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.     

Operability coating windows and frequency response in slot coating flows from a viscocapillary model

Slot coating, indispensable to the manufacturer of flat panel displays and long-life secondary batteries, can be susceptible to unexpected disturbances at high speeds, leading to many kinds of undesirable defects. Operability coating windows for both Newtonian and non-Newtonian (shear-thinning) liquids have been investigated using a simplified viscocapillary model in a slot coating bead flow regime. Stable coating windows, free from leaking (or dripping) and bead break-up, have been determined by the position of upstream meniscus. They quantitatively coincided with those from two-dimensional calculations by a CFD Fluent solver. The pressure range that allowed a stable bead widened as the viscosity of the coating liquid or the capillary number in downstream die region increased. Also, the sensitivity of the slot coating flow through frequency response method was tested by measuring the amplitude of final wet coating thickness with respect to ongoing sinusoidal disturbances at different frequencies imposed to web speed, flow rate, bead pressure and coating gap. The viscocapillary model was compared with a 2D model and was found to be a fast and efficient tool that could enhance the productivity and processability of coating systems.     

Multiple equilibrium shapes of partially constrained menisci: A quasi-static mechanism for instability of a coating bead

The upstream meniscus of an extrusion coating bead operating in the capillary limit is modelled as a cylindrical meniscus that pins to the die and inte     

Capillary pressure and viscous pressure drop set bounds on coating bead operability

In premetered slot or extrusion coating and related sheet coating a “bead” of liquid is held between the coating die and the moving sheet by capillary forces, which depend on gap clearances, surface tension, contact line attachment, and dynamic contact angle; by viscous forces, which depend on clearances, viscosity, meniscus, location, and coating thickness; and by the externally applied pressure difference, which must fall within bounds for the bead to be operable.New bounds are derived for quasi-static beads with variable meniscus location, extending Ruschak's [1] analysis. Viscous effects are modeled by Couette and Poiseuille contributions that account for nonuniform clearances and are important except in limiting cases like Ruschak's. Operating bounds are derived for viscous coating beads.     

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.     

Automatic detection of contact lines in slot coating flows

Slot coating is a versatile method used to manufacture thin films at high speed. The success of the method lies in controlling a coating flow surrounded by upstream and downstream menisci. The meniscus edges that are in contact with either the die lips or the substrate surfaces are called contact lines. Visualizations of such lines are important in coating flow research because their shapes and locations are sensitive to operating conditions. In this study, we propose a robust image analysis algorithm for images acquired from flow visualizations. The images are dissected into three regions with different characteristics that need to be treated using different pre‐processing techniques. A standard optimal edge detector is then sufficient to capture the contact lines, and post‐processing steps can be simplified. We also highlight two applications of the proposed algorithm: coating windows, and transient behaviors under external disturbances. © 2017 American Institute of Chemical Engineers AIChE J, 63: 2440–2450, 2017     

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.     

Effects of shear thinning on forward roll coating

This paper described the forward mode roll coating process of generalised non-Newtonian fluids characterised by the Ellis model. The fluid in the coating bead and the free surface formation are described by the lubrication approximation and the stability is also considered using a perturbation analysis of the downstream meniscus. Results highlight the complex behaviour of this coating process and volume flow rate and film thickness results are obtained for a range of operating conditions. The stability of the downstream meniscus is observed to improve with increasing level of shear thinning when τ_1/2 (the shear stress at which the viscosity is half that of the zero shear stress viscosity) is small, however as τ_1/2 increases the meniscus stability decreases with increasing levels of shear thinning.     

Wetting behavior of the shear thinning power law fluids

The knowledge of the wetting characteristics of a coating solution is a prerequisite of assuring the final quality of thin films manufactured by the slot die coating process. Because the maximum coating speed is limited by defects, such as air entrainment, which are directly related to film quality, an understanding of the coating limits is critical. Despite the existence of a vast body of literature to understand the occurrence of defects and the coating limits to produce defect-free films, the mechanism of air entrainment is still not well understood, especially for various classes of solutions. In this study, the shape of the upstream meniscus of a mildly shear thinning non-Newtonian coating bead has been studied both numerically and experimentally and subsequently linked to the air entrainment threshold. It has been found that the dynamic contact angle reaches its maximum value at the air entrainment threshold, primarily as a function of the capillary number. In addition, this work suggests that the onset of the dripping and air entrainment boundaries of solutions that follow the power law can be predicted based on the dynamic contact angle as a function of the consistency and power law indices.     

Finite element analysis of dip coating with bingham fluids

A finite element analysis of the dip coating process with Bingham fluids is presented. The solution method for the viscoplastic flow problem was based on the augmented Lagrangian method allowing a rigorous treatment of the stress discontinuity. To compute the location of the free surface at equilibrium, an iterative method was used based on the arbitrary Eulerian-Lagrangian approach in conjunction with mesh smoothing. Numerical predictions were validated against experimental data for the Newtonian limit case. Computations were then performed with Bingham fluids. The influence of yield stress on the meniscus flow Is discussed.     

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.     

Bead formation near the contact line in forced spreading

When a plate is dragged out of a pool of non-wetting liquid, the meniscus that results has a bead near the contact line. The problem can be formulated under the lubrication theory approximation. The solution to this problem exists and shows that a bead will form. However, this solution is not valid at its two ends. Near the contact line a separate solution, the inner expansion, is constructed and matched to the base case. At the other end where the meniscus blends into the pool of liquid, it is argued that the meniscus shape is given by the equilibrium profile where gravity is important. This is the outer solution and it is also matched to the base case. The matching provides for the overall solution and the values of the unknown parameters in the base case in terms of the equilibrium contact angle, slip length and gravity are obtained. The matched solution is confined to large equilibrium contact angles and the absolute value of the meniscus height remains unknown. Two results are that the non-existence of the solution is shown to be the wetting case, in contrast to the earlier view that it represented the general condition of entrainment for non-wetting liquids. Further, the issues of how to determine the dynamic contact angles are resolved as the profile shape is known. It is important to note that among methods that relate dynamic contact angles to the capillary number, none of them use a good solution for the film profile to greater or lesser extent. Some differences among standard methods emerge.     

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.     

Sheet coating by drawdown of extruded polymer

An approximate analytic solution for coating a highly viscous Newtonian fluid ontoa substrate is developed (low Poiseuille number and high capillary number). Two particular extrusion angles are considered: parallel and perpendicular to the moving substrate. We obtain expressions for the curtain shape, coating thickness, contact length, contact pressure, drawing force, apparent contact angle, and contact convexity. In this paper, we identify a process indeterminacy that arises in the curtain coating employing a parallel slit. Weshow that, by orienting the extrusion slit perpendicular to the moving substrate, this indeterminacy vanishes. Thus, a unique solution for the contact length is always obtained. The extension to a viscoelastic fluid is also briefly considered. Presented at the 78th Annual Meeting of the FSCT in Chicago, IL October 18–20, 2000. Dept. of Mechanical Engineering and Rheology Research Center, Madison, WI 53706-1572 Dept. of Chemical Engineering, College Station, TX 77843-3141     

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.     

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     

Analytical models for predicting penetration depth during slot die coating onto porous media

A series of analytical models have been developed to predict the penetration depth during slot die coating on porous media. Analytical models for both Newtonian and non‐Newtonian fluids were derived based on Lubrication Theory, Darcy's law, and a modified Blake–Kozeny equation. Using these models, the penetration depth can be quickly solved and the effects of material properties and processing conditions on penetration depth can be easily investigated. Experiments of coating Newtonian glycerin and non‐Newtonian blackstrap molasses onto Toray series carbon paper were conducted to validate developed models. The overall relative error between the predicted and measured penetration depth was found to be typically lower than 20%, which demonstrates the relative accuracy of developed models. Furthermore, based on a parametric study, it was found that the effect of capillary pressure on penetration depth is less than 10% when the ratio of coating bead pressure and capillary pressure is larger than 10. © 2014 American Institute of Chemical Engineers AIChE J 60: 4241–4252, 2014     

A local power‐law approximation to a smooth viscosity curve with application to flow in conduits and coating dies

Coating dies distribute liquid into a uniform layer for coating onto a moving substrate. A die comprises one or two cavities spanning the coating width and adjoining narrow slots of much higher resistance to flow. In modeling coating dies, the flows in the slots and cavities are often approximated as one‐dimensional to achieve a fully geometrically parameterized model of low computational load suitable for optimizing design for multiple liquids and flow rates. The power‐law model is mathematically efficient for one‐dimensional flows of shear‐thinning liquids but does not include limiting viscosities at low and high shear rates that are frequently present. In previous work, the truncated power‐law model, which is terminated at the limiting Newtonian viscosities, was used to alleviate this shortcoming without sacrificing the mathematical advantages. In this work, the Carreau–Yasuda model replaces the truncated power‐law model as an improvement. For flows in slots and cavities, the Carreau–Yasuda model can be approximated accurately by a local power‐law model with little increase in computational load over the truncated power‐law model. In the transition regions of the Carreau–Yasuda model between Newtonian and power‐law behavior, the local power‐law model gives more accurate results than the truncated power‐law model. POLYM. ENG. SCI., 54:2301–2309, 2014. © 2013 Society of Plastics Engineers     

Transient response of slot coating flows of shear-thinning fluids to periodic disturbances

Slot coating is a popular coating method, in which the film thickness is precisely controlled by adjusting the flow rate and production speed. When the coating flow undergoes small-scale disturbances generated by rotating elements such as motors, pumps, or uneven rolls, the downstream meniscus fluctuates, which causes film thickness variation in the flow direction. Although most coating liquids including polymeric and particulate solutions exhibit a shear-thinning rheological property, their effect on transient coating flow behaviors is not deeply understood. Here, the effect of shear-thinning property on film thickness variation under different disturbances is investigated using a computer-aided analysis of transient slot coating flow. In this study, the Carreau model is used to describe the shear-thinning property, and four different disturbances are considered.     

Viscocapillary model of slide coating: Effect of operating parameters and range of validity

Slide coating is one of the premetered high‐precision coating methods. The layer thickness is set by the flow rate and web speed. The uniformity of the layer, however, can be affected by other operating conditions. Modeling the flow in the coating bead is necessary in developing the range of operability conditions where the layer is adequately uniform. Lubrication and viscocapillary models have been used to describe the flow and some of the operability limits of different coating processes. However, the available models of slide coating were developed with adhoc hypotheses that compromise their accuracy. We present a critical review of the available viscocapillary models and proposed changes to improve its range of applicability. The accuracy of the model is tested by comparing its predictions to the solution of the full two‐dimensional Navier‐Stokes equation. The model is valid at low capillary and Reynolds number regime and at low gap‐to‐wet thickness ratio. © 2009 American Institute of Chemical Engineers AIChE J, 2009