Drying Behaviour of Al 2 O 3 Inks Containing Carboxymethylcellulose (CMC) for Use in Colloidal Processing

: One of the most important steps in the extrusion processing of ceramic inks is the initial drying of the ceramic parts. This study aimed to investigate the drying behaviour of an Al 2 O 3 - based ceramic ink optimised to be processed by extrusion processing methods, e.g., direct ink writing. Carboxymethylcellulose (CMC) was singly added to a suspension of deionised water and Al 2 O 3 (50:50 wt.%) to perform as a dispersing and plasticising agent. To assess moisture loss as a function of time, the ceramic inks were extruded into two types of polymeric moulds: one with a completely closed proﬁle producing cylindrical samples (disks) and one with an open proﬁle producing ceramic bars. After the injection of the inks, the moulds were exposed to different controlled temperatures (20 and 40 ◦ C) for up to 180 h; moisture loss and warpage were periodically measured, and exponential mathematical expressions (moisture loss × drying time) were obtained. The Al 2 O 3 -bars dried for 24 h in open moulds at 20 and 40 ◦ C presented longitudinal warpages of 4.5% and 9%, respectively, while the Al 2 O 3 disks dried in closed moulds presented warpages of 3.5% and 7% in these same temperatures (20 and 40 ◦ C, respectively). The samples were sintered at 1610 ◦ C for 4 h and characterised by scanning electron microscopy (SEM), relative density (Archimedes principle), and X-ray diffraction (XRD), presenting a relative density of 92.3 ± 0.5%, α -Al 2 O 3 as crystalline phase and grain with equiaxed morphology varying between 1 and 5 µ m.


Introduction
Rapid prototyping processes based on the additive manufacturing (AM) layer-bylayer principle are characterised by their potential to process customised parts on near-net shapes [1][2][3]. Robocasting, also known as direct ink writing (DIW), is an AM technique based on the direct extrusion of highly concentrated ceramic slurry (ink) through computercontrolled layer-by-layer deposition used to build 3D structures [4][5][6]. In recent years, this technique has attracted much attention as an efficient route to manufacture 3D porous parts or open structures such as scaffolds [7][8][9], as well as multi-layered materials [10,11]. However, there are three major technical limitations to the use of this technique in certain applications: (i) difficulty in achieving full densification, (ii) poor surface quality, and (iii) low geometric fidelity in relation to the reference model (warpage), which is associated with the huge shrinkage observed during the drying and sintering steps [12].
The colloidal processing route is the usual choice for the development of extrudable ceramic ink's [13][14][15][16][17][18]. In this type of processing, anionic and cationic surfactants are added in different and successive steps, depending on the surface charge of the material to be The preparation of the inks for robocasting was carried out by dispersing the Al 2 O 3 powder in CMC aqueous solution, resulting in a gel with pseudoplastic behaviour. According to the supplier, the aqueous solution containing 2 wt.% CMC presents viscosity in the range of η = 1-3 Pa s, which is usually a satisfactory base for inks applied in robocasting. However, the inks prepared in this study at this CMC concentration were unsuitable for extrusion, and the formed parts did not maintain their shape. To achieve the correct rheological behaviour, the CMC concentration was raised stepwise (0.5 wt.%) until smooth filaments with no superficial cracks and good shape retention were achieved. Figure 1 shows the obtained inks and extruded parts.
Spain) were used to develop the ceramic inks. The manufacturer's information regarding the purity of the Al2O3 powder is shown in Table 1. The alumina powder was characterised for particle size distribution using a laserscattering particle size distribution analyser (LA-950; Horiba Ltd., Longjumeau, France), and particle morphology was analysed using a scanning electron microscope (SEM). In addition, the crystallographic composition was analysed via X-ray diffraction (XRD).

Al2O3 Ink Preparation
The preparation of the inks for robocasting was carried out by dispersing the Al2O3 powder in CMC aqueous solution, resulting in a gel with pseudoplastic behaviour. According to the supplier, the aqueous solution containing 2 wt.% CMC presents viscosity in the range of η = 1-3 Pa s, which is usually a satisfactory base for inks applied in robocasting. However, the inks prepared in this study at this CMC concentration were unsuitable for extrusion, and the formed parts did not maintain their shape. To achieve the correct rheological behaviour, the CMC concentration was raised stepwise (0.5 wt.%) until smooth filaments with no superficial cracks and good shape retention were achieved. Figure 1 shows the obtained inks and extruded parts. Initially, the deagglomerated Al2O3 powder was weighed on a precision scale (series M, MW; WebLabor, Brazil). In parallel, a solution of 5 wt.% CMC and deionised water Initially, the deagglomerated Al 2 O 3 powder was weighed on a precision scale (series M, MW; WebLabor, Brazil). In parallel, a solution of 5 wt.% CMC and deionised water was prepared using a magnetic stirring bar until homogenisation (~30 min). During stirring, the suspension was kept at 40 ± 1 • C to facilitate the solubilisation of the polymer in water. As a result of this procedure, a thick gel with 3.1 vol.% CMC was obtained. After that, an ink was formulated by gradually adding Al 2 O 3 powder to the gel aiming to prevent powder agglomeration. The proportion of the final mix was 50 wt.% gel and 50 wt.% Al 2 O 3 powder.

Moulding of the Al 2 O 3 Samples
Two models of moulds were used in this study, one open and the other closed, aiming to simulate extreme heat exchange situations during the drying process to which the extruded moulds are subjected. It was decided to create different geometries of alumina samples depending on the mould used: (1) Open moulds allowed for obtaining ceramic bars. The two-part geometry of the mould facilitated the observation of warping during the drying time. (2) Cylindrical samples (disks) with a surface area different from the bars were obtained from closed moulds.
The moulds employed in the drying tests were produced on an FDM 3D printer (Ender 5 Pro; Creality, Shenzhen, China) with an ABS filament. Figure 2 shows designs and photos of the moulds printed by FDM. A commercial medical syringe (Ø 1.5 mm) was used to simulate the use of robocasting equipment. To this end, the ink was deposited in the syringe and extruded into the moulds until complete filling. vent powder agglomeration. The proportion of the final mix was 50 wt.% gel and 50 wt.% Al2O3 powder.

Moulding of the Al2O3 Samples
Two models of moulds were used in this study, one open and the other closed, aiming to simulate extreme heat exchange situations during the drying process to which the extruded moulds are subjected. It was decided to create different geometries of alumina samples depending on the mould used: (1) Open moulds allowed for obtaining ceramic bars. The two-part geometry of the mould facilitated the observation of warping during the drying time. (2) Cylindrical samples (disks) with a surface area different from the bars were obtained from closed moulds.
The moulds employed in the drying tests were produced on an FDM 3D printer (Ender 5 Pro; Creality, Shenzhen, China) with an ABS filament. Figure 2 shows designs and photos of the moulds printed by FDM. A commercial medical syringe (Ø 1.5 mm) was used to simulate the use of robocasting equipment. To this end, the ink was deposited in the syringe and extruded into the moulds until complete filling.

Drying and Dilatometry
All moulds used in the drying tests were initially weighed on a precision scale of −0.001 g (series M, MW; WebLabor, Mogi das Cruzes, Brazil) and the weight of the experimental devices was registered. The optimised ceramic inks were injected into each mould, and the sets (mould plus ink) were weighed-this point was considered time 0.
The sets of open and closed moulds were placed in a drying furnace and kept at controlled temperatures of 20 and 40 °C for up to 7.5 days. At minimum intervals of 15 min, all sets of moulds were weighed and then replaced in their respective furnace. Thus, after 7.5 days, curves of mass loss (moisture) as a function of drying time were constructed.
The warpage profile of the green samples processed in an open mould was determined as a function of the drying time from the warpage rate (WR) [33,34], as evidenced on Figure 3, which was defined by:

Drying and Dilatometry
All moulds used in the drying tests were initially weighed on a precision scale of −0.001 g (series M, MW; WebLabor, Mogi das Cruzes, Brazil) and the weight of the experimental devices was registered. The optimised ceramic inks were injected into each mould, and the sets (mould plus ink) were weighed-this point was considered time 0.
The sets of open and closed moulds were placed in a drying furnace and kept at controlled temperatures of 20 and 40 • C for up to 7.5 days. At minimum intervals of 15 min, all sets of moulds were weighed and then replaced in their respective furnace. Thus, after 7.5 days, curves of mass loss (moisture) as a function of drying time were constructed.
The warpage profile of the green samples processed in an open mould was determined as a function of the drying time from the warpage rate (WR) [33,34], as evidenced on Figure 3, which was defined by: where H max is the maximum height of the warpage and L is the length of the green body after drying. At different times, images of the samples were obtained using a digital camera, and the digitised images were compared using Image J software [35]. Thus, the H max values were determined and applied to Equation (1). The obtained dry samples, rectangular bars, were measured using a calliper (Absolute Digimatic; Mitutoyo Sulamericana, Suzano, Brazil). Since all dried samples had maximum dimensions of 6 × 6 × 20 mm, representative samples were subjected to dilatometric analysis (DIL 402; Netsch, Selb, Germany) in an argon atmosphere, adopting the sintering cycle shown in Table 2. Shrinkage was measured on a linear variable differential transducer (LVDT) with a sensitivity of 0.01 mm. Tests were performed in duplicate. After the dilatometry tests, the samples were re-sintered at 1610 • C for 4 h in a conventional oven (MAITEC F1650, São Carlos, Brazil) to complement the densification, using a heating rate of 10 • C/min.

= × 100%
where Hmax is the maximum height of the warpage and L is the length of the gre after drying. At different times, images of the samples were obtained using a camera, and the digitised images were compared using Image J software [35]. T Hmax values were determined and applied to Equation (1). The obtained dry samples, rectangular bars, were measured using a callipe lute Digimatic; Mitutoyo Sulamericana, Suzano, Brazil). Since all dried samp maximum dimensions of 6 × 6 × 20 mm, representative samples were subjected tometric analysis (DIL 402; Netsch, Selb, Germany) in an argon atmosphere, a the sintering cycle shown in Table 2. Shrinkage was measured on a linear variabl ential transducer (LVDT) with a sensitivity of 0.01 mm. Tests were performed i cate. After the dilatometry tests, the samples were re-sintered at 1610 °C for 4 h i ventional oven (MAITEC F1650, São Carlos, Brazil) to complement the densifica ing a heating rate of 10 °C/min. The density of the sintered samples was characterised according to the Arch principle [36]. The relative density values of the samples were determined by a 3.98 g/cm 3 as the theoretical density for α-alumina [37].
For microstructural evaluation, the sintered samples were ground and p with SiC sandpaper and diamond suspensions (3 and 1 μm). The conditioned were then thermally etched at 1575 °C for 15 min at a heating rate of 25 °C/min. T undesirable poor conduction of the electron beam, a thin layer of gold was depo the sample surfaces using a K550X metalliser (Quorum Technologies, Lewes, UK a 30 mA current for 2 min. The microstructure of the sintered samples was ana an SEM/FEG microscope (JSM-7100FT; JEOL, Peabody, MA, USA).
The crystallographic composition of the sintered samples was identified usin ray diffractometer (X'Pert PRO; Malvern Panalytical, São Paulo, Brazil) equipped CuKα (λ = 1.54 Å) cathode-ray tube. The diffraction spectra were measured in th 2θ range with an angular step width of 0.01° at an acquisition time of 50 s/step. tected crystalline phases were identified by comparing them with standard cr graphic data obtained from the PDF-4-ICSD database, employing Crystal Ma software.  The density of the sintered samples was characterised according to the Archimedes principle [36]. The relative density values of the samples were determined by adopting 3.98 g/cm 3 as the theoretical density for α-alumina [37].
For microstructural evaluation, the sintered samples were ground and polished with SiC sandpaper and diamond suspensions (3 and 1 µm). The conditioned samples were then thermally etched at 1575 • C for 15 min at a heating rate of 25 • C/min. To avoid undesirable poor conduction of the electron beam, a thin layer of gold was deposited on the sample surfaces using a K550X metalliser (Quorum Technologies, Lewes, UK) using a 30 mA current for 2 min. The microstructure of the sintered samples was analysed in an SEM/FEG microscope (JSM-7100FT; JEOL, Peabody, MA, USA).
The crystallographic composition of the sintered samples was identified using an X-ray diffractometer (X'Pert PRO; Malvern Panalytical, São Paulo, Brazil) equipped with a CuKα (λ = 1.54 Å) cathode-ray tube. The diffraction spectra were measured in the 20-80 • 2θ range with an angular step width of 0.01 • at an acquisition time of 50 s/step. The detected crystalline phases were identified by comparing them with standard crystallographic data obtained from the PDF-4-ICSD database, employing Crystal Match 3.12 software. The results of the particle size distribution analysis, Figure 4a, show a mean size of 1.47 ± 1.1 µm and a bimodal distribution. The two modes are centred at 0.65 and 2.1 µm with a maximum variation of particle sizes between 0.41 and 2.59 µm, respectively. Complementarily, Figure 4b suggests that the morphology of the commercial powder particles resembles semi-spherical shapes with morphological reproducibility. In addition, the X-ray diffractogram, Figure 4c, presents α-Al 2 O 3 (hexagonal) as the only detectable crystalline phase. Figure 4 presents the particle size analysis, XRD, and SEM micrograph representative of the morphology of the Al2O3 particles used in this study. The results of the particle size distribution analysis, Figure 4a, show a mean size of 1.47 ± 1.1 μm and a bimodal distribution. The two modes are centred at 0.65 and 2.1 μm with a maximum variation of particle sizes between 0.41 and 2.59 μm, respectively. Complementarily, Figure 4b suggests that the morphology of the commercial powder particles resembles semi-spherical shapes with morphological reproducibility. In addition, the X-ray diffractogram, Figure 4c, presents α-Al2O3 (hexagonal) as the only detectable crystalline phase.   Drying occurs through the displacement of moisture from the inside of the material to its surface-moisture evaporation and shrinkage in the material [38]. The rate of these retractions should be controlled during the drying process to avoid the appearance of defects in the final product [39]. The drying curve is a graph that correlates the moisture content of the ceramic material as a function of time. Figure 5a shows the drying curves of the extruded Al 2 O 3 ink in both the open and closed moulds at temperatures of 20 and 40 • C. The drying curves present two distinct periods for each temperature. In the first stage, the surface is covered by a continuous water film, and moisture evaporation occurs on the surface of the body, with a linear and constant drop in mass loss caused by a high drying rate. This is the most critical period of the drying process, as it is when defects can occur in the parts, such as fractures and cracks arising from shrinkage; therefore, the use of low temperatures is recommended in this stage [40]. In the second stage, the drying rate decreases, and shrinkage ceases; all moisture, i.e., residual water in capillaries and surface water, is completely removed. In this way, evaporation begins inside the solid material, and the vapour reaches the surface by diffusion through the pores [40]. Figure 4c shows the drying curves of the closed moulds. The first period of the curve occurs at 0-50 h and 180 h, respectively, for temperatures of 40 and 20 • C. Samples in the closed moulds presented a lower drying rate when compared with those on the open moulds. Thus, more time was needed for the former to reach the second period of the curve, where shrinkage ceases. This occurred because the magnitude of the first drying stage was dependent on the area of material that was exposed to drying. It is worth noting that this comparative analysis is not conclusive, given that the heat exchange conditions were different between the two types of moulds and the geometry and surface area of the samples in both cases were different. Drying occurs through the displacement of moisture from the inside of the material to its surface-moisture evaporation and shrinkage in the material [38]. The rate of these retractions should be controlled during the drying process to avoid the appearance of defects in the final product [39]. The drying curve is a graph that correlates the moisture content of the ceramic material as a function of time. Figure 5a shows the drying curves of the extruded Al2O3 ink in both the open and closed moulds at temperatures of 20 and 40 °C. The drying curves present two distinct periods for each temperature. In the first stage, the surface is covered by a continuous water film, and moisture evaporation occurs on the surface of the body, with a linear and constant drop in mass loss caused by a high drying rate. This is the most critical period of the drying process, as it is when defects can occur in the parts, such as fractures and cracks arising from shrinkage; therefore, the use of low temperatures is recommended in this stage [40]. In the second stage, the drying rate decreases, and shrinkage ceases; all moisture, i.e., residual water in capillaries and surface water, is completely removed. In this way, evaporation begins inside the solid material, and the vapour reaches the surface by diffusion through the pores [40]. Figure 4c shows the drying curves of the closed moulds. The first period of the curve occurs at 0-50 h and 180 h, respectively, for temperatures of 40 and 20 °C. Samples in the closed moulds presented a lower drying rate when compared with those on the open moulds. Thus, more time was needed for the former to reach the second period of the curve, where shrinkage ceases. This occurred because the magnitude of the first drying stage was dependent on the area of material that was exposed to drying. It is worth noting that this comparative analysis is not conclusive, given that the heat exchange conditions were different between the two types of moulds and the geometry and surface area of the samples in both cases were different. Mathematical adjustments of the drying curves (moisture loss as a function of time) were performed using the exponential expression represented by Equation (2) for both moulds (open and closed) at different temperatures.

Moisture Loss
The results obtained in this work can be represented using Equations (3) and (4) for open moulds and Equations (5) and (6) for closed moulds, thus making it possible for drying times between 0 and 180 h to determine, with a good fit, what will be the moisture loss of a green body for a given drying time.
where M is moisture loss (%) and t corresponds to a certain drying time (hours).

Warpage
The samples dried in the open moulds, which showed a higher drying rate, were compared as a function of the drying temperature employed. Based on the digitised images presented in Figure 6, a preliminary analysis of the warping degree was performed. Using the procedure described in the ABNT-NBR 14698 standard [41] to verify warping in tempered glasses, the approximate warping degrees for samples dried in closed moulds at different temperatures (20 and 40 • C) were evaluated using scanned images. The results of this warpage analysis as a function of drying time for open moulds are shown in Figure 7. where M is moisture loss (%) and t corresponds to a certain drying time (hours).

Warpage
The samples dried in the open moulds, which showed a higher drying rate, were compared as a function of the drying temperature employed. Based on the digitised images presented in Figure 6, a preliminary analysis of the warping degree was performed. Using the procedure described in the ABNT-NBR 14698 standard [41] to verify warping in tempered glasses, the approximate warping degrees for samples dried in closed moulds at different temperatures (20 and 40 °C) were evaluated using scanned images. The results of this warpage analysis as a function of drying time for open moulds are shown in Figure 7.   It is possible to observe that the warpage was more pronounced in the first 10 h of drying, regardless of the drying temperature adopted. The first hours of drying were considered critical to determining the dimensional quality of the green bodies since the shrinkage variation between the surface and the volume of the green bodies was accentuated. As expected, drying performed at temperatures of 40 °C presented total warpage rates two orders of magnitude higher than samples dried at temperatures of 20 °C, It is possible to observe that the warpage was more pronounced in the first 10 h of drying, regardless of the drying temperature adopted. The first hours of drying were considered critical to determining the dimensional quality of the green bodies since the shrinkage variation between the surface and the volume of the green bodies was accentuated. As expected, drying performed at temperatures of 40 • C presented total warpage rates two orders of magnitude higher than samples dried at temperatures of 20 • C, which led to significantly higher distortions in the dry samples, as observed in Figure 6b,c.
Because of the difficulties of intermediate warpage measurements on disks obtained from closed moulds, intermediate warpage measurements were not carried out. However, after 24 h of drying (Figure 6d), the warpage measured as a function of the reference geometry was estimated to be around 3.5% and 7% for drying temperatures of 20 and 40 • C, respectively. Some strategies to control the drying of extrudable inks have been used to avoid significant warping of Al 2 O 3 and ZrO 2 pieces produced by additive manufacturing automatically controlled extrusion processing techniques, such as direct ink writing. Between these approaches, the control of humidity in the air and the application of steam during the processing of ceramic pieces were investigated in previous works [10,11]. This strategy effectively reduces the warpage of the green body during processing, as well as in the first hours of drying; however, the temperature control extended for the first 10 h can be a primordial factor for the green body to have the least possible distortions.
The results presented in this investigation are limited to evaluating extreme drying behaviours and their interference in the final warping of an alumina ceramic piece. The choice of the appropriate condition should take into account the dimensional accuracy of the parts and the final surface finishing step usual in parts printed by DIW.
Considering possible industrial applications of Al 2 O 3 ceramic pieces obtained by DIW using Al 2 O 3 -H 2 O-CMC inks, the volume of printed material, the final dimensions of the piece and the need for subsequent stages of surface finishing should not be neglected, but the control of the rate of drying should be prioritised. Figure 8 shows the characteristic dilatometry curve of the sample obtained with the Al 2 O 3 -H 2 O-CMC inks. The analysis of the shrinkage curves of the moulded samples after the dilatometric tests showed swelling at temperatures close to 200 • C, which could be associated with the accommodation of the powder particles as a result of the output of the residual molecular water atomically present in the particulate system and which was not eliminated under the drying conditions imposed to the samples during the drying test. A change in the shrinkage behaviour could be noticed around 700 • C, which is related to the evaporation of the CMC additive [42]. The most pronounced shrinkage, which is characterised by the action of the densification mechanisms associated with sintering, began at temperatures >870 • C and continued until test interruption at 1100 • C, indicating the occurrence of material densification in this region. As the objective of this study was to evaluate shrinkage during the heating of the ink, the tests were interrupted at 1100 • C. Then, the samples were sintered at 1610 • C for 4 h, when the final densification of the ceramic was reached. Characterisation results of the sintered samples are shown in Figure 9. A microstructure composed of equiaxed Al2O3 grains with sizes varying between 1 and 5 μm is observed. The XRD pattern suggests α-Al2O3 (hexagonal) as the only crystalline phase present after sintering at 1610 °C for 4 h. These results agree with those reported for alumina ceramics developed by conventional compaction and sintering processes [43].  Figure 10 shows Characterisation results of the sintered samples are shown in Figure 9. A microstructure composed of equiaxed Al 2 O 3 grains with sizes varying between 1 and 5 µm is observed. The XRD pattern suggests α-Al 2 O 3 (hexagonal) as the only crystalline phase present after sintering at 1610 • C for 4 h. These results agree with those reported for alumina ceramics developed by conventional compaction and sintering processes [43]. Characterisation results of the sintered samples are shown in Figure 9. A microstructure composed of equiaxed Al2O3 grains with sizes varying between 1 and 5 μm is observed. The XRD pattern suggests α-Al2O3 (hexagonal) as the only crystalline phase present after sintering at 1610 °C for 4 h. These results agree with those reported for alumina ceramics developed by conventional compaction and sintering processes [43]. Regarding relative density, the values observed for the samples submitted to drying in open and closed moulds at 20 and 40 • C did not show statistically significant differences and, in general, were on the order of 92.3 ± 0.5% (1610 • C for 4 h). Figure 10 shows the individual relative density measured for samples obtained via the colloidal processing route using the Al 2 O 3 -CMC inks, as well as for a group of samples obtained by the powder technology route, conventional uniaxial compaction (100 MPa), using the same raw material shown in Table 1 and sintered at 1610 • C for 2 h (a heating rate of 10 • C/min). As expected, the compacted products resulting from the samples presented higher relative density, on the order of 97.6 ± 0.3%, because of the higher degree of packing of the particles existing in the green compacted product in relation to that of the ceramic ink developed in this study, which had a solid content of 50 wt% and thus hindered the elimination of the pores existing in the green body compared with the compacted products. However, the values obtained in this study are on the same order of magnitude as those reported in previous studies for extrudable ceramic inks [44] and, depending on the final application intended for the sintered alumina, they may be adequate and viable.

Conclusions
Exponential mathematical expressions modelling drying behaviour for extrudable alumina inks composed of Al2O3 (particle size of 1.47 ± 1.1 µ m) + H2O + CMC were obtained using 20 °C and 40 °C as room temperatures using different geometry Al2O3 samples (bars and disks).
The use of opened moulds to dry the alumina samples enabled moisture elimination after 30 h (20 °C) and 10 h (40 °C). On the other hand, despite the longer drying time observed in the samples dried at 20 °C, the accumulated warping after 24 h of drying was 4.5%, while the samples dried at 40 °C showed 9% of warping after the same period, representing a greater loss of dimensional quality. The use of closed moulds (alumina disks) systematically increased the time required for the complete drying of the samples, presenting moisture elimination after 180 or 50 h, respectively, with slight gains in dimensional quality, with warpage of around 3.5% and 7%, for samples dried at 20 °C and 40 °C respectively.
The sintering results indicated that the relative density values of alumina did not present statistically significant differences for the drying temperature or the external environment in which the extruded samples were conditioned. Given the increasing use of AM techniques, the creation of specific drying curves for different ceramic systems is an interesting tool to predict indices of shrinkage, warping and densification, thus optimising the construction of ceramic parts with a high degree of complexity.
Supplementary Materials: The following supporting information can be downloaded at: www.mdpi.com/xxx/s1, Table S1. Weight of the moulds and inks at the initial and final parameters of the drying tests.

Conclusions
Exponential mathematical expressions modelling drying behaviour for extrudable alumina inks composed of Al 2 O 3 (particle size of 1.47 ± 1.1 µm) + H 2 O + CMC were obtained using 20 • C and 40 • C as room temperatures using different geometry Al 2 O 3 samples (bars and disks).
The use of opened moulds to dry the alumina samples enabled moisture elimination after 30 h (20 • C) and 10 h (40 • C). On the other hand, despite the longer drying time observed in the samples dried at 20 • C, the accumulated warping after 24 h of drying was 4.5%, while the samples dried at 40 • C showed 9% of warping after the same period, representing a greater loss of dimensional quality. The use of closed moulds (alumina disks) systematically increased the time required for the complete drying of the samples, presenting moisture elimination after 180 or 50 h, respectively, with slight gains in dimensional quality, with warpage of around 3.5% and 7%, for samples dried at 20 • C and 40 • C respectively.
The sintering results indicated that the relative density values of alumina did not present statistically significant differences for the drying temperature or the external environment in which the extruded samples were conditioned. Given the increasing use of AM techniques, the creation of specific drying curves for different ceramic systems is an interesting tool to predict indices of shrinkage, warping and densification, thus optimising the construction of ceramic parts with a high degree of complexity.

Supplementary Materials:
The following supporting information can be downloaded at: https:// www.mdpi.com/article/10.3390/ceramics6020055/s1, Table S1. Weight of the moulds and inks at the initial and final parameters of the drying tests.