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     

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     

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.     

Two-layer tensioned-web-over-slot die coating: Effect of operating conditions on coating window

Tensioned-web-over-slot die (TWOSD) coating 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. Dual slot TWOSD coating is designed to deposit two thin uniform liquid layers onto a moving web simultaneously. Like in the fixed-gap dual slot coating, the interlayer separation point needs to be at the downstream corner of the mid lip in order to prevent coating defects. Different flow features, like weeping, bead breakup and feed slot vortices, limit the range of operating parameters that ensures uniform coating, and define the operating window of the process. In this study, we analyze dual slot TWOSD coating flow by solving the Navier–Stokes equation coupled with thin cylindrical shell equation using the finite element method. The boundaries in the parameter space that define the operating window or vortex-free window are automatically computed by a direct tracking method of flow features. The effect of operating conditions, such as liquid viscosity, web tension and web speed, on the critical layer thickness at which the coating becomes non-uniform is determined by this study.     

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 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.     

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     

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     

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.     

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.     

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.     

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     

Particle migration and alignment in slot coating flows of elongated particle suspensions

We analyze slot coating flows of elongated particle suspensions and investigate particle concentration and average orientation at the coated film. Shear‐induced particle migration is described by the Diffusive Flux Model, and particle orientation is given by the principal direction of the particle conformation tensor. The conformation evolution and the constitutive equation for the resulting complex liquid are adapted from classical models that describe the behavior of suspensions of cylinders and fibers and polymeric solutions of almost rigid rod‐like molecules. The proposed fully coupled model is applied to slot coating flows, and is solved using the DEVSS‐TG/SUPG finite element method. The results show that the wet coated film is highly nonuniform. Particle concentration and orientation vary along the film thickness and are a strong function of the operating parameters of the process, such as the film thickness‐to‐coating gap ratio and the capillary number of the flow. © 2017 American Institute of Chemical Engineers AIChE J, 63: 3187–3198, 2017     

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.     

Model for a two‐cavity coating die with pressure and temperature deformation

Coating dies uniformly distribute liquid for application as a film to moving substrates using one or two cavities spanning the coating width and adjoining precision narrow slots of much higher resistance to flow. If the slots are deformed by the pressure of the liquid or by temperature gradients in the die bars, degradation in flow distribution can result. Consequently, dies are designed to be sufficiently stiff and are thermally jacketed to keep slot deformations within fabrication tolerances. To aid in design and operation, a model of low computational load is developed in which the flow and deformation analyses are directly coupled. Die deformation is modeled using classical beam theory taking account of the varying thickness of the bars due to cavity geometry. Two‐dimensional finite element analysis of die deformation gives marginally higher slot deformation. Three‐dimensional finite element analysis agrees with the two‐dimensional analysis except near the center of the die where the symmetry boundary condition reduces deformation. The effects of die geometry on deformation and flow distribution are illustrated. POLYM. ENG. SCI., 2012. © 2011 Society of Plastics Engineers     

Mechanics of the low-flow limit in slot-die coating with no vacuum

Slot-die coating is a premetered, film-deposition process compatible with a wide range of materials. Of topical interest to precision electronics applications is the deposition of high-cost nanomaterial dispersions over moderately sized (>10 cm² ) areas with submicron wet film thickness. In this work, a two-dimensional (2D) model has been developed to understand the limits of the process and to predict the thinnest possible film achievable. Coined the low-flow limit, this parametric operating boundary presents the minimum uniform, defect-free film achievable at a given set of liquid properties and die/substrate geometry. We investigate the low-flow limit with a model that allows menisci to locate anywhere on the die lands, faces, and substrates with prescribed contact angles, thereby minimizing the assumptions on the bead configuration. The model is validated via comparison of its low-flow limit predictions to published experimental data. Analysis yields insights into the mechanics of coating bead breakdown at the low-flow limit.     

Coupled fluid‐particle modeling of a slot die coating system

This work seeks to develop a fundamental understanding of particle motion in the slot die coating process through studying the interaction of forces between particles, with the die walls and the fluid phase. Coupled computational fluid dynamics and the discrete element method is employed for evaluating the motion of individual suspended particles near moving surfaces in a complex three‐dimensional flow field, motivated by the flow of particle laden fluid in a slot die coating system, including the presence of free surfaces. Overall, the particles follow the flow streamlines and their final position in the coating depends on the initial entry region of the particles. Particles experiencing adhesion with each other agglomerate in the low velocity regions of the coating gap, and have long residence times near the edge of the die at the end of the feed slot in the coating gap. © 2016 American Institute of Chemical Engineers AIChE J, 62: 1933–1939, 2016     

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     

Hydrodynamic analyses of blade coaters

Simple and complete analyses of Newtonian hydrodynamics in a blade coating system are presented in this paper. The coating behavior of the liquid after it has been pumped to the blade lip is studied. A moving web which is to be coated through a constant gap is partially wrapped over a coating roller under tension. In the simple analysis, the coated liquid film thickness is a function of coating gap, liquid surface tension, viscosity and density, and web speed. In the complete analysis, the film thickness is a function of 15 variables (10 geometric, 3 liquid and 2 operational). Three possible separation conditions at the exit are examined. The optimization of the coater for minimizing liquid film thickness to coating gap ratio is carried out for all 15 variables. Available experimental data are compared with the analyses.