1. Introduction
Ceramic materials have been widely used due to their high hardness, wear resistance, chemical stability, and high-temperature performance. However, due to their inherent brittleness, shaping complex ceramic components by conventional machining is challenging [
1]. Additive manufacturing (AM) offers a solution by building parts layer-by-layer, enabling complex geometries without subtractive machining [
2]. Current ceramic AM technologies can be broadly classified by feedstock form into two categories: (1) powder-based processes such as binder jetting (BJ) and selective laser sintering/melting (SLS/SLM), which spread dry ceramic powder layers and selectively bind or fuse them [
3]; and (2) slurry-based processes that deposit a suspension of ceramic particles (slurry) in each layer (e.g., vat photopolymerization like stereolithography (SLA) or digital light processing (DLP), as well as material extrusion (ME) [
4,
5]. Powder-based methods benefit from well-established machinery but suffer from low packing density in the powder bed (often <50 vol% solid) [
6]. Such poor initial packing leads to low density of green body and large shrinkage upon sintering, resulting in a weak or distorted final sintered body. For example, SLS/SLM of ceramics is limited to relatively coarse powders and can introduce thermal stresses and cracks due to the use of lasers [
7]. Photopolymer-based slurry printing (SLA/DLP) allows finer particles, but the required organic resin content limits the ceramic fraction (typically <50vol% solids) [
8,
9,
10].
To overcome these limitations, slurry-based AM techniques have been actively explored to increase packing density and improve sintered properties. Early pioneering work by Cima et al. [
11] at MIT introduced a slurry-based 3D printing process that used fine ceramic suspensions instead of dry powder. This approach achieved green densities around ~58–60% of theoretical and ultimately ~99.9% of theoretical density after sintering, a remarkable improvement over powder-based methods. For instance, alumina parts printed with a high-solids slurry showed a green density of ~58% and sintered to virtually full density (99.9%). Grau et al. [
12] demonstrated that layering of fine alumina slurry could yield green densities in the 60–67% range, drastically reducing the shrinkage and porosity in the final ceramic. More recently, Zocca et al. [
13] developed the Layerwise Slurry Deposition (LSD) method as a novel route to build ceramic parts with high density. In LSD, a thin layer of ceramic slurry is spread (e.g., by a doctor blade) and dried to form a highly packed powder layer, which can then be selectively bonded by binder jetting in a manner similar to BJ printing. This combined process, so-called “LSD-print,” has been successfully applied to alumina and other ceramics. Lima et al. [
14] demonstrated 3D printing of porcelain using LSD-print, achieving parts with fine feature resolution, smooth surfaces, and mechanical properties approaching those of traditionally formed porcelain. These advances confirmed that slurry-based AM can produce much denser and stronger ceramic components than powder-bed methods, provided that each slurry layer is uniformly deposited with a high solid loading. However, achieving such uniform layers remains a significant challenge due to the high viscosity and particle segregation tendency of the concentrated slurries. Therefore, the coating technique used for layer deposition plays a critical role in ensuring the reliability of slurry-based ceramic AM processes.
In this context, slot-die coating emerges as an attractive solution for slurry layer deposition. Slot-die coating is a pre-metered method that delivers the slurry through a narrow slot onto the substrate, allowing precise control of the wet film thickness by simply adjusting the flow rate and substrate speed [
15]. Unlike a doctor blade method, which relies on gap height and often the fluid’s self-leveling to set the film thickness, slot-die is an active deposition that can produce uniform films, even for high-viscosity suspensions, by maintaining a stable68 coating bead of fluid between the die and substrate. This makes it feasible to coat thin layers of ceramic slurry with minimal variation. Indeed, slot-die coating is widely used in roll-to-roll manufacturing of functional films from printed electronics and displays to solar cells and battery electrodes because it offers excellent uniformity, scalability, and thickness accuracy [
16]. Recent studies have also extended slot-die techniques to polymer film additive manufacturing and multi-layer coatings. For instance, Fang et al. [
17] investigated slot-die coating of multi-layer polymer LED phosphor films, where each layer must be smooth and free of air bubbles. This work investigated how slot-die process parameters can improve coating quality in functional multi-layer films.
Process parameters of slot-die coating must be controlled within certain limits, the so-called coating window, to avoid defects [
18]. If the coating parameters, including coating speed, flow rate, and gap distance, fall outside the stable coating window, various failure modes can occur. At too low a flow rate, the coating bead may collapse or break, leading to incomplete layer coverage. At excessive coating speed or insufficient flow, the liquid can fail to wet the moving substrate fast enough, resulting in air becoming entrained under the film. This typically manifests as air bubbles or uncoated defects in the layer [
19]. Chang et al. observed that relatively low-viscosity slurries tend to exhibit ribbing instabilities, whereas beyond a critical viscosity (~0.075 Pa·s), the dominant defect mechanism shifts to air entrainment at high speeds [
20]. In practice, running the process at an extremely slow speed can eliminate most defects by keeping the coating bead very stable; however, this is economically impractical for manufacturing. Therefore, identifying a robust operating window (in terms of coater speed, flow rate, and slurry properties) is essential for implementing slot-die coating in ceramic AM. In addition to flow instabilities, slurry-specific issues must be considered: one is dynamic capillary characteristics and wetting on porous surfaces, since in a multilayer process, the freshly deposited slurry may partially infiltrate or re-wet the previously dried layer, affecting the coating uniformity [
21]. Another is shear-induced particle migration; under the high shear of slot-die flow, ceramic particles can migrate or segregate, causing concentration gradients in the coated film [
22]. Such effects can lead to non-uniform local solid loading or defects like particle agglomeration and must be understood to ensure each layer dries homogeneously. To date, slot-die coating has been predominantly studied in the context of continuous film manufacturing. However, systematic studies on the coating window for ceramic slurries in an AM context are still lacking.
Researchers have been tasked to better understand and expand the stable coating window by analyzing meniscus dynamics. Pan et al. [
23] conducted a computational fluid dynamics (CFD) study to systematically evaluate how coating speed, inlet velocity, die lip geometry, and coating gap influence the pressure profile and flow behavior in slot-die coating. Malakhov et al. [
24] demonstrated that applying a mild vacuum behind the die lip can suppress air entrainment and lower the minimum flow rate required for continuous coating. Fang et al. [
25] explored vortex formation and dynamic contact angle fluctuations in high-viscosity slot-die coatings. Using both CFD simulations and experiments, they demonstrated that vortex patterns near the upstream meniscus can induce dramatic oscillations in the apparent contact angle from 70° to 140°, ultimately leading to air entrainment through capillary instabilities. However, despite these advances, most existing slot-die studies have focused on relatively low-viscosity fluids such as polymer solutions or electrolytic inks. In contrast, ceramic AM involves highly viscous, particle-suspended slurries, for which the interplay between rheology, shear stress distribution, and interfacial behavior, particularly in multilayer deposition, is not yet well understood in the context of slot-die coating.
In this work, we employed CFD modeling to analyze and optimize the slot-die coating of an alumina slurry for ceramic AM. Two substrate conditions were used for multilayer deposition: (1) glass for the initial layer, and (2) a dried alumina layer representing the built ceramic part. These two cases were selected to reflect the critical changes in wettability that occur between the initial substrate and subsequent layers in a typical ceramic AM process, both of which strongly influence coating stability and uniformity. By using a volume-of-fluid (VOF) multiphase model, which is well-suited for tracking free-surface flows, we simulate the transient coating flow and the formation of the wet film in each case. The goal is to identify the process parameters that yield a uniform, defect-free slurry coating on both types of substrates, and to understand how the substrate nature (wettability, roughness, and absorbency) influences the coating behavior. The findings are expected to provide a guideline for process optimization, including coating speed, gap height, and slurry rheology to achieve consistent, high-density ceramic layers in a layer-by-layer 3D printing environment.
3. Results
The coating characteristics of slot-die coating are critically dependent on coating parameters, particularly the coating speed (
), volumetric flow rate (
) and coating gap (
). To explore the process window for alumina slurry, preliminary simulations were conducted to assess the overall coating behavior as a function of speed while holding the flow rate constant. These simulations provide a basis for identifying flow regimes and critical speed thresholds beyond which defects such as dripping or air entrainment emerge. Rheological and interfacial properties of the alumina slurry were experimentally measured and implemented in the CFD simulations (
Table 2). Viscosity was determined as the apparent viscosity measured at a representative shear rate of 31 s
−1. The properties were applied in the VOF simulation framework via the Continuum Surface Force (CSF) method to accurately model the capillary force at the slurry–air interface [
28]. The contact angles between the slurry and the two substrate types were also measured: 66.7° on glass and 137° on the dried alumina coating. The higher contact angle on the dried Al
2O
3 substrate (~137°) compared to glass (~66.7°) is attributed to the relatively hydrophobic nature of alumina surfaces and the additional contribution of surface porosity, which can further increase the apparent contact angle via air entrapment mechanisms [
29].
In this work, the slot-die coating process was categorized into three distinct flow regimes: overflow, stable, and unstable. These regimes were defined by the dynamic behavior of the upstream and downstream menisci and the presence or absence of entrapped air within the coating bead. The overflow regime occurs when the upstream meniscus climbs over the lip of the upstream die or when the downstream meniscus rises excessively along the downstream die surface. This condition typically results from an excessively high flow rate or an improperly set gap height, which causes the bead volume to exceed the geometrical capacity of the coating head. The stable regime represents the ideal coating condition. Here, the upstream meniscus remains stationary within the lip of the upstream die [
20], and the downstream meniscus remains pinned near the edge of the downstream lip [
30]. No air is entrained into the slurry, and the coating bead maintains a consistent geometry throughout the process. Under these conditions, uniform wet film thickness and well-dispersed particle distributions can be reliably achieved. The unstable regime is characterized by dynamic fluctuations in the meniscus position and curvature, especially near the upstream side. In this state, air is entrained into the coating bead, and the upstream meniscus may retreat toward or even beyond the slot gap, resulting in transient, unstable contact angles. This behavior can not only degrade the uniformity of film thickness but also significantly increase the likelihood of introducing defects such as voids and surface roughness. The classification into three regimes (overflow, stable, unstable) was based on clear experimental and simulation criteria, and further subdivision, while possible, was beyond the scope of this study.
3.1. Effect of Coating Gap
To investigate the effect of coating gap on coating stability, simulations were conducted under a fixed flow rate (0.7 mL/min) and coating speed (1.2 mm/s), while varying the coating gap from 200 µm to 400 µm. The resulting , pressure distribution, flow velocity, and shear rate are analyzed for coating stability and defect formation.
The velocity field (
Figure 3a) demonstrates that narrower coating gaps reduce the fluid velocity near the upstream meniscus. At a 200 µm gap, the velocity magnitude approaches zero in the region adjacent to the upstream die lip, resulting in a stationary meniscus and minimizing dynamic contact angle fluctuations. In contrast, at 400 µm, higher velocities are observed at the same location, leading to meniscus displacement and unstable bead formation. This further supports the notion that smaller gaps promote flow stability by reducing viscous stresses on the free surface. Although a 400 µm gap was included in
Figure 3a to illustrate the effect of large gap sizes on flow dynamics, it was excluded from further analysis due to consistently unstable meniscus behavior and impractical film thickness for multilayer ceramic AM. Thus, subsequent discussions focused on the more relevant 200–300 µm range.
The pressure profiles shown in
Figure 3b reveal a pronounced pressure gradient beneath the downstream die lip in the 200 µm coating gap case, indicative of Poiseuille flow. As the gap increases, this gradient diminishes, indicating a transition to Couette-dominant flow at lower speeds. While this may enhance flow uniformity, it also reduces the stabilizing pressure acting on the bead, rendering the system more susceptible to air entrainment.
Figure 3c illustrates the velocity gradient within the coating bead for various coating gaps, which is proportional to the shear rate. As the coating gap decreases from 300 µm to 200 µm, the magnitude of the shear rate increases significantly, particularly near the upstream meniscus and downstream die lip. The 200 µm case exhibited a highly localized region of elevated shear near the upstream meniscus and the downstream die lip, unlike the broader stress distributions seen in the 250 µm and 300 µm cases. Excessively high shear stress and shear rates can promote aggregation among suspended particles, resulting in clustering and poor film homogeneity [
31,
32].
When the coating speed exceeds a critical threshold, the process becomes unstable due to the onset of air entrainment. This phenomenon, commonly referred to as dynamic wetting failure, occurs when the capillary pressure gradient—driven by the curvature of the liquid interface—fails to displace air sufficiently fast from the dynamic contact line. Once dynamic wetting failure occurs, maintaining a stable and uniform film becomes extremely difficult, leading to significant deterioration in coating quality [
33]. The occurrence of dynamic wetting failure can be explained in terms of the capillary number (
), defined as
, where
is the dynamic viscosity of the fluid,
is the coating speed, and
is the surface tension. The capillary number quantifies the relative importance of viscous forces to surface tension. As either viscosity or speed increases, so does the capillary number. Conversely, lowering
enables the use of higher coating speeds while keeping
within acceptable limits. The onset of dynamic wetting failure is typically observed when
exceeds a critical capillary number,
.
Figure 4a illustrates how the coating gap affects the stable coating window. As the coating gap decreases, the range of coating speeds that maintain a stable bead formation widens, suggesting enhanced process stability at smaller gaps. This is attributed to the suppression of fluid velocity near the upstream meniscus, which helps anchor the contact line and prevents meniscus instability.
Figure 4b shows the dependence of the
on the coating gap at different flow rates. For all tested conditions,
increases as the coating gap decreases, indicating that the onset of dynamic wetting failure is delayed at narrower gaps. The
curves shown in
Figure 4b were based on CFD simulations under fixed parameters; experimental uncertainties were not considered in the model due to computational cost. The CFD-derived
values were deterministic output for fixed coating speed, flow rate, coating gap, and material parameters. Consequently, replicate-based statistical errors were not shown. For each condition,
was determined using a deterministic transition criterion. A single model evaluation per condition was used to identify the transition.
Taken together, these results highlight the critical role of the coating gap in determining the hydrodynamic stability and quality of the coated film. Narrower coating gaps were shown to suppress upstream flow velocity, enhance meniscus pinning through capillary forces, and raise the , thereby delaying the onset of dynamic wetting failure. Though narrow coating gaps favor coating stability, they can also impose a higher risk of defect formation due to high local shear. To prevent this, the coating speed and the flow rate must be carefully controlled to ensure that the induced shear stress remains below the aggregation threshold of the slurry system. Based on this analysis, a coating gap of 200 µm was selected as a representative condition for further investigation in the following sections.
3.2. Coating Behavior on Glass Substrate
To define the coating window and clarify the boundaries between operational regimes, the three coating regimes—stable, overflow, and unstable—were investigated with detailed numerical and experimental analyses. Each regime’s characteristics were analyzed in terms of pressure distribution, velocity field, shear stress, and air entrainment behavior, along with corresponding experimental validations.
3.2.1. Stable Regime
Figure 5 presents the numerical and experimental data under a stable coating condition (
= 1.8 mm/s,
= 0.7 mL/min,
= 200 µm).
Figure 5a displays a bead morphology characteristic of stable flow, with the upstream meniscus pinned at the die lip and the downstream meniscus stabilized at the lip edge. No air entrainment was observed in the coating bead.
In the upstream zone (Zone 1), the pressure gradient is nearly constant, and the velocity near the upper region of the upstream meniscus approaches 0 mm/s (
Figure 5b). This velocity balance prevents dynamic wetting failure and ensures meniscus stability. The measured dynamic contact angle was approximately 119° (
Figure 5d). In the downstream zone (Zone 2), both the pressure gradient and the velocity profile indicate Couette-dominant flow, as the velocity linearly increases toward the moving substrate. This uniform shear condition is conducive to homogeneous particle dispersion.
Figure 5c reveals that the shear stress in this condition is about 600 Pa higher than at lower coating speeds, indicating that excessive velocity can promote particle aggregation. Finally, the film formation region (Zone 3) exhibits a plug-flow profile with negligible velocity or pressure gradients, confirming a stable transfer to the substrate.
Figure 5e shows the experimental result, confirming the absence of air entrainment and demonstrating a continuous coating layer with uniform width.
3.2.2. Overflow Regime
Figure 6 illustrates the overflow condition (
= 0.7 mm/s,
= 0.7 mL/min,
= 200 µm), characterized by an excessive upstream meniscus that climbs beyond the die lip and a downstream meniscus that similarly surpasses the downstream die lip. This phenomenon is indicative of a flow rate significantly higher than the coating speed. In Zone 1, an appreciable pressure gradient and flow velocity (~0.5 mm/s) are observed, indicating strong upstream migration of Al
2O
3 slurry. Compared to the stable regime, this flow may increase the likelihood of particle accumulation near the die.
Despite the relatively high flow rate,
Figure 6d shows that air was entrained into the coating bead. The dynamic contact angle decreased to ~100°, and the meniscus oscillated while seeking equilibrium between flow rate and coating speed. During these transitions, transient air pockets were captured beneath the meniscus, leading to entrainment via dynamic wetting failure. In Zone 2, the pressure gradient (~2000 Pa) is significantly steeper than in the stable case.
Figure 6b reveals a non-linear shear profile, with the maximum velocity occurring approximately 70–100 µm above the substrate, followed by a velocity decline near the die lip. This inhomogeneous shear rate can result in uneven particle dispersion and localized aggregation. The experimental observation (
Figure 6e) shows that the coating width increases with time, confirming instability in film morphology and material deposition.
3.2.3. Unstable Regime
The unstable condition ( = 2.8 mm/s, = 0.7 mL/min, = 200 µm) is defined by an excessive coating speed, which forces the upstream meniscus beyond the slot gap and into the downstream die region. This displacement eliminates the circulation flow in Zone 1 observed in other regimes.
Figure 7a–d illustrate air entrainment through a curved upstream meniscus and rapidly fluctuating bead interface. The velocity field (
Figure 7b) confirms a non-uniform velocity distribution with localized maxima (~2.80 mm/s), particularly near the upstream meniscus. Such non-linear profiles indicate heterogeneous shear stress, which can compromise particle distribution.
Figure 7c shows that the shear stress under this regime peaks at 4437 Pa, the highest among all three conditions. In combination with the non-uniform flow, this level of stress significantly raises the risk of particle agglomeration and coating defects. Air entrainment is further detailed in
Figure 7d, where a dynamic contact angle of ~142° leads to widespread air inclusion in the coating bead. Unlike the overflow condition, the unstable regime induces entrainment through both dynamic wetting failure and a capillary rupture mechanism.
To further clarify the air entrainment mechanism under unstable conditions,
Figure 8 shows a time-resolved sequence of simulated volume fraction fields and dynamic contact angles. These snapshots reveal the evolution of the upstream meniscus and the recurring formation and rupture of the air entrainment over time. At t = 1.50 s (
Figure 8a), the upstream meniscus shifts beyond the slot gap into the downstream die region, forming a steep interface with a dynamic contact angle of approximately 137°. This configuration facilitates initial air entrainment into the coating bead. By t = 1.55 s (
Figure 8b), the meniscus deformation intensifies, creating a distinct capillary ridge near the upstream die lip, with a contact angle of ~140°.
As time progresses to t = 1.75 s (
Figure 8c), the slurry flow begins to block the left side of the capillary ridge, forming a void space within the coating bead. This void collapses at t = 1.90 s (
Figure 8d), resulting in the rupture of the air entrainment being entrained into the bead. At t = 2.00 s (
Figure 8e), the upstream meniscus resumes its forward displacement, initiating the next rupture cycle. These dynamics illustrate a periodic entrainment mechanism, driven by excessive coating speed and unbalanced flow rate, in which capillary ridge growth and collapse cause repeated coating discontinuity and air entrainment.
3.3. Coating Behavior on Dried Alumina Layer
As the coating proceeds layer-by-layer, all layers except for the first are deposited on top of previously dried alumina slurry films. Due to the high contact angle (~137°) between the slurry and the dried alumina substrate (
Table 2), the wettability is significantly reduced compared to hydrophilic substrates such as glass. The hydrophobic nature of the dried alumina layer can reduce meniscus stability and lower the critical capillary number, thereby narrowing the stable coating window and increasing the likelihood of air entrainment and non-uniform film thickness in multilayer coating processes.
Figure 9 presents a comparison between simulation results (left) and experimental observations (right) for three representative coating conditions (overflow, stable, and unstable) performed on dried alumina slurry substrates. The simulations were carried out under fixed flow rate and coating gap (
= 0.7 mL/min,
= 300 μm), while varying the coating speed. While a 200 µm coating gap was selected for the main analysis due to its relatively wide stable window and favorable shear stress profile, a 300 µm gap was additionally considered in
Section 3.3 to explore how coating stability degrades near the upper bound of practical coating conditions. This allows for a broader assessment of gap-dependent flow behavior, particularly under challenging conditions such as dried alumina substrates. Compared to coatings on glass, all three conditions exhibit bulged bead formation and slurry accumulation near the upstream region when deposited on dried Al
2O
3 substrates. This behavior is attributed to the significant difference in wettability. As a result, slurry spreading is suppressed on the dried alumina surface, leading to the rounded meniscus shapes and higher fluid fraction in the central bead region, as observed in the simulation. The experimental observations were consistent with the simulation findings. Under unstable conditions, irregular coating patterns were observed, including uncoated regions and variations in film thickness. These non-uniformities are presumed to be influenced by the substrate’s altered surface characteristics after drying. The simulation results suggest that slurry spreading is hindered due to the low wettability of the dried alumina layer. In particular, the fluid accumulation observed near the upstream meniscus in simulations is consistent with the experimental evidence of localized slurry retention. These findings indicate that surface energy and absorption behavior of the dried layer can strongly influence the coating dynamics in multilayer processes.
These results highlight a crucial aspect of multilayer coating in slurry-based ceramic additive manufacturing. While the dried ceramic layer serves as the substrate in all but the first layer, its wettability fundamentally alters the coating dynamics compared to non-porous substrates. Therefore, accurate prediction and control of slurry saturation behavior, particularly in relation to the drying degree and resulting pore size distribution, are essential to achieving consistent film thickness and interlayer adhesion. Furthermore, understanding the interplay between slurry properties and substrate surface energy will be critical in defining the coating window in slurry-based additive manufacturing.
Figure 10 shows stable coating windows constructed for three different gap heights (
= 200 µm, 250 µm, and 300 µm). As the coating gap increased, the range of stable coating speed narrowed significantly for a given flow rate. In particular, the 200 µm condition consistently exhibits the widest stable window across all tested flow rates, while the 300 µm condition is highly susceptible to instability, especially at lower flow rates. This observation aligns with earlier velocity field analysis, where narrower gaps suppressed upstream meniscus motion and promoted meniscus stability. These results confirm that precise gap control is crucial in multilayer ceramic AM, especially when dealing with hydrophobic dried alumina layers that amplify coating instabilities.
The present study examined a 50 wt% alumina slurry. Higher solid loadings (>60 wt%) are expected to result in increased viscosity and yield stress, which may lead to a reduced stable coating window and earlier formation of defects such as air entrainment and particle aggregation. Future studies should extend this analysis to more concentrated slurries to map out the coating window as a function of both solid content and rheological properties.