Flow in tensioned-web-over-slot die coating: Effect of die lip design

Tensioned-web-over-slot die (TWOSD) coating is one of the most successful high-speed liquid coating process. It deploys elastohydrodynamic interaction to control the distance between the moving substrate and the coating die lip surface in order to be able to coat an ultra-thin liquid layer. However, flow instabilities that come from the gas–liquid interface and microvortices inside the flow may lead to coating defects. Therefore, the range of operating conditions of uniform coating is limited. The operating window of the process is a strong function of the geometry of the die. However, this relationship and, in general, the fundamental mechanisms of the elastohydrodynamic interaction are not known. In this study, we analyze TWOSD coating flow by solving the Navier–Stokes equation coupled with thin cylindrical shell equation using the finite element method. The boundaries that define the regions in the parameter space of uniform coating are automatically computed by a direct tracking method, based on multi-parameter continuation. The results show that the coating window of the process can be enlarged by designing the appropriate lip geometry.     

Two-layer tensioned-web-over-slot die coating: Effect of die lip geometry

Tensioned-web-over-slot die coating (TWOSD) takes advantage of the elastohydrodynamic interaction between the curved web under tension and the coating liquid to sustain a very small coating gap that enables ultra thin coating at relatively high speed. When the product requires two liquid layers, dual slot TWOSD coating can be used to coat those layers simultaneously. In this case, the liquid pressure along the coating bead sets not only the web configuration and meniscus locations but also the interlayer separation point. An easy way to control the pressure distribution is through the die lip geometry.Here, we analyze the effect of four different die lip geometric parameters, e.g. the downstream lip radius, the mid lip radius, the downstream lip offset and the mid lip apex point, on the coating window of the dual slot TWOSD coating. Using the model proposed by Nam and Carvalho (2009c) and a direct tracking of flow features, the boundaries of the vortex-free operating window, area inside the parameter spaces that ensure a uniform coating without vortex inside the flow, were obtained and compared for each die lip configuration.We found that the mid lip radius is one of the important parameters to control the location of the upstream meniscus. Also the location of the interlayer separation point can be controlled by the lip offset and location of the apex point.     

Flow visualization and operating limits of tensioned-web-over slot die coating process

Tensioned-web-over-slot die (TWOSD) coating is one of the most successful high-speed liquid coating process. It deploys elastohydrodynamic interaction to control the distance between the moving substrate and the coating die lip surface in order to be able to coat an ultra-thin liquid layer. However, flow instabilities that come from the gas–liquid interface and micro vortices inside the flow may lead to coating defects. Therefore, the range of operating conditions of uniform coating is limited.Nam and Carvalho [1] proposed a two-dimensional computational model to examine the role of the elastohydrodynamic interaction between the liquid and flexible substrate in tensioned-web-over-slot die (TWOSD) coating process, with the goal of predicting the operability limits of the process.Here, we use flow visualization on a laboratory-scale TWOSD coating apparatus to study limit flow states which are related to various flow instabilities and appearance of vortex in the flow. The visualizations show the progression of flow states beyond critical flow parameters which cannot be predicted by the model as three-dimensional features of these limit flow states. Furthermore, the critical flow rates, that define the operability window of the process, were determined experimentally and were used to validate the computational model.     

Operability limits of slide coating

Slide coating is one of the pre-metered methods used for high precision single and multilayer coatings. The thickness of each liquid layers is set by the flow rate and web speed only and it is independent of other process parameters. The uniformity of the deposited layer, however, is affected by the operating conditions. In the design of coating processes, it is crucial to know the set of conditions at which the deposited layer is adequately uniform, i.e. to define the operability window of the process. We developed a theoretical model of slide coating flow by solving the full two-dimensional Navier–Stokes equations and used it to uncover the mechanisms of coating bead breakdown at low vacuum, high vacuum, and low flow limits. With full understanding of the bead breakup processes, we then constructed a theoretical coating window as a function of coating thickness, web speed, and applied vacuum. A simple stability criterion was used to predict the onset of ribbing instability and deployed to add the onset of ribbing limit inside the coating window.     

Effect of sloped die lip geometry on the operability window in slot coating flows using viscocapillary and two-dimensional models

As an indicator for determining the operability window in slot coating flow, the viscocapillary model considering various configurations of upstream and downstream slot die lips was tested and compared with Navier–Stokes two-dimensional model. Bead pressure and sloped lip angle conditions for uniform coating operation demarcated from leaking and bead break-up defects were quantitatively predicted from the position of upstream meniscus from both models. By comparing the results, it is confirmed that the viscocapillary model for many kinds of sloped die lips could predict the operability window accurately. It is also found that there exists vortex or recirculation regimes inside upstream and downstream coating bead regions, depending on the angles of sloped die lips, even for the stable coating flow. The flow control by die lip structure will be usefully applied to design the strategy for the reliable and optimal coating process, including vortex-free windows.     

Response of slot coating flows to periodic disturbances

Slot coating is a common method in the manufacture of a wide variety of products. It belongs to a class of coating method known as premetered coating: in a steady-state operation, the thickness of the coated liquid layer is set by the flow rate fed to the die and the speed of the substrate moving past, and is independent of other process variables. Thus premetered methods are ideal for high precision coating. However, even the best designed slot coating operations are subjected to small oscillations on the process conditions, such as flow rate, vacuum pressure and gap fluctuations. These oscillation may lead to unacceptable variation on the thickness of the deposited liquid layer. The effect of process condition disturbances on the coated layer has to be minimized to assure a wet thickness as uniform as possible.The effect of an imposed periodic perturbation on the liquid flow rate or on the gap clearance in the coated layer thickness is explored in this work by computer-aided analysis. The amplitude of the thickness variation is determined at different process conditions and die configurations by solving the transient, two-dimensional, viscous free surface liquid flow in the coating bead. The system of equations, with appropriate boundary conditions, was solved by the Galerkin/finite element method, and an implicit time integration. The results show the response as a function of the imposed perturbation frequency and of the die geometry. They indicate that the die geometry may be optimized in order to minimize the film thickness oscillation of a slot coating operation.     

Start‐up of slot die coating

A flow visualization technique was employed to observe the start‐up of slot die coating. The effects of five variables, i.e., prewetting on the die surface, fluid viscosity, slot gap, coating gap, and die lip length on the start‐up time were investigated. Prewetting on the die surface can effectively reduce the start‐up time. Any variable that enlarges the steady‐state coating bead would increase the start‐up time. Therefore, increasing the fluid viscosity, coating gap, slot gap and decreasing the die lip length can be helpful in reducing the start‐up time. It was found that there exist four distinct modes for the establishment of steady‐state coating bead. The four distinct modes can be distinguished by a Reynolds number, which is defined as the ratio of the inertial force of the coating solution impinging on the moving web to the viscous force needed to pull the coating solution on the web. Comparison of the experimental observation with the theoretical prediction based on the commercial package Flow3D was also performed; the four modes can be found in the numerical simulations, the start‐up time computed to reach steady state is shorter. POLYM. ENG. SCI., 2009. © 2009 Society of Plastics Engineers     

A macroscopic mathematical model for tensioned‐web slot coating

A mathematical model was developed to predict the performance of tensioned‐web slot coating (TWSC), in particular, the minimum wet thickness. The model was based on the lubrication approximation for the coating solution flow and a simplified membrane theory for the moving web. The theoretical predictions compared reasonably well with available experimental data. The effects of fluid viscosity, web tension, coating speed, and wrapping angle on the performance of TWSC were evaluated. An example was presented to illustrate how die lip design could be varied to improve its performance. POLYM. ENG. SCI., 2008. © 2007 Society of Plastics Engineers     

Trailing edge formation during slot coating of rectangular patches

Different products, such as adhesives, pharmaceutical patches, batteries, and fuel cell membranes, require coating discrete patches onto moving substrates. For coating rectangular patches, intermittent slot die coating is the preferred method. The patches can be obtained by rapidly starting and stopping the flow out of the coating die. Controlling the flow start-up and shutdown to produce sharp and uniform leading and trailing edges of each patch is challenging. Different ways to control the liquid feeding are used to optimize the process. Even if the start-up and shutdown of the feeding system are well designed, the transient flow in the coating bead contributes to the formation of nonuniform leading and trailing edges of coated patches. In this work, we analyze how the operating conditions, die geometry, and liquid properties affect the coating bead breakup process and the trailing edge configuration. The process is directly related to the contact line dynamics. The results show that the uniformity of the trailing edge of each coated patch can be improved by changing the die shoulder angle and wetting characteristics of the die surface.     

A review of the operating limits in slot die coating processes

Slot die coating is a pre‐metered process commonly used for producing thin and uniform films. It is an important film fabrication method for applications where precise coating is required. A major concern in slot die coating processes is how to determine the operating limits to set the appropriate range of operating parameters, including coating speed, flow rate, vacuum pressure, coating gap, liquid viscosity and surface tension, etc. Operating limits directly determine the effectiveness and efficiency of the process. In this article, the current state of academic research on operating limits in slot die coating processes is reviewed. Specifically, the theories, mechanisms, and empirical conclusions related to the limits on vacuum pressure, the low‐flow limit, the limit of wet thickness for zero‐vacuum‐pressure cases, the limit of dynamic wetting failure, and the limits of coating speed for a specific flow rate are reviewed. The article concludes with some recommendations for future work. © 2016 American Institute of Chemical Engineers AIChE J, 62: 2508–2524, 2016     

Transient response of two‐layer slot coating flows to periodic disturbances

Coating uniformity requirement is becoming more severe as new products come into the market. Coating processes have to be designed not only based on the steady‐state operation but also taking into account how the flow responds to ongoing disturbances on process conditions. These disturbances may lead to thickness variation on the deposited liquid layers that may be unacceptable for product performance. This study extends available transient analysis of single‐layer slot coating to determine the amplitude of the oscillation of each individual coated layer in two‐layer slot coating process in response to small periodic perturbation on different operating parameters. The predictions were obtained by solving the complete transient Navier–Stokes equations for free surface flows. The results show the most dangerous perturbations and how the deposited film thickness variations of each layer can be minimized by changing the geometry of the die lip and liquid viscosities. © 2015 American Institute of Chemical Engineers AIChE J, 61: 1699–1707, 2015     

Minimum wet thickness for double‐layer slide‐slot coating of poly(vinyl‐alcohol) solutions

A combined slide‐slot coating die, with the slide coating on top, was designed and built to investigate the double‐layer coating of poly(vinyl‐alcohol) solutions. The operating coating windows were examined as a function of flow rates and viscosities of the two coating layers. The top coating layer could be made much thinner as compared to the double‐layer coating so long as a stable thin film could be formed on the slide. A minimum wet thickness of the top layer was found to be as thin as 5 μm or less. A large viscosity ratio of the two layer solutions appears to be helpful in expanding the coating windows. Addition of a small quantity of polymer, such as carboxymethyl cellulose, can further enhance the coating speed and reduce the top layer thickness. A flow visualization technique was employed to observe the coating bead region. It was found to be easier to change the flow direction in the slide‐slot coating die than the double‐layer slot die, resulting in a more stable coating flow and much thinner top layer. POLYM. ENG. SCI., 45:1590–1599, 2005. © 2005 Society of Plastics Engineers.     

Effect of upstream meniscus shape on dynamic wetting and operating limits of Newtonian coating liquids in slot coating bead flows

The coating bead flow and operability window for Newtonian coating liquids are theoretically and experimentally investigated in the slot coating process, with a focus on the shape of the upstream meniscus and contact angles. From the flow visualization in the coating bead region, the contact angles of the upstream meniscus were measured by changing the flow rate and web speed under uniform operating conditions. It was confirmed that the dynamic contact angle is closely related to the capillary number in this process, based on the Hoffman–Voinov–Tanner model. The viscocapillary and two-dimensional Navier–Stokes models using the experimentally observed contact angles accurately predicted the coating bead dynamics and operability windows for two Newtonian liquids.     

Model for the outer cavity of a dual‐cavity die with parameters determined by two‐dimensional finite‐element analysis

A coating die forms liquid layers of uniform thickness for application to a substrate. In a dual‐cavity coating die an outer cavity and slot improves flow distribution from an inner cavity and slot. A model for axial flow in the outer cavity must consider the ever‐present cross flow. A 1‐D equation for the pressure gradient for a power‐law liquid is obtained as a small departure from a uniform flow distribution and no axial flow. The equation contains a shape factor dependent on cavity shape, Reynolds number, and power‐law index. The shape factor for five triangular cavity shapes is obtained by finite‐element analysis and correlated for application to die design up to the onset of flow recirculation which arises at the junction of the cavity and outer slot. The performance of the combined cavity and slot is considered and the most effective design determined. © 2017 American Institute of Chemical Engineers AIChE J, 64: 708–716, 2018     

Analysis of slot coating flow under tilted die

Slot coating is a high precision coating method, where the film thickness is controlled by the flow rate fed to the die and the production speed. The range of desirable operating conditions for uniform coating is limited by the shape and locations of upstream and downstream menisci, which are controlled by the pressure gradient within the coating flow. The gradient can be controlled by the shape and orientation of the slot coating die, that is, die configuration. Here, the tilted die, the so‐called angle‐of‐attack configuration is considered. The configuration is similar to underbite and overbite configurations, but it has a sloped die lip due to tilting. Coating flows with such a configuration are examined by computer‐aided analysis using the Galerkin/finite element method. Using steady‐state analysis, the effect of the angle of attack on the upstream meniscus location is discussed. In transient analysis, the amplitude of the thickness variation is predicted under different types of disturbances, namely flow rate and gap oscillations. The analysis shows that die lip configurations affect the thickness uniformity under periodic disturbances. The effect of die tilting can be similar to or different from the underbite/overbite configurations, depending on the type of oscillation. During the analysis, the flow rate apportioning inside the coating flow and decomposing thickness variations into two separating oscillations are useful in understanding the results is found. © 2015 American Institute of Chemical Engineers AIChE J, 61: 1745–1758, 2015     

Slot die coating window for a uniform fuel cell ink dispersion

The continuous roll-to-roll slot die coating technique has shown great potential for fuel cell electrode fabrication. It is essential to determine the particulate coating window to obtain a defect-free film of uniform thickness and uniform particle dispersion. For this dual-purpose, an additional upper operating limit has been proposed via a “flow field analysis scheme” that combines analysis and simulation. In this analysis, the fundamentals of flow pattern transition (Poiseuille–Couette–bubbly flow) behind coating limits are clarified. The Couette flow is advantageous for uniform shear rate and dispersion. Furthermore, phase-field simulations systematically investigate the effect of fluid and geometrical parameters and quantitatively present the flow limit with explicit expression. Results reveal that the slope of the upper limit is inversely correlated with shear-thinning index n while proportional to the coating gap H. Combining the bubble entrainment boundary, lower n and H are favorable for a larger particulate coating window.     

Process limits in two-layer reverse roll transfer

Reverse roll coating in which a thin single layer of liquid is applied onto a substrate has been used in industry for decades and has been extensively analyzed in the literature. Modern coatings, however, are often composed of more than one layer to improve the product performance and to reduce the manufacturing cost. Premetered methods such as slot, slide, and curtain coatings are typically used to produce such multilayer coatings. If the caliper of the substrate to be coated is not constant, then the coating gap and consequently the final film thickness deposited on the web will also be nonuniform. In this study, we focused on the use of reverse roll technique with slot die liquid delivery system to produce a uniform thin two-layer coating. The use of this coating technique to produce such a coating has not been previously explored. The liquid film surface as it is transferred from a rigid steel roll to a deformable urethane-covered roll was visualized to find out how the uniformity of the two-layer coating is affected by the speed ratio between two rolls, layers’ wet thicknesses, and liquid viscosities. The effect of these parameters on the ribbing frequency and amplitude was also investigated. The results show that in the two-layer coating, as in the single layer reverse transfer, there is a critical web speed above which ribbing occurs. The critical speed is determined by the bottom layer viscosity.     

Numerical analysis for predicting the operability window of slot-die coating onto porous media

The ability to coat porous media is critical for forming composite functional thin films. A major technical concern for accurately predicting this process is that the flow of the coating bead and the penetration process must be considered. These phenomena strongly influence each other. Therefore, both the flow into porous media and the coating-bead flow should be simultaneously treated. In this study, the target is a high-productivity coating system based on a roll-to-roll process using a slot die. Slot-die coating is a premetered, precision coating method. We investigated the coating of porous media to estimate the practical operability window and the penetration depth using two-dimensional numerical analysis. For this purpose, both the coating-bead pressure and the capillary pressure were considered as driving forces of penetration. Moreover, the curvature of the backup roll opposite the slot die was also taken into account to achieve an accurate estimation. We demonstrate that the penetration depth and operability window for defect-free coatings can be well estimated and that the results are consistent with experimental results.     

Frequency response analysis of slot coating

Frequency responses to the slot die coating process is analyzed using empirical modal analysis to predict the effects of periodic process disturbances such as gap oscillation and variations in vacuum pressure, web velocity, and flow rate. A type of empirical modal analysis known as an experimental modal approach was used, and an oscillator basis model was assumed by using a linearized governing equation, and the coefficient of the basis model was determined by curve‐fitting. By completing the process, we were able to decompose each mode, during which process it was found that the modes are of two types: a squeeze mode related to viscous characteristics and sinuous modes that are identical to capillary waves. Observation of the meniscus shapes of each mode revealed, in the third mode near the lip edge, significant fluctuations that can induce other coating defects. © 2010 American Institute of Chemical Engineers AIChE J, 2010     

Slot coating flows of non‐colloidal particle suspensions

Slot coating is used in the manufacturing of functional films, which rely on specific particle microstructure to achieve the desired performance. Final structure on the coated film is strongly dependent on the suspension flow during the deposition of the coating liquid and on the subsequent drying process. Fundamental understanding on how particles are distributed in the coated layer enables optimization of the process and quality of the produced films. The complex coating flow leads to shear‐induced particle migration and non‐uniform particle distribution. We study slot coating flow of non‐colloidal suspensions by solving the mass and momentum conservation equations coupled with a particle transport equation using the Galerkin/Finite element method. The results show that particle distribution in the coating bead and in the coated layer is non‐uniform and is strongly dependent on the imposed flow rate (wet thickness). © 2016 American Institute of Chemical Engineers AIChE J, 63: 1122–1131, 2017