Upstream Meniscus Research Articles

Bubble Defect Generation Mechanism in Slot Die Coating of High-Viscosity Fluids.

Slot die coating is a widely used technique for the production of high accuracy films. One of the main challenges in slot die coating processes is determining the optimal range of operating parameters to prevent defects, such as bubbles, in high-viscosity films. In this study, both simulation and experimental methods were used to investigate the changes in the upstream meniscus under various coating parameters. Two types of air entrainment processes were considered, dominated by fluid inertia and viscous force. The formation of anticlockwise and clockwise vortex flows near the bottom of the upstream meniscus was found to alter the apparent dynamic contact angle of the upstream meniscus, leading to fluctuations in the apparent dynamic contact angle within a range of 70°-75° to 135°-140°. These fluctuations eventually resulted in air entrainment. This research is important for improving the quality and efficiency of slot die coating processes.

CFD model of slot die coating for lithium-ion battery electrodes in 2D and 3D with load balanced dynamic mesh refinement enabled with a local-slip boundary condition in OpenFOAM

Slot die coating is a state-of-the-art process to manufacture lithium-ion battery electrodes with high accuracy and reproducibility, covering a wide range of process conditions and material systems. Common approaches to predict process windows are one-dimensional calculations with a limited expressiveness. A more detailed analysis can be performed using CFD simulations, which are often based on in-house code or closed-source software. In this study, a two-phase CFD model in two and three dimensions was created in OpenFOAM with the intent to provide a method for more detailed investigations of the slot die coating process with open access to source code and files. A custom boundary condition enables the proper description of the wetting behavior in the two-dimensional model. The combination of standard no-slip boundary conditions at the substrate boundary with the volume-of-fluid solution algorithm leads to a method-related air entrainment, which was prevented by allowing local slip at the dynamic wetting line at the upstream meniscus in the two-dimensional model. Additionally, a load-balancing dynamic refinement algorithm was implemented to minimize the computational effort and increase the ease of use of the simulation environment. The simulation was validated by comparing the simulated process limits to experimental observations, showing good agreement. As a result, this model enables detailed analyses regarding the influences of slot die geometries, material properties, and process parameters on the coating stability and wet-film profile.

Slot-die-coating operability windows for polymer electrolyte membrane fuel cell cathode catalyst layers

Roll-to-roll (R2R) slot-die coating of polymer electrolyte membrane fuel cell (PEMFC) catalyst layers represents a scalable deposition method for producing 10–20 m2·min−1 of catalyst-coated gas diffusion layers (GDLs). This high-throughput production technique will help lower the cost of PEMFC catalyst layers. The uniformity of the wet layer applied by slot die deposition is affected by process parameters such as substrate speed, vacuum pressure applied at the upstream meniscus, gap between the slot die lips and substrate, ink rheology, and other ink and substrate properties. The set of conditions for producing a defect-free coating with a dilute ink typically requires little to no upstream vacuum pressure, so suitable operating conditions can be found easily through trial and error and operator intuition. However, the higher viscosity of more concentrated inks dramatically shifts the range of settings that result in a homogeneous coating to higher vacuum levels, which are harder to find through hit or miss. A predictive model showing the range of operable conditions decreases material wastage inherent in experimentally searching for suitable parameters. In this study, the defect-free coating parameter window is explored experimentally and theoretically for two concentrations of PEFC cathode inks. Both a full capillary hydrodynamic model and a computationally cheaper viscocapillary model successfully predict the experimentally determined coating window within the experimental and model uncertainty limits for inks with 5.3 wt% and 12.0 wt% solids ink while maintaining the 0.1 mgPt·cm−2Pt areal loading target. This paper demonstrates a viable pathway for meeting the $30/kWnet ultimate cost target of the United States Department of Energy (U.S. DOE) Hydrogen Fuel Cells Technologies Office (HFTO). The concentrated ink lowers the thermal energy and capital expenditure (CapEx) budget of the coating process by decreasing the amount of time, energy, and floorspace required for drying the coating.

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.

Operability windows in viscoelastic slot coating flows using a simplified viscoelastic-capillary model

The viscoelastic-capillary model to predict approximately coating windows for the stable operations of viscoelastic coating liquids is derived using a lubrication approximation in slot coating processes. Pressure distributions and velocity profiles for viscoelastic liquids based on the Oldroyd-B and Phan-Thien and Tanner (PTT) models are solved in the coating bead region considering the Couette-Poiseuille flow feature and the pressure jumps at upstream and downstream menisci. Practical operating limits for the uniform coating of rheologically different liquids that are free from leaking and bead break-up defects are constructed under various conditions, incorporating the position of the upstream meniscus as an important indicator while determining limits. The shift of the uniform operating range shows different patterns for the Oldroyd-B liquid with a constant shear viscosity and the PTT liquid with a shear-thinning nature in comparison with the Newtonian case. The windows predicted by the simplified model are corroborated with experimental observations for one Newtonian and two viscoelastic liquids.

Operability coating window of dual-layer slot coating process using viscocapillary model

The viscocapillary model for predicting the operability windows in a dual-slot coating process for two Newtonian liquids has been derived by means of a lubrication approximation technique from two-dimensional (2-D) Navier-Stokes equations. The flow rates per width and the pressure differences simplified in several sub-regions within the coating bead regime have been integrated together with approximations of the upstream and downstream menisci and the interlayer between the top and bottom layers. Coating limits or onsets for leaking and bead break-up defects have been determined on the basis of the position of upstream meniscus of the bottom layer as an indicator. Operability coating windows predicted from the viscocapillary model show a good agreement with those by 2-D CFD solver and experiments. In addition, the pressure profiles within the coating bead regime compared between the viscocapillary and 2-D models are qualitatively similar. This simplified model can be applied as a fast tool for usefully manipulating the stable operations in dual-layer slot 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

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.

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.

Operability window of slot coating using viscocapillary model for Carreau-type coating liquids

Based on the simplified viscocapillary models for Newtonian and power-law coating liquids reported in Lee et al. (2011a), the one-dimensional (1-D) viscocapillary model for Carreau-type liquids containing zeroshear viscosity information has been developed for constructing the operability window in slot coating. Velocity distribution and position of upstream meniscus were numerically solved to determine onsets of leaking and bead break-up defects. The results obtained by 1-D model are quantitatively corroborated by two-dimensional (2-D) fluent calculations.

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.

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.

Operating windows of slot die coating: Comparison of theoretical predictions with experimental observations

AbstractThe objective of the present study is to examine the validity of the theoretical predictions on the operating windows of slot die coating. The operating window is defined as a domain inside which stable and uniform coating is possible; different types of coating defects are found outside the window. A flow visualization technique was applied to observe the coating bead, particularly the positions and shapes of the downstream and upstream menisci, just before and after coating defects appear at high coating speeds. Special features of coating bead shapes, which lead to onsets of ribbing and air entrainment, were identified. The two‐dimensional flow in the coating bead region was computed by the commercial software package FLOW‐3D®. Critical features observed experimentally for the onset of coating defects were used to judge whether the coating flow was within the operating window. The theoretically evaluated operating windows were found to be much larger than those determined experimentally in terms of coating speeds. However, the qualitative trends of theoretical predictions agree with experimental observations. © 2010 Wiley Periodicals, Inc. Adv Polym Techn 29:31–44, 2010; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/adv.20173

Coating Flows of Power-Law Non-Newtonian Fluids in Slot Coating

One-dimensional flow equations were derived for non-Newtonian fluids in slot coating and a simple numerical method was proposed to solve the equations. We investigated non-Newtonian effects on coating performance and coating quality in slot coating. In some cases, computational results and experimental data were compared and both agreed well. A series of numerical computations showed that the one-dimensional approach can describe non-Newtonian flow under lips in a few minutes and that a pressure field equation proposed by Higgins can determine the location of an upstream meniscus. Moreover, it was found that the non-Newtonian characteristics of coating liquids affect both coating performance and coating quality. Because each non-Newtonian effect is quite different, we should optimize the conditions of slot coating and die geometries according to the target problem.

The Effect of Bead Vacuum on Slot Die Coating

Abstract The effect of bead vacuum on the minimum wet thickness obtained on horizontal and vertical slot die coatings was experimentally examined using a flow visualization technique. The commercial software package FLOW3D was used to simulate the two-dimensional coating flow. Macroscopic material balances were applied to estimate the effect of bead vacuum. Applying vacuum on the coating bead was found to reduce the minimum wet thickness and increase the maximum coating speed, with the effect on horizontal slot die coating being more pronounced. Visual observations revealed that with increasing vacuum, the upstream meniscus against the moving web was pulled back significantly for a low-viscosity solution, and the dynamic contact angle was reduced for a high-viscosity solution. The observed upstream wetting length for a low-viscosity solution subject to bead vacuum was consistent with the prediction using macroscopic balances. The sizes of coating beads predicted by FLOW3D were generally larger than those observed from flow visualization. Coating failures caused by high bead vacuum could be predicted with the aid of numerical simulations.

Numerical Simulation of Initial Development of Fluid Flow and Heat Transfer in Planar Flow Casting Process

This article describes the initial development of fluid flow and heat transfer in a planar flow casting (PFC) process for amorphous ribbon formation using a two-dimensional (2-D) model of fluid flow with free surface and surface tension, and heat transfer with phase transformation. The heat transfer in the rotating copper roller is incorporated into the model. A coupled fluid-solid (the puddle/roller surface) solution is employed for identifying the ideal interfacial heat transfer. The initial developments of puddle shape and flow and temperature distribution, including the air and the melt in the puddle zone, over time are presented. The time-dependent theoretical interfacial heat-transfer-coefficient and temperature profiles in the rotating roller are investigated. The effect of the varying roller speed, the PFC configurations (slit width and gap distance), and the roller parameters (roller radius and roller layer thickness) on the development of the melt flow and heat transfer in a PFC process are discussed. Numerical results show that a stable puddle shape can be formed within a very short period of time (on the order of milliseconds). The time evolution of the upstream meniscus is different from that of the downstream meniscus. The recirculation flows both in the surrounding air and in the melt of the puddle zone can be observed at a quasi-steady-state condition, but show different flow and thermal behaviors. The interfacial heat-transfer coefficient and temperature distribution of the rotating roller change with different cycles of the roller revolution until the heat-flux balance is reached. The varying parameters associated with the roller speed, slit width, gap distance, roller radius, and roller layer thickness affect the time evolution of the flow and thermal behavior in the puddle and the temperature distribution in the rotating roller.

In situ manipulation of cooling rates during planar-flow melt spinning processing

Planar-flow melt spinning (PFMS) is a single stage rapid manufacturing/solidification technique for producing thin metallic sheet or foil. A new technology, envisioned to allow real-time manipulation of the local cooling rates and properties in melt-spun ribbon, has been tested successfully when casting Al–7%Si. Pulsed laser heating, directed low on the upstream meniscus, or on the substrate, leaves patterns of ‘dimples’ in the ribbon. Typical cooling rates of 10 4 K/s have been measured using a control-volume approach. Secondary dendrite arm spacing (SDAS) has been measured through the thickness of ribbons showing areas both affected by the laser heating and unaffected by the laser. Through a correlation of cooling rates and SDAS, it is shown that the unmodified ribbon has an average cooling rate similar to that measured macroscopically. The cooling rate underneath a laser dimple is estimated to be six times slower near the contact surface. It is envisioned that the technology described may bring the concept of ‘casting-by-design’ one step closer to realization.

Three minimum wet thickness regions of slot die coating

An experimental study was carried out to determine the minimum wet thickness of slot die coating for low-viscosity solutions. There exist three distinct coating regions (I, II, and III), depending on the physical properties of the coating fluid, die geometry, and flow conditions. A critical Reynolds number was found, below which viscous and surface tension effects are important. In Region I, the minimum wet thickness increases with increasing capillary number and becomes independent of capillary number in Region II. Region III exists above the critical Reynolds number where fluid inertia is dominant. In this region, the minimum wet thickness decreases as Reynolds number increases. Flow visualization on the coating bead reveals that the position of the downstream meniscus of the coating bead determines the types of coating region, whereas the shape and position of the upstream meniscus determine the type of coating defects. It was also observed that the downstream meniscus was not located at the die lip corner and both the static and dynamic contact angles varied under different conditions. These findings are critical for realistic theoretical study of slot die coating.

Capillary stability limits for liquid metal in melt spinning

Single roll planar-flow melt spinning (PFMS) is a rapid solidification technique for producing thin metal sheets or ribbons. The key physics occur in a liquid metal puddle (bead) held by capillarity between the entry nozzle and a rotating metallic wheel. We present a semi-empirical analysis that (1) provides a theoretical basis for a previously reported empirical stability window, and (2) predicts an extension to the stability limits by adjusting the pressure outside the upstream meniscus relative to the pressure outside the downstream meniscus. A device capable of altering this pressure has been constructed and demonstrates extended operability.

Bead-break instability

Flow is considered in a “fluid bead” located in the nip between two contra-rotating rolls, and bounded by two curved menisci. Such a flow arises in meniscus roll coating where fluid is transferred from the lower applicator roll to a substrate, in contact and moving with the upper metering roll, by means of a transfer jet (snake). Equilibrium of the bead is maintained through a balance of hydrodynamic and capillary stresses, the stability of which is considered experimentally by increasing the speed of the metering roll while that of the applicator roll remains constant. At a critical speed ratio, the upstream meniscus becomes unstable; the bead contracts as the meniscus accelerates forward and merges with its downstream counterpart—giving rise to “bead-break.” A mathematical model, based on lubrication theory, exhibits multiple solutions and a limit point for the existence of steady solutions. A linear stability analysis identifies the stable solution and shows that the flow becomes unstable at the limit point—which is taken to be the onset of bead-break. The criterion for bead-break is (d/dX)[P+σ/Ru]<0 at the upstream meniscus, where P, σ, and Ru represent fluid pressure, surface tension, and radius of curvature of the upstream meniscus, respectively. The effect of the pressure gradient is shown to stabilize the fluid bead whereas that of the surface tension term is to destabilize once the upstream meniscus—and hence the whole bead—is located downstream of the nip. For a given geometry and flow rate, the critical speed ratio decreases with increasing characteristic capillary number. Theoretical predictions compare well with experimental data.