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     

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.     

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.     

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     

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 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.     

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     

The effect of shear‐thickening on the stability of slot‐die coating

Slot‐die coating is an economical roll‐to‐roll processing technique with potential to revolutionize the fabrication of nano‐patterned thin films at high throughput. In this study, the impact of shear‐thickening of the coating fluid on the stability of slot‐die coating was investigated. For the coating fluid, a model system fumed silica nanoparticles dispersed in polypropylene glycol was chosen. These dispersions exhibit shear and extensional thickening characterized through steady shear and capillary break‐up measurements. The critical web velocity for the onset of coating defect for different flow rates was measured, while the type of coating defect was visualized using a high speed camera. For the shear thickening particle dispersions, the coating failed through the onset of a ribbing instability. The critical web velocity for the onset of coating defect was found to decrease with increasing particle concentration and increasing fluid viscosity. The minimum wet thickness was studied as a function of capillary number for the particle dispersions and compared with a series of Newtonian fluids with similar viscosities. In all cases, shear‐thickening behavior was found to stabilize coating by reducing the minimum wet coating thickness when compared against a Newtonian fluid with similar viscosity at the same capillary number. Conversely, the shear‐thinning fluids tested destabilized the coating by increasing the minimum wet thickness when compared against a Newtonian at the same capillary number. The impact of shear‐thickening on slot‐die coating was further studied by quantifying the evolution of the ribbing instability with increasing web speed and by conducting tests over a wide range of coating gaps. © 2016 American Institute of Chemical Engineers AIChE J, 62: 4536–4547, 2016     

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.     

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     

Theoretical prediction on double-layer coating in wet-on-wet optical fiber coating process

A theoretical investigation is conducted on the wet-on-wet (WOW) process for double-layer resin coating of optical glass fiber. The coating process in the secondary coating die is modeled as a simple two-layer Couette flow of two immiscible fluids in an annulus with an assigned pressure gradient. The assumption of fully developed flow permits an exact solution to the Navier–Stokes equations. The solution discloses the relevant parameters in design and operation of a WOW coating applicator of optical fiber. For a given diameter of glass fiber and primary coating thickness, the secondary coating thickness is a function of the applied pressure gradient, the diameter of coating die, the viscosity ratio, and the fiber drawing speed. The influences of each of these control parameters on double-layer coating are scrutinized. A practical concept of thermal control of the coating process utilizing temperature-dependent viscosity of coating resins is explored.     

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.     

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     

Dynamic modeling of blown‐film extrusion

Past dynamic studies of blown‐film extrusion have been confined to the stability analysis of the linearized equations. The full set of nonlinear equations comprises a system of partial differential and algebraic equations with boundary conditions that vary from author to author. In this paper, the Numerical‐Method‐of‐Lines, which combines finite‐difference methods with ordinary differential/algebraic equation integrators, is used to solve the full system. Appropriate boundary conditions are selected to give physical results that compare well with experiment. An important boundary condition is the “minimum order reduction” condition on the gradient of the bubble‐tube radius with respect to distance above the extrusion die (the axial position). Transient startups and operational disturbances are examined. Calculations show the influence of oscillations in operating conditions such as heat transfer or inflation pressure on the bubble‐tube radius and film thickness. Steady‐state results obtained by integrating the transient equations for a sufficiently long time are qualitatively in agreement with experiment, in contrast to past simulations of these equations.     

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     

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     

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 slot-die configurations on coating gap dependence of maximum and minimum wet thicknesses

The dependence of the maximum and minimum wet thicknesses on the coating gap is derived for the slot-die coating process, under different slot-die configurations. Analytical expressions for the wet thickness and its derivative with respect to the coating gap are obtained using a simple flow model. The results indicate that, as expected, the minimum wet thickness increases linearly with the coating gap; however, the maximum wet thickness demonstrates a counterintuitive trend of decreasing as the coating gap increases, when a specific slot-die configuration is assumed. Moreover, the results are also validated by numerically solving the complete two-dimensional (2D) Navier–Stokes equation.