Ind. Eng. Chem. Res. 1991,30,453-461 Activities. Adu. Catal. 1969,20, 97-133. Numaguchi, T.; Kikuchi, K. Intrinsic Kinetics and Design Simulation in a Complex Reaction Network; Steam-Methane Reforming. Chem. Eng. Sci. 1988,43(8),2295-2301. Rostrup-Nielsen, J. R. Steam Reforming Catalysts; Danish Technical Press: Copenhagen, Denmark, 1975. Rostrup-Nielsen, J. R. Criteria for Carbon Formation (Steam Reforming and Methanation). NATO Adv. Study Inst. Ser. E 1982, NO.54,127-149. Shimada, H.; Kurita, M.; Sato, T.; Yoshimura, Y.; Nishijima, A.; Yoshitomi, S. Effect of Pore Size Distribution on the Catalytic Performance for Coal Liquefaction. Bull. Chem. SOC.Jpn. 1984, 57,2000-2004.
453
Singh, C. P. P.; Saraf, D. N. Simulation of High-Temperature Water-Gas Shift Reactors. Ind. Eng. Chem. Process Des. Dev. 1977,16 (3),313-319. Suzuki, M.; Onuma, K. Hydrotreating Catalysts for Heavy Oils (Part 2)Reaction Performance and Aging Behavior of Bimodal Alumina Based Catalysts for Desulfurization and Demetallation. J . Jpn. Pet. Inst. 1984,27 ( 5 ) , 420-428. Van Hook,J. P. Methane-Steam Reforming. Catal. Rev.-Sci. Eng. 1980,21 (l),1-51.
Received for review January 8, 1990 Revised manuscript received August 7, 1990 Accepted August 16, 1990
MATERIALS AND INTERFACES Role of Dynamic Surface Tension in Slide Coating Jose Esteban Valentini,* William R. Thomas, and Paul Sevenhuysen Imaging Systems Department, E. I. du Pont de Nemours, Brevard, North Carolina 28712
Tsung S. Jiang, Hae 0. Lee, Yi Liu, and Shi-Chern Yen Department of Chemical and Biochemical Engineering, Rutgers-The State University of New Jersey, Piscataway, New Jersey 08855-0909
Gelatin solutions (5 wt 5%) with different dynamic surface tensions and elasticities were coated in the slide coater. The experiments, which consisted of either one or two layers, were performed a t speeds in the range of 0.35-2.03 m/s and 40 "C. The vacuum under the bead at the onset of rivulet was correlated to the dynamic surface tension and the curvature of the upper meniscus. The dynamic surface tensions were measured with a maximum bubble pressure technique at frequencies in the range of 0.5-5 bubbles/s and adjusted with commercial surfactants. The variation of the dynamic surface tension with respect to the bubble frequency was correlated to both the solution Gibbs surface elasticity and the vacuum range measurements a t the onset of ribbing. The dynamic and rheological properties of the surface impact the wettability, the coatability window, and the surface forces that control flow and deformation.
Introduction Coating is a fundamental operation in the silver halide photographic industry, and the current necessity of more uniform and better quality products requires a thorough understanding of this process. There are two major classes of coaters, self and premetered. The most attractive feature of premetered devices, and the reason for their use in the photographic industry, is that the thickness of the coated layer can be controlled within precise limits. The slide coater (Figure 1)belongs to this category and has been widely used to apply coating solutions on a moving support in either a single-layer or multilayer approach. The coating process is highly dynamic and involves generation and extension of surfaces at a high rate. In the case of the slide coater a free surface is formed at the slot from which the liquid flows onto an inclined plane forming a thin film. The bead, where most of the stretching of the surface occurs, is established between the moving support of web to be coated and the front of the slide. The bead is bounded by both the upper meniscus and the lower one
* Author to whom correspondence should be addressed.
which usually is maintained at subatmospheric pressure. The effect of surface forces on coating was presented in the literature by several authors. Deryagin and Levi (1964) derived expression 1 for the radius of curvature of the upper meniscus R as a function of the thickness of the coated layer H and the capillary number Ca in the case of dip coating and small Ca and We (Weber) numbers.
R = (H/1.33)(1/Ca)2/3
(1) where Ca M V / Uand We p V H l u , in which p is the viscosity, V is the coating speed, u is the surface tension at the bead, and p is the density. Galehouse and Colt (1984) described a similar expression (2) for the slide coater operated at low capillary numbers. R =2~(1/~41/3 (2) Recently, Hens and Boiy (1986) concluded that in industrial coating applications capillary forces are considerably less important than the viscous or inertial ones, especially at coating speeds of 2.2 m/s or higher. In all cases, the capillary forces have been accounted for only by the bead surface tension. Typical photographic solutions consist of silver halide particles suspended in gelatin and additives, including surfactants. Particularly,
0888-58851911263O-O453$O2.5O/O 0 1991 American Chemical Society
454 Ind. Eng. Chem. Res., Vol. 30, No. 3, 1991
L V a c u u m Chamber
Figure 1. Side view of slide coater. The coating solution (dark) is shown flowing down the slide and on the moving web.
the gelatin and the surfactants are able to diffuse to the new surface on both the slide and the bead. However, the equilibration of the surface tension is not instantaneous (Ziller et al., 1985). The transient surface tension at any instant is termed “dynamic”. Therefore, the capillary forces are expected to vary along the entire free surface, to induce Marangoni effects, and to affect “coatability”. The term “coatability” refers to the process of coating a solution on a web. The purpose of this study is to present experimental results on the effect of surface rheology, in particular the dynamic surface tension on multilayer coatings, and to define the relationship between this variable and the “apparent” Gibbs surface elasticity. Finally a new and simple flow visualization technique to study the bead geometry is also described. Experimental Setup Gelatin solutions in the range of 5-10% (w/w) were prepared with Kind and Knox deionized gelatin and deionized water. The solid gelatin is added into a faststirred container with water, and the suspension is kept a t 18-20 “C for 5 min. After the slurry is soaked, it is heated up to 60 ‘C during 20 min until complete dissolution of the gelatin particles. Finally the gelatin solution is filtered. Different surfactant solutions were used to be able to adjust both the dynamic and static surface tensions of the gelatin solutions. They include fluorocarbon surfactants such as Lodyne 107 B (Ciba-Geigy) and Zonyl FSN (Du Pont), nonionic surfactants such as Triton X-100 (Rohm and Haas) and Renex (ICI),and anionic Surfactants such as Standapol (Henkel). Since all the surfactants are of commercial grade, the solution concentrations are made on the basis of that of active material as reported by the vendor. Additional experiments were performed with highly pure poly(ethy1ene oxide) alkyl ether (C12En, n = 3,6,8; where indicates the hydrocarbon chain and E denotes the ethylene oxide group) surfactants made by Nikkol (Japan) and supplied by Mitsui & Co. (USA). To characterize these surfactants, aqueous solutions were prepared by using doubly distilled water produced with alkaline potassium permanganate. The dynamic surface tensions (DST) were measured with a Sensadyne 6000 surface tensiometer, which is based on the maximum bubble pressure method (Adamson, 1982). The bubble generation rate was kept in the time scale range of 200-1000 ms or 5-10 bubbles/s. Both the calibration and surface tension reading$ were performed
Figure 2. Sony XC-77 TV camera used to view the slide flow from the side. The light sheet projector directs a light beam parallel to the flow.
at 40 “C. The calibration range for surface tensions was 33.8-70.0 mN/m. The accuracy of the measurement is k0.2 mN/m. The static surface tensions (SST)were determined with a Fisher Surface Tensiomat Model 21, which operates on the Du Nouy ring method (Adamson, 1982). Calibrations and readings were performed at 40 “C. The viscosities of the solutions were measured with a Brookfield digital viscometer at 40 “C. The densities of the solutions were measured with a Mettler Paar-DMA46 densitometer, and all the values were in the range of 1.010-1.030 g/cm3. The “apparent” Gibbs surface elasticities were measured with a modified Langmuir trough and an electrobalance (CAHN Instruments Inc.) at 1 cycle/min. Details of this technique have been described elsewhere by Jiang and Valentini (Jiang et al., 1990). Coating Experiments 1. Flow Visualization. Slide coaten with two different slide angles were used for the study. Both provide more than one slot so different layers can be coated simultaneously in a multilayer approach. The web, which is a 13.75-cm-wide polyester base, had a previously applied gelatin subcoating to ensure proper wettability. The static contact angles of the coating solutions were measured with a goniometer at 2 min after the formation of the drop. The values were in the range of 18-24’. All the coatings were performed at 40 “C, and the slide was also kept at the same temperature to ensure constant delivery temperatures up to the bead. The solutions were filtered prior to coating and fed into the slots by use of gear pumps (Zenith Co). Two general views of the coating flows on the coating head were used: (1)a view of the free surface of the slide flow both at the bead and at the slob and (2) a view of the underside of the lower meniscus via the view through the stationary glass “coating roll”. To accomplish 1, a Sony XC77 black and white solidstate camera with an 8.8 X 6.6 mm sensor containing 768 X 493 pixels, each with a size of 11 X 13 pm, was used. The bead or flow profile is visualized by projecting a sheet of light onto the flow. The line is projected vertically 80 that the projected line is parallel to the direction of flow. Viewing this line from the side and slightly above the plane of the flow, the profile of the flow shape can be seen
Ind. Eng. Chem. Res., Vol. 30, No. 3, 1991 455 c1m / w*
Bar Stationary Coating Roll
HE-NE Laser Llne
Monozoom 7
Figure 3. Combination of laser line projector and B&L Monozoom 7 to generate a light line on the tip of the slide.
(Figure 2). Resolution problems, which arise from any coater vibrations, are reduced by using an electronic flash synchronized to the T V camera picture-taking rate. The profiling line itself is formed by using a disk-to-line fiber-optic light pipe. The fibers are arranged at one end in a 0.124-in.-diameter disk and at the other into a line of fibers 1in. long by 0.012 in. wide (Dolan-Jenner Industries x904). The line end was plotted into a Nikon lens cap so it could be attached to a Nikon bellows with a 55-mm lens on the other end. This permitted projection of a sharp line image from the fiber-optic light source (either continuous light or an EG&G electronic strobe) onto the surface of the flow to be profiled. Working distance was about 2-5 in. depending on how the bellows was adjusted. Calibration of the camera view in a plane orthogonal to the slide and flow is made possible by capturing an image of a glass reticle (a 0.5 mm grid pattern) mounted perpendicular to the plane of the slide in the plane of the light beam. From this image the x and y pixel calibrations are obtained for the optical/TV system. Since it is desirable to reference all images to the same coordinate zero, it is necessary to have a reference point in all pictures. The bar lip tip was chosen as the zero coordinate point; however, since it is not visible when covered with coating liquid, a wire tip was used as reference while coating. Before any experiment the coordinates of the wire tip with respect to the slide tip were obtained by taking a reference picture. The underside view (2) is viewed by looking radially through a 0.25-in.-thick optical-quality glass skid plate (Karl Lambrecht Co.) mounted on a stationary “coating roll” as mentioned above (Figure 3). The mirror is required to redirect the bar lip and underbead image from radial to axial direction into a scope. The scope (Bausch and Lomb Monozoom 7), which is used with a 0.75X objective, 3X amplifier at 3X zoom, is attached to the Sony XC-77 camera. As shown in Figure 3, the scope is slid into the open end of the coating roll so the axes of both the coating roll and the scope lens are aligned. As shown in Figure 3, profiling of the shape is done by aiming a sharply focused line of light at the underside of the bead at a grazing angle. A He-Ne laser beam is focused with a cylindrical lens‘(V-SLM-015Newport) to form a line that is projected on the bottom part of the slide tip and underside of the coating flow. From the shape of this line it is possible to determine the location of the “landing point” of the bead both on the slide and’on the web. The procedure is similar to determining the height of a building by measuring the size of its shadow. 2. Coatability Window. The stability of the bead was characterized by measuring the vacuum range at the onset
4
4
.7
4
-5
Log Concentration (Moler/Cz)
Figure 4. Static and dynamic surface tensions of poly(ethy1ene oxide) surfactants of the series C12En (n = 3, 6, 8).
of two different coating defects. At a certain coating speed, subatmospheric pressures are required under the lower meniscus to maintain the bead. This pressure, above which one of the edges usually breaks, is known as the minimum vacuum, P,. Once the coating has been stabilized, it is possible to increase the vacuum up to a new level P,, in which fine lines or “ribbing” can be observed on the surface of the coating in the machine direction. Ribbing is the primary manifestation of a flow instability or a three-dimensional flow. The difference between these two extreme pressures, P, - P,, is the vacuum range for ribbing, and it characterizes the coatability window of the system. Practically the onset of ribbing is difficult to detect unless a skillful operator is properly positioned in the path of a reflected light beam from the coated web. All the ribbing studies were performed in the 40’ slide coater. Once ribbing occurs, the underbead pressure can be reduced even further (or the vacuum increased) to a new value, P,,, at which the ribbing lines evolve into obvious streaks of alternate high and low coating thickness visible by transmitted light, or “rivulets”,in the machine direction also. In this case, the vacuum range P , - P, is another commonly used indicator of coating latitude (Steinberg, 1982).
Results and Discussion 1. Surfactants. As previously reported in the literature (Defay and Petre, 1971; Lange, 1967) we found that the behavior of surfactants under dynamic conditions in general is different from that at equilibrium. For instance, the results presented in Figure 4 show both DST and SST readings for the series of poly(ethy1ene oxide) alkyl ethers C12En (n = 3, 6, 8). The equilibrium surface tensions, especially for concentrations above the cmc (critical micelle concentration), increase for increasing numbers of ethylene oxide units. This suggests that the surface pressure decreases with increasing n. On the contrary, an increase of the E proportion reduces the DST readings for a certain age and equimolar solutions. Similar conclusions were
456 Ind. Eng. Chem. Res., Vol. 30, No. 3, 1991
-
Triton X-100 I Water Lodyne I Water
BO 80
70
560 c $c 5 0 f 4 0
a!
4 % 820 10 1-0E-4
0.0
40 1.OE-3
1.OE-2
0.1
1.o
Concentration (%)
Figure 5. Static and dynamic surface tensions at 1 bubble/s for Triton X-100 and Lodyne 107 B.
reported by Schick (Schick, 1962; Shick et al., 1963), who investigated the equilibrium and dynamic surface tensions of 1-dodecanoland 1-octanolsolutions. Finally, for a given surface age, increasing the surfactant concentration lowers the dynamic surface tension of its solutions. Lucassen and Giles (1975) derived the diffusion coefficients of these surfactants from elasticity measurements and concluded that the kinetics of equilibrium attainment before the cmc is diffusion controlled. Most of our measurements were performed at concentrations above the cmc, where the shape and form of the micelles may also influence the dynamic surface tension readings. Since the micellar growth and shape are different for each surfactant and a function of the number of ethylene oxide groups in the molecule (Lindman, 1984),it is conceivable that C12E8, which has small-size micelles, might dissociate faster thah C12E6 and C12E3 and be more effective to reduce the solution DSTs. Similar results were found from the experiments carried out with the pair Lodyne 107 B/Triton X-100 as shown in Figure 5. Like most fluorocarbon surfactants, Lodyne 107 B is highly surface active at equilibrium as reflected by the low SST, but it has very little effect on the fresh surface. Thereby, the DSTs of the low concentration solutions are close to those of the pure solvent. On the contrary, Triton X-100 apparently diffuses faster while the surface is still being developed, reducing its free energy and also the DST. Therefore, while the fluorocarbon surfactants are recommended to promote low static surface tensions, the polyethoxylated ones are more likely to reduce the solution DSTs. In this last case, the addition of polyethoxy units to the structure increases the rate of monomer transfer to the interface and its ability to reduce the dynamic surface tension. 2. One-Layer Coatings: Rivulets. Early in our studies we found that the type and amount of Surfactants used in the coating solutions have a major impact on the vacuum range readings. Moreover, solutions having similar surfactant compositions and surface equilibrium properties may exhibit different coating behavior. For instance, Figure 6 shows vacuum range measurements obtained from a 2 X 2 factorial design experiment in which both the coating speed and the dynamic surface tension of the solutions were varied at constant SST. Different amounts of Zonyl FSN and Triton X-100 were used to adjust the SST and DST values of the coating solutions. A t the high coating speed (2.03 m/s), the vacuum range readings increase as the DSTs of the solutions decrease. However, at the low coating speed (0.51 m/s), the results are the
50 60 Dynamic Surface Tension (dynlcm)
Figure 6. Vacuum range at the onset of rivulets as a function of DSTs from a 2 X 2 factorial experiment. Single-layer 5% gelatin solutions coated at 1.52 m/s.
= a
1.6
0.6
40
1
I
50
60
70
Dynamk Surface Tension (dynkm)
Figure 7. Vacuum range at the onset of rivulets as a function of DSTs from a flow visualization experiment using 5% gelatin solutions. Single layer coated at 1.52 m/s.
opposite. In a similar observation, Steinberg (1982) proposed two different coating mechanisms to explain the fact that the vacuum range as a function of the coating speed reaches a maximum. At low coating speeds, the gap between the web and the coater slide lip is flooded and the contact line is unstable. In this regime, the maximum vacuum at the onset of rivulets increases monotonically with the coating speed. At high coating speeds, the lower meniscus of the bead spans the gap between the top corner of the coater and the web at an upward angle and does not flood the gap. In this case, the contact line is stable and the maximum vacuum range decreases with the coating speed. While the preliminary factorial study was performed in a 23O slide coater, the results were confirmed in a subsequent experiment using a 40° slide coater and a different set of solutions. But in this case, the dynamic surface tensions were adjusted mainly with Triton X-100 and only a small amount of Zonyl FSN. This surfactant was used in quantities enough to bring all the SSTs to the same value. In each run, we measured the vacuum range at constant coating speed (1.5 m/s) and then determined the geometry of the free surface at the same speed while the vacuum level was kept constant (Okin. of HzO). As shown in Figure 7, reducing the DSTs of the solutions from 66 to 42 mN/m increased the vacuum range by a factor of 2, which is in agreement with the results from the previous factorial experiment and those of Beitelshees (1987),who reported similar observations. We speculate that as the Triton X-100 bulk concentration increases, the replenishment of surfactant to the nearly created liquid/air interface is accelerated. In turn,
Ind. Eng. Chem. Res., Vol. 30, No. 3, 1991 457 Table 1. Vacuum Range Measured at the Onset of Rivulets as a Function of the Dynamic Surface Tension (DST) for Gelatin Solutions of Two Different Viscosities" ~ ~ _ _ _ _ _ _ _ vacuum range, in. of solution I.D. H,O DST. dvn/cm viscoaitv. CP 5-40 1.5 40.7 5.1 5-50 0.9 47.2 5.2 5-60 0.5 58.2 5.0 10-40 1.4 42.7 17.9 10-50 0.0 49.1 16.7 10-60 0.0 60.0 17.4 ~
E 1.0.
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.
" " 0.0 -1.0 4.5 0.0 0.5
" ' ' ' ~ 1.0 1.5 2.0 2.5 3.0 3.5
' ' ' 4.0 4.5 5.0 5.5
"
6.0
6.5
7.0
x,mm
Figure 8. Effect of dynamic surface tension on the profile of the solutions down the slide. Single-layer coatings of 5% gelatin solutions with Triton X-100.
40' slide coater; coating speed 1.5 m/s.
s
0.8
s8
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Figure 9. Effect of the curvatures at constant vacuum (0.4in. of H20).Five percent gel solutions coated in single layers.
this reduces the surface tension along the surface, and presumably it improves the coatability window. These conclusions were partially confirmed after examination of the profile of the free surface of the coating solutions, three of which are shown in Figure 8. The profile looks similar to a damped wave with the "valley" located on the upper meniscus of the bead and the "hump" extending on the slide. It has been calculated by Ziller et al. (1975) that, between the initial state of the freshly formed surface at the slot and the bead far from the slot, the surface tension is descreasing. Also from the model, they predict lower surface tensions along the free surface for highly diffusible surfactants. The data from Figure 8 support their conclusions and show that as the surfactant concentration increases the "valley" becomes deeper, due to the low bead surface tension and probably the improved wetting of the tip of the slide. For each solution, the data points obtained with the flow visualization technique were fitted to a circle of radius R and the resulting curvatures (1/R) were correlated with their vacuum range readings. The linear correlation shown in Figure 9 suggests that the curvature of the upper meniscus at constant vacuum is one of the predictors of how large of a vacuum can be applied under the bead before the coating breaks into rivulets. The distance at which the previously mentioned wave or "hump" levels off on the slide is alsola function of the surfactant concentrations, and it may be related to coatability performance. For instance, while the wave of the solution with DST = 40 mN/m damps down near the tip of the slide (Figure 8), it extends on the slide up to 5 mm in the case of the solution with DST = 60 mN/m. In other words, surfactants impact the geometry of the surface beyond the bead, where traditionally the capillary forces have been considered to be important. Additionally, an analysis of the coating process shows that the solution residence times on the slide and at the bead are 0.1 and 0.001 s, respectively, while most of the dynamic surface tensions were measured at 0.1-1 s. The
reason why the dynamic surface tension and the bead curvatures show a reasonable correlation (Figure 9), given the time scale difference, is not obvious and could lead to some speculations. One possibility is that our dynamic surface tension value is a good predictor of the surfactant concentration of the bead upper meniscus and its curvature, regardless of the difference between the measurement time and that to generate the bead. Another possibility is that the curvature values obtained experimentally are strongly influenced by the shape of the fluid profile on the slide, which in turns is controlled by the gradient of dynamic surface tension. In this case, the time scale of the measurement and the solution residence time on the slide are similar. Recent calculations by Schunk (1989) show that the addition of surfactants to the coating solutions affects both the curvature of the upper meniscus and the flow profile on the slide. Zeldes (1985), who compared the effect of Zonyl FSN vs saponin on two-layer coatings, concluded that the use of the fluorocarbon surfactant is advantageous to reduce the static surface tension and therefore to promote increased vacuum range windows. Although our results partially support his observations, the interpretation of the data disclosed in Zeldes's patent is difficult given their qualitative nature. An immediate application of the results reported in Figure 8 is modeling of fluid flow. Particularly in the case of heterogeneous mixtures, it is necessary to include the curvature of the meniscus as well as the gradient of surface tension along the interface as part of the boundary conditions. Undoubtedly, both variables in conjunction with the fluid properties determine the geometry of the liquid layer on the inclined plane. Levich (1941a,b) showed theoretically that the spreading of a surface-active film over the surface of a viscous liquid results in a radical alteration of the boundary conditions at the liquid-gas interface. The gradient of surface tension on the slide may also be critical to the onset of rivulets. Schweizer (1988),using a sophisticated flow visualization technique, showed a clear example in which the "hump" of a long wave not only extends far on the slide but is the place where under certain conditions the liquid may detach from the metal surface originating vortices. It could be speculated that if these vortices are necessary for rivulets to occur, by reducing the dynamic surface tension, the surface forces on the slide can be reduced and the surface smoothed. Under this condition a higher underbead vacuum would be required to detach the liquid from the surface, generage vortices under the "humpn, and induce vacuum streaks. In order to further investigate the same variables at higher viscosities, the gelatin concentration of the coating solutions was increased from 5% to 10%. As shown in Table I, the trend is essentially the same and the solution with low dynamic surface tension has a wider coating range than that with the higher dynamic surface tension.
_
458 Ind. Eng. Chem. Res., Vol. 30, No. 3, 1991 Table 11. Vacuum Range Determined at the Onset of Ribbing and Surface Dynamic Properties at Various Concentrations of Triton X~1000 vacuum Triton DST, dyn/cm (DSTh range, in. of X-100 concn, run no. 5% SST, dyn/cm 0.5 bubbles/s 2 bubbles/s dyn/cm 14,dyn/cm viscosity, CP H20 0.1 22 4.56 0.4 1 0 50.9 66.1 66.0 24 4.76 1.9 0.1 2 1E-6b 49.4 65.8 65.9 4.81 2.5 0.2 25 65.7 65.9 3 5E-6 49.2 2.4 0.1 25 4.76 65.8 50.8 65.7 4 1E-6 2.4 0.1 13 4.56 5 4E-5 50.6 65.6 65.7 4.84 7 0.1 0.9 65.7 50.6 65.6 6 1E-4 4.81 0.4 5 1.3 65.5 46.8 64.2 7 4E-4 1.5 4.76 0.4 5 63.6 65.1 8 1E-3 42.5 3.9 4.81 0.1 5 9 1E-2 34.1 55.4 59.3 4.81 5 3.5 41.7 45.2 0.0 10 1E-1 32.3 4.56 0.1 22 0.4 11 0 50.9 66.1 66.0 24 4.76 65.8 65.9 0.1 0.3 12 1E-6 49.4 4.81 2.3 0.2 25 65.7 65.9 13 5E-6 49.2 4.76 2.1 0.1 25 65.7 65.8 14 1E-5 50.8 13 4.56 50.6 65.6 65.7 0.1 1.8 15 4E-5 4.84 0.1 7 16 1E-4 50.6 65.6 65.7 1.8 4.81 1.3 1.0 5 46.8 64.2 65.5 17 4E-4 4.76 1.5 0.4 5 63.6 65.1 18 1E-3 42.5 4.81 5 3.9 0.5 55.4 59.3 19 1E-2 34.1 4.81 3.5 5 41.7 45.2 0.6 20 1E-1 32.3 '40' slide coater, coating speed 1.5 m/s. *lE-6 represents 1 X lo4, etc.
}
:
Ribbing. It has been noticed that occasionally as the bulk surfactant concentration increases and the DST of the solution approaches the asymptotic lowest value (e.g., 41-42 mN/m for Triton X-loo), the vacuum range reaches a maximum and then decreases. In other words, in spite of the low bead surface tension, these findings suggest that there are other surface properties which seem to affect the coating performance. Ribbing is the prelude to the formation of vacuum streaks, and although it is very imperceptible, this defect is extremely sensitive to the vacuum level. Therefore, we used ribbing to further explore our preliminary observations. We coated 10 different gelatin ( 5 % ) solutions with increasing amounta of Triton X-100 and properties described in Table 11. The appearance of clusters of lines on the coated surface was chosen as the vacuum level at which ribbing takes place. The results of two different experiments are also shown in Table 11. In this protocol, we also included the difference of DSTs measured at 2 and 0.5 s, respectively (called (DST),), and the "apparent" elastic modulus. The first parameter, which is proportional to the time derivative of the dynamic surface tension, is a measure of how much the diffusion of the Triton X-100 contributes to the relaxation of a freshly formed surface. The "apparent" elasticity modulus is the magnitude of the surface tension change that follows stretching or compression of any surface. The importance of this last parameter is discussed by Jlang et al. (1990). Both the results from Table I1 and Figure 10 confirm that the chemical composition of the surface modifies the onset of ribbing. As expected, the dynamic and static surface tensions of the solutions monotonically decrease as the surfactant concentration increases. At low surfactant concentrations, the (DST), values are small and the dynamic properties of the interface are essentially those of the pure gelatin. Most solutions exhibit a considerable resistance to ribbing and the vacuum ranges reached up to 2.4 in. of water. The exception was the solution with concentration of lo4 wt %, in which the unstable edges rather than the sensitivity to ribbing prevented it from having a larger vacuum range than 1.1 in. of water. As the Triton X-100 concentration increases, the surfactant diffuses toward the air-liquid interface at a faster
:
2.3
22
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=c la
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P
#
9 r4
Oa
0.3 1.OE6
1.OE-6
1.OE4
i
1.OE4
Trlton X-100 Log Concmtmtion(%)
Figure 10. Gibbe elasticities and vacuum ranges at onset of ribbing as a function of Triton X-100 concentrations in 5% gelatin solutions. Solution coated at 1.52 m/s in a 40° slide coater.
rate than the gelatin (high (DST), values). The surface elasticity IEI is low and essentially determined by the surfactant rather than the gelatin. At this point, the bead seems to be less resistant to stretching and ribbing occurs at lower vacuum. The vacuum range results (VR) from Table I1 were correlated to the values of SST, DST, (DST)*and [El using nonlinear regression analysis and fitted to an exponential model. In particular, the (DST), readings are best fitted by (3), which explains 80% of the variability observed in the vacuum range. VR = 0.17[(DST),]-1~6exp(-2.69[(DST), - 0.28I2/(DST),) (3) Also, there is an inverse relationship between the Gibbs elasticity modulus IEI and the time derivative of the dynamic surface tension (DST),. This was confiimed by the correlation shown in (4), which suggesta that the elasticity IEl = 0.899 + 7.822/(DST), - 0.6177/[(DST)J2 (4) of the coating solutions is intimately related to the time derivative of the dynamic surface tension, (DST),. Perhaps, a more meaningful correlation may have been obtained if both measurements had been performed at the same frequency. In summary, we speculate that, in dealing with gelatin coatings, the mechanisms that lead to ribbing and rivulets might not be the same. The results reported so far suggest
Ind. Eng. Chem. Res., Vol. 30, No. 3, 1991 459
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c
Figure 11. Two-layer coating solutions flowing down the slide. The overcoat (shaded) has a higher DST than the underlayer and promotes dewetting and receding edge defects.
that the surface properties of the coating solutions impact the onset of these two defects in a different way. The resistance to ribbing decreases at surfactant concentrations equivalent to the cmc or higher, and it is a function of the (DST), or the dilational elasticity. Once ribbing occurs, the coating breaks into rivulets either immediately or at higher vacuum levels depending upon the surfactant package and chemical composition of the solution. During coating of gelatin solutions that have poly(ethy1ene oxide) or fluorinatedsurfactants,the vacuum level can be further increased before the rivulets become visible. Also these solutions exhibit higher vacuum ranges at lower dynamic surface tension up to a certain surfactant concentration in which the vacuum range begins to decrease. The addition of large quantities of alcohol into the coating solutions induces formation of ribbing and rivulets at very low vacuum levels, and both defects seem to occur almost simultaneously (Valentini, 1987). 3. Two-Layer Coatings: Rivulets. In the case of two-layer coatings, wettability on the slide is an additional variable to be considered, especially when a surfactant is used in the underlayer. Therefore, the ratio of dynamic as well as static surface tensions between the two layers should be considered. A factorial experiment to investigate the effect of both ratios on coatability was performed with 5% gelatin solutions in both the top and bottom layers. The flows were adjusted so that the final gelatin coating weight was equivalent to that for the single-layer factorial experiment. Both the DSTs and SSTs of the solutions were adjusted with Triton X-100, Standapol ES-3, Zonyl FSN, and Lodyne 107 B. One of the most interesting findings from this experiment is that, above a certain ratio of upper to lower layer DST (1.2-1.3), dewetting of the bottom layer occurs and the edges of the top solution recede toward the center of the slide as shown in Figure 11. This phenomenon, which is independent of the ratio of SSTs of the solutions, is clear evidence of the dynamic behavior of surfactants especially when dealing with more than one layer of coatings. When dewetting occurs, attempts to manually spread the overcoat solution on the slide show that there is a capillary force, possibly generated at the edges, that reduces the area and free energy of the top layer. This process invariably leads to the exposure of the underlayer surface, as we found by using different color dyes in each layer. In other words, although there is not a true liquid/liquid interface between the two solutions, the system behaves as such. From this experiment we also concluded that the SSTs have little impact on vacuum range, which, provided that
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High Undercoat Dynamic Surface Tension Dynamic Surface Tension Effects %layer
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Figure 13. Solution profiles down the slide for a two-layer coating as a function of DSTs. Underlayers with high DSTs.
other variables are constant, is controlled by the ratio of DSTs (Figure 12). This finding may revolutionize our conventional view that the static surface tension of the top layer ought to be smaller than that of the bottom layer to ensure a good coating. The ratio of dynamic surface tensions between the two layers could be the dominating factor. The geometry of the bead was studied by coating gelatin solutions, which contained Triton X-100 and Zonyl FSN in order to maintain the same protocol as for the singlelayer study. However, we only varied the surfactant concentration of the top layer and used two different underlayers as shown in Table 111. The bead was profiled as reported before, and the profiles are shown in Figures 13 and 14, respectively. It is worth noting, however, that these figures need to have the same x-y scales to calculate the curvatures. Table I11 shows that the curvatures obtained with both the high and low DST underlayers are not significantly different. Moreover, this is the case when there is a large surfactant gradient between the upper and lower layers like in the 3B/low DST run. In this example, although some surfactant diffusion in the upward direction occurs, it is not significant enough to affect the concentration of the air-liquid interface and thereby the bead curvature. On the contrary, the vacuum range readings in both sets are different. The vacuum ranges from the high DST underlayer runs are consistently higher than those from
460 Ind. Eng. Chem. Res., Vol. 30, No. 3, 1991 Table 111. Vacuum Range Measured at the Onset of Rivulets and Curvature Determined at Constant Vacuum Level (4 in. of H 2 0 ) for Two-Layer Coatings vacuum range, curvature, layer solution ID SST, dyn/cm DST, dyn/cm viscosity, CP surfactant composn, % in. of H20 mm-' High DST UnderlayeP top 3A 27.0 62.4 4.5 3.0 X 5-3 Triton X-100 0.6 2.7 4.7 x Zonyl FSN 3.0 X Triton X-100 1.0 4.4 49.9 4.6 3B 27.2 9.0 X Triton X-100 1.o 4.4 43.0 4.5 9c 27.0 1.8 X lo-' Triton X-100 0.9 4.4 41.6 4.6 18D 27.8 3.6 X lo-' Triton X-100 1.0 8.0 41.0 4.6 30E 27.8 58.3 4.3 1.0 X Triton X-100 B 31.5 bottom top
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the other set, in agreement with our conclusions from the factorial experiment described in Figure 12. On run 3B/low DST, for instance, we were able to establish the coating bead and measure its curvature but the vacuum range reading was negligible. Possibly the wettability problems may not have been as severe as those seen on run 3A/low DST; nevertheless, the solutions did not exhibit any coating latitude due to the destabilizing effect of the high DST ratio. Analysis of the data from the underbead profile indicates that the position of the underbead varies from solution to solution without any specific pattern, although it is a function of the underbead pressure (Thomas, 1990). In summary, large curvatures or low surface tensions at the bead do not always correlate with a wide operability window, as we have reported on single-layer coatings. In this case the DST of the underlayer must also be considered, and in general the higher this value the wider the operating window. This is particularly relevant to the photographic industry where chemicals that are not strictly wetting agents but reduce the solution DST may be used as additives in the lowermost layers with unexpected detrimental results on the coatability. Similarly, vegetable oil mixtures, which are used for fundamental coating studies, may contain proteins that affect the dynamic surface properties. Ribbing. The solutions used in both the top and bottom layers were made in 5% gelatin as before and coated at 1.52 m/s. Therefore their flows were half of those re-
Figure 15. Vacuum range at onset of ribbing vs concentration of Triton X-100 in the bottom layer. The Gibbs elasticity of the top layer is 24 mN/m.
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Figure 16. Vacuum range at onset of ribbing vs concentration of Triton X-100 in the bottom layer. The Gibbs elasticity of the top layer is 5 mN/m.
ported in the single-layer ribbing experiment. Also the concentrations of Triton X-100 and the properties of the bottom layer were the same as reported in Table 11. The two solutions used in the top layer, which also were 5% gelatin, had their (DST), readings adjusted to 0.1 and 3.5 mN/m, which correspond to surface elasticities of 2+24 and 3-5 mN/m, respectively. As explained before, by using this protocol, the dynamic behavior of the upper surface is controlled either by the gelatin or by the surfactant. Otherwise the experiment was conducted as for the single-layer study and the results for all runs with each
Ind. Eng. Chem. Res., Vol. 30, No. 3, 1991 461 overcoat solution are shown in Figures 15 and 16, respectively. When the overcoat ( D ! J ~ T is)3.5 ~ mN/m, or its elasticity is low, the vacuum ranges are 0.8-0.9 in. of water and independent of the composition of the underlayer (Figure 15). Similarly, when the (DST), of the upper layer is 0.1 mN/m and essentially determined by the gelatin concentration, the results seem to be a function of the surfactant composition of the underlayer. In this case, the vacuum range readings start a t a constant value of 1.2-1.3 in. of water and steadily decrease as the Triton X-100concentration of the underlayer increases. In other words, as soon as the elasticity of the bottom layer becomes smaller than that of the upper layer, so does the coatability window. Also we observed for this surfactant package that when the underlayer surfactant concentration is larger than lo%, dewetting occurs due to the rapidly increasing ratio of upper to lower layer DSTs. In summary, we speculate that in the case of two-layer coatings the overall resistance to ribbing seems to be controlled by the layer with the highest (DST), or the lowest surface elasticity. The analogy to this interpretation is a parallel circuit in which the lowest resistance branch determines the overall current through the system. Very little information is available regarding this topic, but it has been recently suggested by Hempt et al. (1985) that the rheology of the surface may be responsible for disturbances in the coating process and our data strongly support that view. Conclusions The dynamic surface tension is an appropriate parameter to characterize the surface energy of a nonequilibrium air-liquid interface as found in slide coating. In singlelayer gelatin coatings, the solution DSTs measured at different ages in the range of 0.2-2 s correlate with the vacuum range readings at the onset of rivulets. Also the geometry of the upper free surface, which is a function of the solution DSTs, correlates with the vacuum ranges. In multilayer coatings, the ratio of DSTs between the top and bottom layer is significant. It' seems to predict the degree of wettability of the solutions on the slide and the coating performance. Meanwhile, the ratio of SSTs has little impact on coatability although it affects the quality of the coated film. In coating more than one layer, by and large the curvature of the upper meniscus is determined by the surfactant concentration of the top layer. And, low surface tensions at the bead do not always result in a wide coating latitude. The time derivative of the dynamic surface tensions as above reported is a good index to predict ribbing in both single- and two-layer coatings. Ribbing seems to be prevalent at high (DST), or low elasticity, both of which occur at high surfactant concentrations. This defect, which in general is the primary evidence of a flow disturbance, may occur prior to or at the onset of rivulets depending upon the formulation. This is an area that should be further studied, since this defect seems to be a function of the molecular structure of the surface. Different surfactant combinations can be used to adjust the dynamic and static surface tensions of coating solutions. In general, nonionic Surfactants with ethylene oxide
groups diffuse very readily to the surface and reduce the dynamic surface tensions of nonequilibrium surfaces. Fluorinated surfactants, on the contrary, are more effective at equilibrium and ideal to reduce the static surface tensions. Finally, the flow visualization technique used in this undertaking has proved to be extremely valuable to study the geometry of the flow on the slide in both single-layer and multilayer coatings. Acknowledgment This work is financially supported by E. I. du Pont de Nemours and Co. We appreciate the suggestions offered by Drs. R. I. Hirshburg, C. P. Beitelshees, and N. Steinberg. Also, we acknowledge Mr. J. T. Chandler for the excellent lab work. Literature Cited Adamson, A. W. Physical Chemistry of Surfaces; Wiley-Interscience: New York, 1982; pp 23-24. Beitelshees, C. P. Personal Communication, E. I. Du Pont de Nemours, 1987. Defay, R.; Petre, G. Surface and Colloid Science; Matijevic, E., Ed.; Wiley-Interscience: New York, 1971; Vol. 3, pp 27-81. Deryagin, B. M.; Levi, V. B. Film Coating Theory (translation of 1959 Russian edition); Focal: London, 1964. Galehouse, D.; Colt, J. Simplified Analytical Solutions of the Free Surfaces Associated with Slide Coating. Presented at the AIChE Symposium on Coating Fundamentals, Atlanta, 1984; paper 16c. Hempt, C.; Lunkenheimer, K.; Miller, R. On the Experimental Determination of the Dilational Elasticity and the Exchange of Matter of Mixed Gelatin Surfactant Adsorption Layers. 2.Phys. Chem. (Leipzg) 1985,266, 713-720. Hens, J.; Boiy, L. Operation of the Bead of a Pre-metered Coating Device. Chem. Eng. Sci. 1986,41, 1827-1831. Jiang, T. S.; Lee, H. 0.;Liu, Y.;Yen, S. C.; Valentini, J. E.; Thomas, W. R.; Sevenhuysen, P. The Essence of Surface Dilatational M e dulus in Thin Film Coating. Presented at the AIChE Spring Meeting, Orlando, FL, March 18-22, 1990. Lange, H.Nonionic Surfactants; Schick, M. J., Ed.; Marcel Dekker: New York, 1967; pp 443-475. Levich, V. The Damping of Waves by Surface-Active Substances I. Acta Physicochim. URSS 1941a,14, 307-320. Levich, V. The Damping of Waves by Surface-ActiveSubstances 11. Acta Physicochim. URSS 1941b, 14,321-328. Lindman, B. Surfactants; Tadros, Th. F., Ed.; Academic Press: 1984, pp 82-109. Lucassen, J.; Giles, D. J. Chem. Soc., Faraday. Trans. 1 1975, 71, 217. Schick, M. J. J. Colloid Sci. 1963, 18, 378. Schick, M. J.; Atlas, S. M.; Eirich, F. R. J. Phys. Chem. 1962, 66, 1326. Schunk, P. R. Polymer and Surfactant Additives in Coating and Related Flows. PbD. Dissertation, University of Minnesota, 1989. Schweizer, P. M. J. Fluid Mech. 1988, 285-302. Steinberg, N. PPRD 82-319, E. I. du Pont de Nemours Report, 1982. Thomas, W. R. IMG-89-B-9, E. I. du Pont de Nemours, 1990. Valentini, J. E. Notebook 52928, E. I. du Pont de Nemours, 1987; p 114. Zeldes, M. A. Coating Process Employs Surfactants. US. Patent 4508764, 1985. Ziller, M.; Miller, R.; Kretzschmar, G. A Model of the Adsorption Kinetics for a Flowing Liquid Layer of a Surfactant Solution. 2. Phys. Chem. (Leipzig) 1985, 266, 721-730.
Received for review May 16, 1990 Reoised manuscript received September 10, 1990 Accepted September 25, 1990
