev, 2008).
Zapp g_ j yad
Gravity forces Inertia forces Viscous forces Surface tension forces Gravity, m/s2 Wet thickness, mm Coating gap or Stand-off height, mm Horizontal diameter of air bubble at pinch-off Consistency index, Pa-sn Coating bead length, mm Mass of PET coated with solution, kg/s Mass of dry PET, kg/s Power-law index Pressure, Pa Flow rate, mm3/s Flow rate per unit slot die width, mm3/mm-s Density of the coating solution, kg/mm3 Width of sawtooth Length of sawtooth Time, s Slot gap, mm Apparent viscosity, Pa-s Shear rate, 1/s Angle made by the sawtooth structures with horizontal, deg. Apparent dynamic contact angle, deg.
204
ys,a ys,d uw uw,max vin VL wf
K. Bhamidipati et al. / Chemical Engineering Science 80 (2012) 195–204
Upstream Static contact angle, deg. Downstream Static contact angle, deg. Substrate velocity, mm/s Air entrainment velocity, mm/s Inlet velocity, mm/s Vertical diameter of air bubble at pinch-off Width of the film, m
References Ablett, R., 1923. An investigation of the angle of contact between paraffin wax and water. Philosophical Magazine Series 6 (46), 244–256. Benkreira, H., Ikin, J.B., 2010a. Dissolution and growth of entrained bubbles when dip coating in a gas under reduced pressure. Chemical Engineering Science 65, 5821–5829. Benkreira, H., Ikin, J.B., 2010b. Dynamic wetting and gas viscosity effects. Chemical Engineering Science 65, 1790–1796. Benkreira, H., Khan, M.I., 2008. Air entrainment in dip coating under reduced air pressures. Chemical Engineering Science 63, 448–459. Bhamidipati, K.L., Didari, S., Bedell, P., Harris, T.A.L., 2011. Wetting phenomena during processing of high-viscosity shear-thinning fluid. Journal of Non-Newtonian Fluid Mechanics 166, 723–733. Blake, T.D., Ruschak, K.J., 1979. A maximum speed of wetting. Nature 282, 489–491. Burley, R., Jolly, R.P.S., 1984. Entrainment of air into liquids by a high speed continuous solid surface. Chemical Engineering Science 39, 1357–1372. Burley, R., Kennedy, B.S., 1976. An experimental study of air entrainment at a solid/liquid/gas interface. Chemical Engineering Science 31, 901–911. Chang, H.-M., Chang, Y.-R., Lin, C.-F., Liu, T.-J., 2007a. Comparison of vertical and horizontal slot die coatings. Polymer Engineering and Science 47, 1927–1936. Chang, Y.-R., Chang, H.-M., Lin, C.-F., Liu, T.-J., Wu, P.-Y., 2007b. Three minimum wet thickness regions of slot die coating. Journal of Colloid and Interface Science 308, 222–230. Chin, C.-P., Wu, H.-S., Wang, S.S., 2010. Improved coating window for slot coating. Industrial and Engineering Chemistry Research 49, 3802–3809. Cohu, O., Benkreira, H., 1998a. Air entrainment in angled dip coating. Chemical Engineering Science 53, 533–540. Cohu, O., Benkreira, H., 1998b. Entrainment of air by a solid surface plunging into a non-newtonian liquid. AIChE Journal 44, 2360–2368. Deryagin, B.V., Levi, S.M., 1959. Film Coating Theory. Focal Press, London.
Glagla, P., ImageGrab 5.0.6En. Gutoff, E.B., Kendrick, C.E., 1982. Dynamic contact angles. AIChE Journal 28, 459–466. Harris, T.A.L., Walczyk, D.F., 2006. Development of a casting technique for membrane material used in high-temperature PEM fuel cells. Journal of Manufacturing Processes 8, 8–20. Higgins, B.G., Scriven, L.E., 1980. Capillary pressure and viscous pressure drop set bounds on coating bead operability. Chemical Engineering Science 35, 673–682. Johnson, J., Harris, T., 2010. Full-field optical thickness profilometry of semitransparent thin films with transmission densitometry. Applied Optics 49, 2920–2928. Krebs, F.C., 2009. Polymer solar cell modules prepared using roll-to-roll methods: Knife-over-edge coating, slot-die coating and screen printing. Solar Energy Materials and Solar Cells 93, 465–475. Lee, K.-Y., Liu, L.-D., Ta-Jo, L., 1992. Minimum wet thickness in extrusion slot coating. Chemical Engineering Science 47, 1703–1713. Lin, F.-H., Liu, C.-M., Liu, T.-J., Wu, P.-Y., 2008. A macroscopic mathematical model for tensioned-web slot coating. Polymer Engineering and Science 48, 307–315. Miyamoto, K., Scriven, L.E., 1982. Breakdown of air film entrained by liquid coated on web, 1982 Annual Meeting - American Institute of Chemical Engineers. AIChE, Los Angeles, CA, USA, pp. AIChE, New York, NY, USA. Nam, J., Carvalho, M.S., 2010. Flow in tensioned-web-over-slot die coating: Effect of die lip design. Chemical Engineering Science 65, 3957–3971. Rasband, W., ImageJ. National Institutes of Health. Romero, O.J., Scriven, L.E., Carvalho, M.S., 2006. Slot coating of mildly viscoelastic liquids. Journal of Non-Newtonian Fluid Mechanics 138, 63–75. Ruschak, K.J., 1976. Limiting flow in a pre-metered coating device. Chemical Engineering Science 31, 1057–1060. Severtson, Y.C., Aidun, C.K., 1996. Stability of two-layer stratified flow in inclined channels: applications to air entrainment in coating systems. Journal of Fluid Mechanics 312, 173–200. Shikhmurzaev, Y.D., 2008. Capillary flows with formaing interfaces. Chapman & Hall/CRC, New York, NY, USA. Veverka, P.J., 1995. An investigation of interfacial instability during air entrainment, Institute of Paper Science and Technology. Georgia Institute of Technology, Atlanta. Veverka, P.J., Aidun, C.K., 1991a. Flow visualization of air entrainment and dynamic contact line instability in low-speed roll coating, 1991 TAPPI Engineering Conference Proceedings,. Atlanta TAPPI Press, Nashville, pp. 719–725. Veverka, P.J., Aidun, C.K., 1991b. Using high-speed cinematography to obtain visual evidence on air entrainment in low-speed roll coating. ETATS-UNIS, TAPPI, Norcross GA.
Contents lists available at SciVerse ScienceDirect
Chemical Engineering Science journal homepage: www.elsevier.com/locate/ces
Experimental Study on Air Entrainment in Slot Die Coating of High-Viscosity, Shear-Thinning Fluids Kanthi Bhamidipati, Sima Didari, Tequila A.L. Harris n George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, 813 Ferst Dr. Atlanta, Georgia, 30332, USA
H I G H L I G H T S c c c c c
Two distinct mechanisms are identified by which air bubble breakup occurs in slot die coating of shear-thinning solutions. Mechanism I is assisted by the solution in coating gap, while Mechanism II is facilitated by solution exiting slot die. Slot gap has no impact on air entrainment velocity, but smaller slot gaps produce smaller air bubbles. Smaller coating gaps delay air entrainment and generate smaller air bubbles. Bubble break up shifts from a predominant Mechanism I to Mechanism II as the slot gap or coating gap increases.
a r t i c l e i n f o
abstract
Article history: Received 29 December 2011 Received in revised form 16 June 2012 Accepted 18 June 2012 Available online 26 June 2012
The effects of slot die geometry, substrate geometry, and fluid properties on air entrainment in coatings have been extensively investigated by several researchers in the past. However, no studies exist to explain the bubble breakup mechanisms during slot die coating of highly viscous, shear- thinning solutions. An experimental study is performed to understand the bubble breakup mechanisms and the qualitative impact of geometric conditions and viscosity of the coating solution on the sizes of the air bubbles. Blackstrap molasses and dilute blackstrap molasses are used as the primary test solutions in this study. Two bubble breakup mechanisms were identified based on the shape of the sawteeth formed prior to air entrainment. In addition, smaller slot and coating gaps and high viscosity solutions were found to produce smaller bubble sizes. For example, reducing slot gap by 41% resulted in a 58% reduction in the effective bubble diameter. It was also found that as the dynamic contact angle approaches 1801 with increasing velocity, the behavior follows that of the interface formation model. & 2012 Elsevier Ltd. All rights reserved.
Keywords: Slot die High viscosity Shear-thinning Air entrainment Bubble breakup mechanisms Sawteeth structures
1. Introduction Many industrial processes involve applying coatings to a moving substrate for manufacturing thin films such as photographic, optical and energy functional films. Several coating processes exist for manufacturing thin films among which the slot die coating process is commonly used process (Harris and Walczyk, 2006). Slot-die coating is a common manufacturing method for producing plastics and polymer films (Krebs, 2009) with thicknesses ranging from few to several microns (Chin et al., 2010; Lin et al., 2008; Nam and Carvalho, 2010). There is a constant demand to increase the processing speed for thin films while simultaneously decreasing the film thickness. However, the film quality will not necessarily be maintained. Film quality is based on the type (e.g., pin holes, bubbles, etc.) and quantity of defects present and can be drastically altered depending upon the
n
Corresponding author. Tel.: þ11 404 385 6335; fax: þ 11 404 894 9342. E-mail address: [email protected] (T.A.L. Harris).
0009-2509/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ces.2012.06.033
material properties of the solution, the fabrication process and the processing conditions (Benkreira and Khan, 2008; Burley and Kennedy, 1976; Cohu and Benkreira, 1998a, 1998b; Gutoff and Kendrick, 1982; Veverka, 1995). The maximum speeds at which defect-free coated films can be produced are limited by the inception of air entrainment (Ablett, 1923; Deryagin and Levi, 1959; Higgins and Scriven, 1980; Ruschak, 1976). Air entrainment during thin-film coating occurs at the microscopic (up to a micron) and the macroscopic (a few tens to hundreds of microns) scales. Miyamoto and Scriven (Miyamoto and Scriven, 1982) found that conjoining pressure instabilities are responsible for the bubble breakup occurring during microscopic air entrainment. Microscopic air entrainment is less of a concern due to the ability of the relatively smaller bubbles to dissolve fast (Miyamoto and Scriven, 1982) compared to the bubbles that are formed during macroscopic entrainment. On the other hand, air entrainment at the macroscopic level is the more commonly observed form of bubble entrainment, due to the large size of air bubbles entrained in the film. There is an ambiguity in literature regarding the conditions at which air entrainment
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occurs; Carvalho et al. and Romero et al. (Carvalho and Kheshgi, 2000; Romero et al., 2006; Romero et al., 2004) determined the onset of air entrainment while vacuum was applied to the upstream meniscus as the application of vacuum delays the air entrainment. On the other hand, Chang et al., Lin et al., and Ning et al. (Chang et al., 2007a, 2007b; Lin et al., 2010; Ning et al., 1996) considers no upstream vacuum conditions but consider air entrainment as the point at which a critical velocity is reached and air is entrained in the material as bubbles. Burley and Kennedy, and Chang et al. (Burley and Kennedy, 1976; Chang et al., 2007a) performed a series of experiments to analyze the effects of viscosity and surface tension forces on air entrainment, using a continuously moving tape in a fluid bath, which is analogous to dip coating. The studies were limited to a low dynamic viscosity range, between 0.0059–1.9335 Pa-s. They observed that smaller air bubbles get entrained while coating high viscosity solutions versus low viscosity solutions. They also noticed that the velocity at which air entrainment occurred is lowered with decreasing surface tension. However, a study performed by Veverka (Veverka, 1995) for a side driven free surface cavity setup showed that for high viscosity, Newtonian solutions, lowering the surface tension increased the velocity at which air entrainment occurred. Gutoff and Kendrick (Gutoff and Kendrick, 1982) developed an empirical relationship between the air entrainment velocity and the viscosity of the coating solution for Newtonian solutions. A study performed by Cohu and Benkreira (Cohu and Benkreira, 1998a, 1998b) showed that the air entrainment velocity for non-Newtonian solutions obtained by dissolving a polymer in a solvent, was mostly a function of the solvent rheology and independent of bulk rheology. Benkreira and Khan (Benkreira and Khan, 2008) performed dip coating experiments under reduced air pressures to find the effects of air viscosity on air entrainment. They found that as the air viscosity reduced due to decreasing air pressures, the air entrainment velocity increased. It was also found that the size of the sawteeth structures reduced while the total number of sawteeth increased, resulting in delayed air entrainment. Bhamidipati et al. (Bhamidipati et al., 2011) found that relatively low processing speeds must be used when processing relatively high viscosity, shear thinning solutions compared to the low viscosity counterparts. In addition to the viscosity of the solution being coated, the viscosity of surrounding air or gas was found to impact the air entrainment phenomenon and sawteeth sizes. Effect of air viscosity on air entrainment is demonstrated by Benkreira and Khan (Benkreira and Khan, 2008) using dip coating experiments. They found that the air entrainment velocity nearly doubled as the ambient pressure was reduced from atmospheric value to around 2000 Pa. A reduction in the viscosity of air resulting from a reduced pressure condition caused the sawteeth structures to shrink in size while increasing the total number of sawteeth formed. Similar observations were made by Benkreira and Ikin (Benkreira and Ikin, 2010a, 2010b) when other gases like CO2 and helium were used in the study. Contrary to observations at atmospheric conditions, low-viscosity solutions experienced smaller air entrainment velocities than high-viscosity solutions. Benkreira and Ikin (Benkreira and Ikin, 2010a) did not observe breaking of entrained thin gas film into bubbles prior to dynamic wetting failure, which is contrary to the observations made by Miyamoto and Scriven (Miyamoto and Scriven, 1982) during curtain coating at atmospheric pressure. While performing dip-coating experiments, Ablett (Ablett, 1923) recognized that the apparent dynamic contact angle (the angle between the film and substrate) approaches 1801 during air entrainment. Later, Deryagin and Levi (Deryagin and Levi, 1959) conducted several experiments using a flexible substrate moving under a roller immersed in a coating hopper and captured the phenomena along the dynamic contact line (DCL) by observing the contrast in the illumination. They found that as the coating
speed increases, the apparent dynamic contact angle moved from 01 to approximately 1801, and the originally straight contact line broke into ‘‘vee’’ structures (also termed as sawteeth), which directly leads to air entrainment. They used mixtures of water and gelatin, which produced mildly shear-thinning solutions. However, they found that air entrainment occurred regardless of the coating solution used, however, the length and width of the sawteeth varied. Blake and Ruschak (Blake and Ruschak, 1979) performed experiments with a plunging tape, i.e., dip coating. They found that at low substrate speeds, the DCL remained straight, but when the substrate speed increased, the DCL split into multiple straight lines, forming angle j with the horizontal plane, which is perpendicular to the direction of substrate motion. Blake and Ruschak found that the magnitude of j adjusted such that at any location along the DCL, the perpendicular velocity would not exceed a maximum wetting speed, the speed at which air entrainment ensues. However, the mechanism by which the bubbles pinched off from the sawteeth was not investigated by Ablett or Deryagin and Levi, or Blake and Ruschak. Geometric considerations of the processing tool or equipment on air entrainment have been studied (Chang et al., 2007a; Lee et al., 1992). Lee et al. (Lee et al., 1992) showed using Newtonian solutions that smaller coating gaps facilitated higher velocities before air entrainment ensue, for slot die coating. Chang et al. (Chang et al., 2007a) observed similar trends for solutions with viscosities of 0.075 Pa-s and 0.2 Pa-s. On the other hand, the effect of slot gap on the air entrainment speed is inconclusive due to the contradicting findings between Lee et al. (Lee et al., 1992) and Chang et al. (Chang et al., 2007a). While Lee et al. (Lee et al., 1992) found that the slot gap had no influence on the air entrainment speed, Chang et al. (Chang et al., 2007a) noticed that the air entrainment speed was lowered for low viscosity solutions (0.003 Pa-s) when smaller slot gaps were used. However, neither of these studies focused on the effect of geometric conditions on the sawteeth and the bubble sizes. The inception of air entrainment has been extensively studied, as previously discussed. However, very few studies (Severtson and Aidun, 1996; Veverka and Aidun, 1991a, 1991b) focused on the mechanism that causes a bubble (entrained pocket of air) to break from the DCL. Veverka and Aidun (Veverka and Aidun, 1991a, 1991b) investigated the air entrainment mechanism at the macroscopic scale while coating a Newtonian solution on a rotating roll and concluded that air bubbles nucleated from the side of a sawtooth and broke off from the tip of that sawtooth. Severtson and Aidun (Severtson and Aidun, 1996) used long-wave stability analysis to explain the air entrainment mechanism in thin film coating of Newtonian solutions onto inclined channels. They found that the flow is unstable at the side of a sawtooth air pocket causing nucleation of air bubbles, while the flow in the middle was stable. However, none of these studies (Severtson and Aidun, 1996; Veverka and Aidun, 1991a, 1991b) focused on the bubble breakup mechanisms in pre-metered coating processes, e.g., slot die extrusion. The focus of the current study is to investigate the bubble breakup mechanisms and understand the impact of geometric parameters and viscosity on the sizes of the sawteeth and bubbles during slot die coating of relatively high-viscosity ( Z1 Pa-s), shear-thinning solutions. A custom designed experimental apparatus is used to capture the bubble break up mechanism, the location of the DCL, and the sawtooth formation. The effect of the slot die geometry on the sawtooth and entrained bubble sizes is investigated. Vacuum is not applied in this study.
2. Material properties Two shear-thinning, non-Newtonian, relatively high viscous fluids were used to conduct the experiments in this study;
K. Bhamidipati et al. / Chemical Engineering Science 80 (2012) 195–204
blackstrap molasses (BSM) and dilute blackstrap molasses (DBSM). BSM was used as purchased. DBSM solution was obtained by mixing 10 parts BSM with 1 part water, by volume. Silicone oil was used as a Newtonian solution for comparison. The viscosity of the solutions was measured using an ARES rheometer. The tests were conducted by employing a steady shear rate sweep between 1 to 100 s 1, using a parallel plate configuration. As shown in Fig. 1, the apparent viscosity of the non-Newtonian solutions Zapp, are functions of shear rate and can be defined by power-law model. The power-law model for the isothermal condition is:
Zapp ¼ kg_ n1
ð1Þ
where k is the consistency index and n is the power law index (k and n are listed for BSM and DBSM in Table 1). The consistency and power law indices are derived by fitting a curve through the data points. The curve fit predicted the viscosities within 710% of experimentally measured viscosities. From these measurements, it is evident that the solutions are non-Newtonian, shear-thinning solutions. The slot-die is made of stainless steel 316 and the moving substrate is polyterephthalate (PET). The contact angles (with respect to stainless steel 316 and PET) and surface tensions were measured using a Rame´-hart Goniometer Model 250. Sessile drop and pendant drop methods were used to measure contact angles and surface tensions, respectively, for both solutions. The densities of the solutions were obtained by dividing the weight of the fluid by its volume. The volume and weight measurements were obtained by using a standard methodology: The solution was poured into a graduated beaker, to a desired volume. The weight of the empty jar and the weight of the fluid filled jar were recorded. Then the total weight of the empty jar was subtracted from the fluid filled jar to obtain the fluid weight. All of these fluid properties are given in Table 1.
10
197
3. Experimental set-up and procedure A custom designed and built roll-feed imaging system (RFIS) (Johnson and Harris, 2010), was used to monitor the dynamics of the solutions0 behavior as they were being deposited onto a moving substrate to investigate the air entrainment mechanism, shape and location of DCL, and formation of sawteeth. A schematic of the experimental set up (RFIS) is shown in Fig. 2. The RFIS is equipped with a temperature controlled pressured tank, a temperature controlled roll-to-roll feed system with adjustable speed and tensioning, a temperature controlled fabrication tool (slot die) and feedback control vision system. The feedback control vision system consists of a microscope with camera (Olympus Zoom Stereo Microscope-model SZ61TR and Olympus SIS-UC30 digital camera, 14 frames per second at 1040 772 resolution or a 2-megapixel Phantom V9.1 high-speed camera, 1,016 frames per second at 1632 1200 resolution). As illustrated in Fig. 2, a transparent plate is nestled below the slot die to allow for image capture as the solution is cast onto the substrate. Nitrogen supplied from a pressurized tank forces the solution through the slot die onto the moving substrate/web. A schematic detailing the parameters of the lower section of the slot die and the substrate is illustrated in Fig. 3. The slot die has an upstream and a downstream half, which is offset by a shim to control the slot gap, W, the distance between the two plates. The solution (coating fluid) is pumped through the die in the y-direction at a flow rate, Qin, and is caused to impact onto a moving web/substrate traveling at a speed, uw, in the x-direction. The flow rate is more conveniently defined by using volumetric flow rate per unit width, Q0 , which is obtained by dividing the volumetric flow rate, Qin, by the width of the slot die. The suspended fluid displaces the air that was originally in contact with the substrate forming the upstream and downstream menisci with the bottom surface of the slot die walls. The DCL is formed between the substrate and solution along the z-direction or the slot die width. The distance between the slot die and the substrate is referred to as the coating gap or stand-off height, H. The coating gap is adjusted
BSM Apparent Viscosity, Pa-s
DBSM Curve Fit
Nitrogen Tank
Pressure Gauge Pressure Vessel Ball Valve
1 0.1
1
10 Strain Rate, 1/s
100
1000
Fig. 1. Apparent viscosity of BSM and DBSM.
Slot Die Light Platen
Platen
Plate
Computer Camera & microscope
Table 1 Fluid properties of test solutions and silicone oil. Parameter
BSM
DBSM
Silicone Oil
Contact angle on stainless steel (deg.) Contact angle on PET (deg.) Surface tension, s (N/m) Density, r (kg/m3) Power-law index, n Consistency index, k (Pa-sn) Viscosity (Pa-s)
69 62 0.047 1452 0.83 8.07 –
68 74 0.049 1411 0.63 6.47 –
– – – 971 1 9.7 9.7
Feed Roller
Take-up roller Motorized roller
Roller with load cells Fig. 2. Illustration of experimental set up, RFIS (Bhamidipati et al., 2011).
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(2) Simultaneously, as the dynamic contact line cannot move beyond a critical speed (maximum coating speed) perpendicular to itself, sawtooth structures form (Blake and Ruschak, 1979). (3) Due to the three-dimensional nature of the sawtooth, a layer of coating solution exists above the layer of air. Interfacial instabilities between the air and fluid films cause bubble breakup (Severtson and Aidun, 1996). Four forces are primarily found (Chang et al., 2007a; Romero et al., 2006) to influence the stability of the coating bead in the slot die coating process; viscous forces, surface tension forces, inertia forces and gravity.
Fig. 3. Schematic of slot die coating.
with a vertical rail system equipped with worm gears. When the slot die engages a feeler gauge of a certain thickness, the coating gap is set. The distance between the menisci is the coating bead length, L. The final thickness of the coated film is the minimum wet thickness, h. The angle made by the upstream meniscus with the substrate is the apparent dynamic contact angle, yad. The angles made by the upstream and downstream menisci with the bottom surface of the slot die are the static contact angles,ys,a and ys,d, respectively. The point of air entrainment is a function of the substrate speed, as described by the coating window (Chang et al., 2007a; Higgins and Scriven, 1980; Ruschak, 1976). For a given pressure exerted by the Nitrogen tank on the coating solution in the slot die, there exists a maximum substrate speed beyond which air entrainment ensues. This is identified as the air entrainment velocity, uw,max. 3.1. Calculation of Q0 Because the coated solution does not solidify, measuring the film thickness is not practical without causing some film distortion. In order to analyze the results independently of geometry, the volumetric flow rate per unit width (across the die), Q0 , is calculated corresponding to the pressure, P exerted by the Nitrogen tank on the coating solution. Q0 is calculated by setting the pressure, P, and the substrate speed, uw, to the desired values. A known length, Lf, of the coated PET is weighed and the weight, mf, recorded. The mass of dry PET, mPET, is then recorded after it is cleaned and dried. The total time, tf, required to coat the known length of PET, Lf, is obtained by dividing Lf by uw. The volumetric flow rate per unit width, Q0 , is then obtained by Eq. (2). Q0 ¼
ðmf mPET Þ wf t f rcs
ð2Þ
where the casting solution density is given by rcs and wf is the width of the film.
4. Results and discussion Combining the observations made by past researchers, the steps involved in the air entrainment mechanism can be summarized in three steps: (1) When the pressure drop across the coating bead that is required to produce a stable bead is not maintained due to an imbalance with the externally imposed pressure gradient causing flow through the slot die, the bead becomes unstable (Higgins and Scriven, 1980) and the originally two-dimensional flow-field becomes three-dimensional.
The viscous forces, Fm, arise due to the viscous nature of the solution coated on the moving substrate. These forces are dominant in the coating gap region and influenced by the coating gap, H, viscosity parameters of the shear-thinning solution; consistency index, k and power-law index, n, and the substrate speed, uw. In terms of these parameters, viscous forces, Fm, are defined by Eq. (3): m n F m pk w ð3Þ H The surface tension, Fs, forces play an important role in determining the shape of the upstream meniscus formed by the coating bead, which in-turn dictate the stability of the coating bead (Chang et al., 2007b). Surface tension forces, Fs, can be described by Eq. (4): Fsp
s H
ð4Þ
where s is the surface tension of the shear-thinning solution in air. The inertia forces, Fi, arise due to the momentum of the fluid exiting the slot die. As presented by Chang et al. (Chang et al., 2007a), these are determined by the velocity of the fluid exiting the slot die, vin, and the density of the fluid, r, as given by Eq. (5): F i pru2in
ð5Þ
Finally, as observed by Chang et al. (Chang et al., 2007a), the orientation of the slot die and the substrate with respect to the direction of gravity is found to influence the air entrainment velocity. In this study, the coating solution flows in the direction of gravity (vertical coating). Eq. (6) describes the force due to gravity, Fg: F g prgH
ð6Þ
where g is gravity. A depiction of the four forces acting on the coating solution (in the region near the bottom portion of the slot die) is shown in Fig. 4: It can be seen from Fig. 4 that the horizontal component of surface tension force acts in the direction opposite to the substrate motion. Two important non-dimensional numbers derived from the forces that are applicable to this study are the capillary number (ratio of viscous to surface tension forces) and the Reynolds number (ratio of inertia to viscous forces). The capillary number, Ca, for shear-thinning solutions is presented in terms of Eq. (7): Ca ¼
Fm kðmw =HÞn1 mw ¼ Fs s
ð7Þ
K. Bhamidipati et al. / Chemical Engineering Science 80 (2012) 195–204
Downstream Die
Upstream Die
Fig. 4. Depiction of forces acting on the coating solution.
VL SHL SVL
HL
Fig. 5. Dimensional features of (a) sawtooth and (b) bubble.
Reynolds number, Re, defined by Eq. (8) as: Re ¼
ru2in Hn Fi ¼ Fm kmnw
ð8Þ
4.1. Bubble pinch-off Mechanisms The bubble entrainment mechanisms were captured using the microscope and high-speed camera, using the aforementioned approach. ImageGrab version 5.0.6En (Glagla software was used to create still shots of the video feed correlating to the data of interest. The sawteeth and bubbles were quantified using ImageJ 1.45 (Rasband image processing and analysis software. The features of the sawtooth and bubble are illustrated in Fig. 5. The sawtooth length is denoted by SVL, while the sawtooth width is represented by SHL. Parameters HL and VL denote the horizontal and vertical lengths of the bubble at pinch-off. Two distinct mechanisms that cause bubble pinch-off resulting in air entrainment were noticed for both shear-thinning and Newtonian solutions, and are subsequently discussed. Mechanism I: Pinch-off of an entrained bubble by Mechanism I occurs when the length of the sawtooth (SVL) is equal to or greater than its width (SHL). In this mechanism, bubble pinch-off is assisted by the solution present in the coating gap. As the substrate reaches the air entrainment speed, sawteeth or air pockets form. At this juncture, the viscous forces acting on the coating solution, which causes it to be pulled in the direction of substrate motion, as shown in Fig. 4, become dominant over the surface tension forces acting in the opposite direction because the upstream contact angle approaches 1801. This results in an interfacial instability causing the coating solution already present in the coating gap to entrain the air film from all sides. Air bubble pinch-off occurs when the solution fully surrounds the sawtooth. Then surface tension acts on the bubble causing it to shrink, after which the bubble moves
199
downstream and becomes entrained in the coated film. In other words, Mechanism I is dictated by the capillary number as described by Eq. (7). As the length of the sawtooth approaches a value equal to its width, the pinch-off location shifts closer to the base as shown in Fig. 6(a). When the sawtooth length is greater than its width, the pinch-off is observed to occur closer to the tip of the sawtooth as shown in Fig. 6(b). The line X0 Y0 -X0 Y0 marked on the top view denotes the location of the side (sectional) view. Fig. 6(c) shows the experimental images of bubble pinch-off by Mechanism I. Mechanism II: In this mechanism, the broken dynamic contact line is displaced by a new wave of fluid. Hence, Mechanism II only occurs in pre-metered coating processes like slot die coating, where there is a continuous supply of coating solution at a given flow rate. When the width of the sawtooth (SHL) is much greater than its length (SVL), the bubble pinch-off occurs by Mechanism II. Due to the presence of a wider sawtooth, it becomes difficult for the solution upstream of the sawtooth to enclose the larger air pocket. Instead, the bubble pinchoff mechanism is aided by fresh solution exiting the slot die, which encloses the air pockets formed by the broken dynamic contact line. Therefore, a combination of pre-metering and the presence of a larger air pocket spread over a wide area are required for Mechanism II to occur. The absence of an upstream solution feed source would cause the air pocket to expand over a wider area, thereby making it impossible for the solution on the substrate to bind the pocket. Since the contact line is spread over a wider area, the new fluid coming out of the slot displaces a large part of the contact line, as illustrated in Fig. 7(a). The line X0 Y0 -X0 Y0 marked on the top view denotes the location of the side (sectional) view. In the bubble formation by Mechanism II, the pinch-off could extend over a larger area. The extent to which the sawtooth spreads before pinch-off occurs depends on the relative strength of inertia to viscous forces as determined by the Reynolds number. If inertia forces are dominant, then the sawtooth has less time to spread before pinch-off occurs and vice-versa. Since the bubble sizes are generally proportional to the sawtooth sizes, the bubble might look elongated in the direction perpendicular to the substrate motion. Subsequently, the elongated bubble can either remain intact or split into smaller bubbles. Experimental images demonstrating bubble pinch-off by Mechanism II is shown in Fig. 7(b). 4.2. Effect of geometric parameters and viscosity on air entrainment The effects of slot gap, coating gap and viscosity on sawtooth and bubble sizes are captured using the microscope and digital camera described previously. Digital images are presented to show the comparison between various cases. The average sizes of sawteeth and bubbles are presented in terms of sawtooth width (SHL), sawtooth length (SVL), and effective bubble diameter at pinch-off (approximated qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi as H2L þ V 2L . Because of the difficulty associated with capturing the thickness of the sawteeth and air bubbles, the sizes presented in the study only correspond to 2D projections of the sawteeth and air bubble as viewed from the camera placed under the substrate. 4.2.1. Effect of slot gap The impact of slot gap on the sawtooth geometry for BSM is illustrated in Fig. 8, Three slot gaps were tested W¼0.178 mm, 0.25 mm and 0.30 mm for H¼0.30 mm and Q0 ¼0.53 mm3/mm-s. Four images taken at different time intervals of the coating process are illustrated in Fig. 8(a) through (c) for W¼0.178 mm, 0.25 mm and 0.30 mm, respectively. A comparison between the sawtooth geometry from the pictures show that the width of the sawtooth increases with increasing slot gap, while the difference in the sawtooth0 s length are relatively small. The air entrainment speed is found to be approximately 3.50 mm/s in each case, which corresponds to a capillary number of
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Fig. 6. Pinch-off of air bubbles by Mechanism I (a) illustration of air bubble pinch-off closer to the sawtooth base), (b) illustration of air bubble pinch-off closer to the sawtooth tip), and (c) images from experiment demonstrating bubble pinch-off by Mechanism I.
Fig. 7. Pinch-off of air bubbles while slot die coating of silicone oil (a) images from experiment demonstrating bubble pinch-off by Mechanism I, (b) images from experiment demonstrating bubble pinch-off by Mechanism II.
0.40. Therefore, the differences in the viscous forces experienced by the solution due to the substrate motion are negligible. Since the flow rate per unit width is maintained constant, the velocity (vin) of
the coating solution through the slot die increases as the slot gap decreases. Therefore, the inertia forces are more dominant when the slot gap is smaller resulting in a smaller sawtooth.
K. Bhamidipati et al. / Chemical Engineering Science 80 (2012) 195–204
Contact Line
10
Sawtooth
W = 0.178 mm
201
W = 0.250 mm
W = 0.300 mm
Average Length (mm)
9 8 7 6 5 4 3 2 1.3
1.5
1 0
Fig. 9. Quantitative representation of the impact of slot gap, W, on the sawtooth and air bubble sizes at the air entrainment boundary for BSM solution, H¼ 0.30 mm and Q0 ¼0.53 mm3/mm-s.
Contact Line
Fig. 8. Qualitative representation of the impact of slot gap, W, on the sawtooth sizes at the air entrainment boundary for BSM solution, H ¼0.30 mm and Q0 ¼ 0.53 mm3/mm-s, dashed lines represent boundaries of die lips for (a) uw,max ¼ 3.54 mm/s (Ca¼0.41) for W¼ 0.178 mm, (b) uw,max ¼ 3.5 mm/s (Ca¼ 0.40) for W ¼0.25 mm and (c) uw,max ¼ 3.48 mm/s (Ca ¼0.40) for W ¼0.30 mm.
1.3
Sawtooth
1.5
The average sawtooth and air bubble sizes for the three cases specified in Fig. 8 are presented in Fig. 9. It is evident that the sawtooth and the bubble sizes increase with increasing slot gap. Even though bubble pinch-off occurs by both mechanisms in most of the cases, the pinch-off occurs predominantly by Mechanism I in the case of smaller slot gaps, while Mechanism II becomes dominant as the slot gap increases. This is evident in Fig. 9, where the increase in the width of the sawtooth is significant compared to the increase in its length as the slot gap increases. When the slot gap increases by 41%, from 178 mm to 300 mm, the sawtooth width, length and the effective bubble diameter increased by approximately 67%, 31%, and 58%, respectively. It is therefore advantageous to work with smaller slot gaps as they produce smaller sawteeth, which produces smaller bubbles. In addition, smaller bubbles would be expected to dissolve faster than larger bubbles, as shown by Miyamoto and Scriven (Miyamoto and Scriven, 1982).
4.2.2. Effect of coating gap The effect of coating gap on the sawtooth structures at the air entrainment boundary is illustrated in Fig. 10. DBSM is used as a solution. Three coating gaps were tested, H¼0.178 mm, 0.25 mm and 0.30 mm for slot gap, W¼ 0.178 mm. The air entrainment velocities corresponding to a flow rate per unit width, Q0 ¼0.62 mm3/m-s are 7.5 mm/s (Ca¼0.26), 5.5 mm/s, (Ca¼0.25) and 4.5 mm/s (Ca¼0.23) for H¼ 0.178 mm, 0.25 mm and 0.30 mm, respectively. From Fig. 10,
Fig. 10. Qualitative representation of the impact of coating gap, H, on the sawtooth sizes at the air entrainment boundary for DBSM solution, W ¼ 0.178 mm and Q0 ¼ 0.62 mm3/mm-s, dashed lines represent boundaries of die lips for (a) uw,max ¼7.50 mm/s (Ca¼ 0.26) for H¼0.178 mm, (b) uw,max ¼ 5.50 mm/s (Ca¼0.25) for H¼0.25 mm and (c) uw,max ¼ 4.50 mm/s (Ca¼0.23) for H¼0.30 mm.
it is observed that both the length and width of the sawtooth increase as the coating gap increases. However the increase in the sawtooth width is greater than the increase in its length. The increase in
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sawtooth geometry is due to two primary reasons. The air entrainment velocity decreases as the coating gap increase. As shown in Eq. (3), since the stresses experienced by the solution are proportional to the ratio of air entrainment velocity, uw,max to the coating gap, H, raised to power-law index, n, ([mw,max/H])n, the stresses decrease as the coating gap increases. Therefore, the stresses take longer to propagate upstream causing the sawtooth to spread over a larger area before pinch-off occurs. The larger area results in a larger air pocket, which makes it difficult for the solution in the coating gap to fill the void. This gives additional time for the sawtooth to spread. However, the presence of opposing forces (surface tension) that prevent the sawtooth from stretching in the direction of the substrate motion limits the length of the sawtooth from becoming too large. This can be explained by Eq. (4), which shows that surface tension forces, which pull the coating solution in the opposite direction (opposite to the direction of substrate motion), are proportional to (1/H), implying that surface tension forces are also lowered as the coating gap increases. But, as long as the surface tension forces are finite, they limit the extent to which the sawtooth extends lengthwise. Instead, the sawtooth spreads over a wider area causing the width of the sawtooth to increase more significantly. The relative differences in the sawtooth and bubble sizes pertaining to the conditions specified in Fig. 10 for the three coating gaps are depicted in Fig. 11. When the coating gap increases by 41%, from 178 mm to 300 mm, the sawtooth width, length and the effective bubble diameter increased by approximately 55%, 27%, and 51%, respectively. Due to the higher sawtooth0 s width compared to its length, it is observed that the bubble pinch-off mechanism shifts from a significant Mechanism I to a significant Mechanism II, for the larger coating gap. Larger sawteeth generated at higher coating gaps produces bigger bubbles, which is undesirable. Hence, in addition to obtaining larger coating speeds, smaller coating gaps are also advantageous because of the smaller bubble sizes. Another interesting observation is that when the coating gap is above 250 mm the sawtooth length is significantly lower than the sawtooth width, by approximately 40%, however this effect seems to be less dominant when the coating gap is 178 mm, having a percent difference of only 2%. Thus, as the coating gap decreases, the percent difference between the sawtooth width and length becomes less significant. When considering the sawtooth length and width of the coating gap to that of the slot gap a similar trend is observed, as seen in Fig. 9. At a slot gap below 250 mm the percent difference is
6
H = 0.178 mm
H = 0.250 mm
approximately 44%. However, the percent difference increases to approximately 73% when the slot gap is 300 mm. The significant increase in the sawtooth width compared to its length explains the shift in bubble breakup from Mechanism I to Mechanism II at larger slot gaps and coating gaps. 4.2.3. Effect of viscosity The effect of viscosity on the sawtooth structures is illustrated in Fig. 12(a) and (b) for DBSM and BSM, respectively, at W¼0.178 mm and H¼0.25 mm. For a volumetric flow rate per unit width, Q0 ¼0.55 mm3/mm-s, the air entrainment speeds were found to be 5.6 mm/s (Ca¼0.25) for DBSM, and 4.3 mm/s (Ca ¼0.46) for BSM. The inverse relationship between the viscosity and the air entrainment speeds was demonstrated by several researchers (Burley and Jolly, 1984; Chang et al., 2007a, 2007b; Gutoff and Kendrick, 1982; Lee et al., 1992). It can be observed that both the sawtooth length and width are larger for DBSM solution, which is a relatively low-viscosity solution compared to BSM. These results are consistent with the observations made by Burley and Kennedy (Burley and Kennedy, 1976). The reason for the differences in the sawtooth sizes is because the stresses experienced by the coating solution are proportional to the viscosity (consistency-index in the case of shear-thinning solutions) of the solution as presented by Eq. (3). Thus, higher viscosity solutions are expected to experience higher stresses. However, since high-viscosity solutions experience air entrainment at lower coating speeds, there would be a reduction in the stresses. Veverka (Veverka, 1995) showed that the effect of viscosity is dominant compared to the effect of air entrainment speed on the stresses. Thus, the slope of the air entrainment speed versus viscosity curve (air entrainment speed plotted on the vertical axis and viscosity plotted on the horizontal axis) is less than 1. In addition, for shear-thinning fluids the stresses are proportional to ðuw,max Þn , (the air entrainment speed raised to the power-law index -which is less than one) which further reduces
Contact Line
Sawtooth
H = 0.300 mm
Average Length (mm)
5 4 1.3
1.5
3 2 1 0
Fig. 11. Quantitative representation of the impact of coating gap, H, on the sawtooth and air bubble sizes at the air entrainment boundary for DBSM solution, W ¼0.178 mm and Q0 ¼0.62 mm3/mm-s.
Fig. 12. Qualitative representation of the impact of solution viscosity on the sizes of the sawtooth at the air entrainment boundary for W ¼0.178 mm, H¼ 0.25 mm and Q0 ¼ 0.55 mm3/mm-s, dashed lines represent boundaries of die lips for (a) uw,max ¼5.6 mm/s (Ca¼ 0.25) for DBSM and (b) uw,max ¼ 4.3 mm/s (Ca¼ 0.46) for BSM.
K. Bhamidipati et al. / Chemical Engineering Science 80 (2012) 195–204
the effect of the air entrainment speed on the stresses. Combining all the effects on the stresses, it can be concluded that the stresses follow the same trend as the viscosity. Since the stresses experienced by the low-viscosity solution are smaller (Fm,DBMS/Fm,BSM)o1, the sawtooth extends over a larger area before the bubble pinch-off occurs as shown in Fig. 12. The average sawtooth and bubble sizes corresponding to the conditions specified in Fig. 12 for the two solutions are presented in Fig. 13. As seen in Fig. 13, the presence of a larger sawtooth for DBSM compared to BSM confirms the assumption presented in the previous paragraph that the smaller viscous stresses experienced by the relatively low-viscosity solution causes the sawtooth to spread over a larger area. The sawtooth lengths, widths and the effective bubble diameters of the DBSM were found to be approximately 24%, 52%, and 7% larger than those for BSM. It was found that HL is 40% and 60% larger than VL for DBSM and BSM, respectively. This is consistent with the observations that BSM experienced a higher chance of bubble breakup by Mechanism II compared to DBSM. The change in the apparent dynamic contact angle of BSM with respect to the substrate speed has been captured by a monitoring system installed at the set up. The variation of dynamic contact angle versus the capillary number is show in Fig. 14. The measurements were done at the constant flow rate and geometrical configuration, while changing the substrate speed from the dripping to the threshold of air entrainment. As illustrated in the figure the values of the contact angle increased continuously until approaching a value close to 1601 at the point of air entrainment. The experimental data are compared by the interface formation theory proposed by Shikhmurzaev (Shikhmurzaev, 2008), which is based on Newtonian fluids. As
Average Length (mm)
5
DBSM
BSM
4 3 2
5. Conclusions A study is performed to explain the mechanisms by which air bubble pinch-off occurs prior to bubble entrainment in a coated film, for relatively high viscosity, shear thinning solutions. In addition, the effects of the geometric parameters and the viscosity of the coating solution on the sawtooth and air bubble sizes are analyzed. It has been found that there are two mechanisms that cause air bubble pinch-off. In the first mechanism, the bubble pinch-off is aided by the solution present in the coating gap, while in the second mechanism, the bubble pinch-off is assisted by the new solution coming out of the slot die. The comparative studies between the geometric parameters revealed that Mechanism I is dominant in smaller slot gaps, smaller coating gaps and low viscosity solutions. Mechanism II was found to be dominant when wider sawteeth are present. Bubble sizes were found to vary proportionally with the sawteeth sizes. Slot gap did not have any impact on the air entrainment speed, while smaller slot gaps have the advantage of producing smaller sawtooth and bubble sizes. Smaller coating gaps produce higher air entrainment speeds and smaller sawtooth/bubble sizes. Further, solutions can be processed at higher maximum coating speeds as the viscosity decreases, however, the sawtooth and air bubble sizes are larger at the air entrainment boundary. As Miyamoto and Scriven (Miyamoto and Scriven, 1982) have shown, smaller air bubbles tend to dissolve faster, which might nullify the impact of smaller bubbles on the properties of the coated film. This work can be useful in increasing the air entrainment velocity by determining the optimum slot and coating gaps for a given system when the limits of bubble sizes are known.
Nomenclature
Fig. 13. Quantitative representation of the impact of solution viscosity on the sawtooth and the air bubbles sizes at the air entrainment boundary for W ¼0.178 mm, H¼ 0.25 mm and Q0 ¼ 0.55 mm3/mm-s.
Experimental data
Dynamic Contact Angle (º)
shown in the Fig. 14 the presented experiential data follows the same trend of the model, although some discrepancy between them can be observed, which can be attributed to the uncertainty the experimental measurement.
1 0
Interface formation model (Shikhmurzaev 2008)
170 150
Fg Fi Fm Fs g h H HL k L mf mPET n P Q Q0
130
rcs
110
SHL SVL tf W
90 0.15
203
0.2
0.25
0.3 Ca
0.35
0.4
0.45
Fig. 14. The variation of apparent contact angle of BSM with respect to the substrate speed and comparison with the interface formation theory (Shikhmurzaev, 2008).
Zapp g_ j yad
Gravity forces Inertia forces Viscous forces Surface tension forces Gravity, m/s2 Wet thickness, mm Coating gap or Stand-off height, mm Horizontal diameter of air bubble at pinch-off Consistency index, Pa-sn Coating bead length, mm Mass of PET coated with solution, kg/s Mass of dry PET, kg/s Power-law index Pressure, Pa Flow rate, mm3/s Flow rate per unit slot die width, mm3/mm-s Density of the coating solution, kg/mm3 Width of sawtooth Length of sawtooth Time, s Slot gap, mm Apparent viscosity, Pa-s Shear rate, 1/s Angle made by the sawtooth structures with horizontal, deg. Apparent dynamic contact angle, deg.
204
ys,a ys,d uw uw,max vin VL wf
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Upstream Static contact angle, deg. Downstream Static contact angle, deg. Substrate velocity, mm/s Air entrainment velocity, mm/s Inlet velocity, mm/s Vertical diameter of air bubble at pinch-off Width of the film, m
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