A Combined Experimental and Modeling Study for Pellet-Fed Extrusion-Based Additive Manufacturing to Evaluate the Impact of the Melting Efficiency

To improve the product quality of polymeric parts realized through extrusion-based additive manufacturing (EAM) utilizing pellets, a good control of the melting is required. In the present work, we demonstrate the strength of a previously developed melt removal using a drag framework to support such improvement. This model, downscaled from conventional extrusion, is successfully validated for pellet-based EAM—hence, micro-extrusion—employing three material types with different measured rheological behavior, i.e., acrylonitrile-butadiene-styrene (ABS), polylactic acid (PLA) and styrene-ethylene-butylene-styrene polymer (SEBS). The model’s validation is made possible by conducting for the first time dedicated EAM screw-freezing experiments combined with appropriate image/data analysis and inputting rheological data. It is showcased that the (overall) processing temperature is crucial to enable similar melting efficiencies. The melting mechanism can vary with the material type. For ABS, an initially large contribution of viscous heat dissipation is observed, while for PLA and SEBS thermal conduction is always more relevant. It is highlighted based on scanning electron microscopy (SEM) analysis that upon properly tuning the finalization of the melting point within the envisaged melting zone, better final material properties are achieved. The model can be further used to find an optimal balance between processing time (e.g., by variation of the screw frequency) and material product performance (e.g., strength of the printed polymeric part).

EAM allows us to overcome several limitations of filament-based AM, which is also known as fused filament fabrication (FFF). Specifically, soft polymers can be manufactured that are difficult to process through traditional 3D printing [19,20]. Printing employing In the process of scaling down SSE, a reduction in the viscous dissipation was thus witnessed in our previous work. This could be made clearer upon comparing the melting profiles for micro-extrusion and conventional extrusion under typical operation conditions for each technique on its own [38], consistent with preliminary results [47]. We also put forward in our previous theoretical study that screw parameters such as the screw frequency and pitch angle and material parameters such as the power-law index influence the relative position of the final EAM melting point.
One can thus not generalize the melting behavior of one polymer directly to another, highlighting the relevance of the development of more generic theoretical frameworks to support the identification of ideal EAM conditions. Furthermore, it can be expected that good printed macroscopic properties require a good melting. Consistent with this, the relevance of an adequate melting was also presented in previous studies for PLA [48] and ABS [49], showing how low printing temperatures can cause a steep decrement in the properties of the final parts. Hence, an understanding of the melting can help to better identify better printing conditions.
In the present work, we therefore further increase the impact of our modeling framework by benchmarking the EAM melt model to in-house determined experimental data. To record these data, we perform a series of so-called screw-freeze experiments [28] to visually inspect the positioning of the solid bed and melt pool at distinct screw positions. The material portfolio is also expanded beyond simply ABS to include several rheological behaviors. The first polymeric material ABS is characterized by an amorphous structure, the second polymeric material is polylactic acid (PLA) which has, in contrast, a semicrystalline structure, and the third polymeric material is styrene-ethylene-butylene-styrene polymer (SEBS), which falls into the class of thermoplastic elastomers. A comparison is included regarding the melting mechanism for the three different materials, through a comparison of the Brinkman number variation [39][40][41][42][43]. Moreover, the quality of the printed parts is related to the melting efficiency, as accessible for any set of operating conditions through application of the modeling framework. In addition, a first step toward a full macroscopic property analysis is included by including imaging and tensile results.

ABS PLA SEBS Unit
Density (at 300 K) 1.01-1.08 1. 22 The micro-extrusion machine geometry is the same for all of the material processing and simulations, and its details are reported in Table 2. The dimensions of the geometry are consistent with our previous work [38] and resemble a typical micro-extruder design.

Melting Model
The melting profile was simulated using the melting model and the micro-extruder geometry described in our previous theoretical study [38]. For completeness, the main model parameters are reported in Table 3, making a differentiation between the three polymer types and extracting values from the previous Tables (Tables 1-6). Essential in the model is the calculation of the melting rate per unit of channel width q:   In this equation, reported from our previous work [38], X is the width of the solid bed (initially X is equal to the channel width W), ρ m is the density of the molten phase, V bx is the velocity of the molten phase at the barrel in the x direction (as reported in Figure  S1 of the Supplementary Materials), λ is the heat of fusion, c m is the specific heat capacity of the molten phase, c s is the specific heat capacity of the solid phase, Θ is the average temperature of the melt that is related to the Brinkman number Br [39][40][41][42][43], T m is the melting temperature, k is the thermal conductivity, and T b is the barrel temperature.
Br is a dimensionless number that indicates the ratio between the viscous heating and the (molecular) conduction heating [39][40][41][42][43]. The viscous heating is generated by the friction between the flowing elements at different velocities and is finally supplied by the engine that turns the extrusion screw. The conduction heat, on the other hand, is supplied by the external heater bands. Br is defined in Equation (2), reported from our previous work [38], and was used to evaluate differences in the melting mechanism between the materials tested.
In Equation (2), η is the shear rate dependent melt viscosity, V j is the velocity difference between the velocity of the solid bed in the z direction V sz and the velocity of the melt layer at the barrel surface V b , n is the pseudo-plasticity index, and δ is the average thickness of the molten layer that can be assessed and updated along the unwounded screw as explained in our previous work [38]. Note that V bx , reported from our previous work [38], is a function of the screw frequency N, the inside diameter of the extruder barrel D b , and the helix pitch angle of the screw θ: It should be stressed that V sz is dependent on the volumetric flow rate at the inlet of the extruder, Q 0 . The value of Q 0 was estimated by assuming stationary conditions in the extruder and weighing the extruded amount for defined intervals of time. Hence, no ball-park value was selected, but for each polymeric material, a true value based on actual steady-state experiments was considered.

Rheological Measurements and Cross Model Fitting
Small amplitude oscillatory shear (SAOS) tests were performed using a MCR 702 rheometer (Anton Paar, Graz, Austria). The storage modulus (G ) and loss modulus (G ) were monitored as a function of frequency (1 × 10 −1 to 6 × 10 2 rad s −1 ), using the parallel plate configuration with a 25 mm diameter, a gap of 1 mm and an amplitude of 1%. The tests were performed under nitrogen atmosphere at the same (target or average) processing temperatures used for the actual EAM experiments utilizing the operating settings as reported in Table 3. The latter table provides an overall summary of parameters directly relevant for the results and discussion. Specifically for ABS, the processing temperature is higher, as preliminary screening has shown that the viscosity is higher. The disks were obtained by compression molding of dried pellets at the same temperatures, considering a diameter of 25 mm and 1 mm thickness. The discs were also dried before the rheological measurements.
As shown by the symbols in Figure 1, the three polymeric materials, with specifications in Table 1, globally have a similar rheological behavior, with the viscosity η exhibiting a shear thinning behavior after the Newtonian region, as is most evident in the case of PLA, shown in Figure 1b. There are, however, keeping in mind the different temperatures at which the curves were obtained, some clear differences in the values for (η 0 ), which is the Newtonian viscosity limit before the critical shear rate (γ cr ). It particularly follows that ABS is considerably more viscous than SEBS, with PLA exhibiting the lowest (η 0 ) value among the three polymeric materials. A previous study [58] observed that the rheological behavior of ABS is strongly dependent on the (average) molar mass of the SAN (styreneacrylonitrile) phase. In particular, an increase in the mass average molar mass of the SAN phase leads to the increase in viscosities under both shear and uniaxial extension. This increment in average molar mass leads to longer SAN chains being grafted onto the PB (poly-butadiene) particles. This results in the formation of a denser structural "network", with a higher yield stress and storage modulus in the low frequency plateau region. For completeness, it is mentioned here that strong shear thinning effects are also indicative of a wide molar mass distribution for the SAN phase [59]. Furthermore, for SEBS, a more complex rheological behavior is recorded in Figure 1c. In a previous work [60], it has been observed that the shear thinning effect in the region between 0.1 and 1.0 rad s −1 is only present at temperatures at which the SEBS' microphase-separated state changes into a single-phase state, which is called the order-disorder transition (ODT). This effect is a strong indication of the presence of several melt structures, and the extreme shear thinning behavior at low shear rates can be associated with a melt yield stress.
The experimental rheological data for each polymer were also used to formally fit a Cross flow model at the selected temperature: In Equations (4) and (5), reported from our previous work [38], η is the shear rate dependent melt viscosity, n is the pseudo-plasticity index (or shear thinning factor), τ* is the critical Cross model stress at the transition to shear thinning, and γ is the shear rate (formally assumed equal to the frequency), whileη 0 is a short notation to retrieve the Newtonian limit thus before the critical shear rate . γ cr . a wide molar mass distribution for the SAN phase [59]. Furthermore, for SEBS, a more complex rheological behavior is recorded in Figure 1c. In a previous work [60], it has been observed that the shear thinning effect in the region between 0.1 and 1.0 rad s −1 is only present at temperatures at which the SEBS' microphase-separated state changes into a single-phase state, which is called the order-disorder transition (ODT). This effect is a strong indication of the presence of several melt structures, and the extreme shear thinning behavior at low shear rates can be associated with a melt yield stress.  Table 1), taking the same temperatures as the (target/average) EAM processing parameters. Fitting parameters via the Cross model listed in Table 3.
The experimental rheological data for each polymer were also used to formally fit a Cross flow model at the selected temperature: * (4) 1 *

(5)
In Equations (4) and (5), reported from our previous work [38], η is the shear rate dependent melt viscosity, n is the pseudo-plasticity index (or shear thinning factor), τ* is the critical Cross model stress at the transition to shear thinning, and γ is the shear rate (formally assumed equal to the frequency), while is a short notation to retrieve the Newtonian limit thus before the critical shear rate . The corresponding fits are highlighted as lines in Figure 1a-c, and the Cross-model parameters are reported in Table 3. It follows from Figure 1 that for ABS and PLA, good  Table 1), taking the same temperatures as the (target/average) EAM processing parameters. Fitting parameters via the Cross model listed in Table 3.
The corresponding fits are highlighted as lines in Figure 1a-c, and the Cross-model parameters are reported in Table 3. It follows from Figure 1 that for ABS and PLA, good descriptions are obtained with the Cross model, but for SEBS, the curve's fit is less accurate. A cross-model only grasps an average overall behavior or one structure, and thus not the ODT.

Thermal Properties
The thermal conductivity k of the polymeric samples was measured using the Transient Plane Source method with a Hot Disk TPS 2500S (Hot Disk, Göteborg, Sweden) according to ISO 22007-2. The conditions of the experiments are reported in Table 4. The k value was obtained by an average of 3 measurements and is assumed to be representative (during the processing) at all temperatures by taking the average over all data in Table 4.
The specific heat capacities c s (solid) and c m (melt), the heat of fusion λ, and the "melting" temperature T m of the polymeric materials were evaluated through differential scanning calorimetry (DSC), using a Polyma DSC 214 from Netzsch. The measurements were obtained using the ASTM standard E1269, which requires three scans: (i) a baseline scan, (ii) a scan using a sapphire standard, and (iii) the sample scan. The specific heat capacity was measured at 300 K, which was the initial temperature of the three materials, and at 460 K, at which all materials were in the molten state. The experiments were conducted at a heating rate of 5 K min −1 . The conditions and results are reported in Table 5. Again, constant (average) values were considered in what follows, further supported by the sensitivity analysis in our previous work [38].
To take into account a possible difference in the PLA crystallinity (special case in Table 1 regarding crystallinity) between the injection molded samples for the Hot Disk and the solid pellets for EAM, further DSC tests were conducted at 10 K min −1 . A variation of only 1.70% was found for the area of the crystalline peak, as shown in Figure S2 in the Supporting Information. The effect of this variation in the PLA crystallinity during the sample preparation was neglected, as previous studies observed a marginal impact of the degree of crystallinity on the thermal conductivity [61]. Moreover, previous studies on the melting mechanisms in SSEs observed that small variations in the thermal conductivity have a neglectable impact on the solid bed profile (SBP) [21,38].

Solid and Melt Density
The density of the solid phase was measured according to the Immersion Method of ISO/DIS 1183-1, weighing the pellets in air and in ethanol as an auxiliary liquid. The weight scale used was a Precisa XR205SM-DR manufactured by Precisa Gravimetrics AG (Dietikon, Switzerland).
A Melt Indexer MPX 62.92 by GÖTTFERT ® (Buchen, Germany) was used to measure the Melt Volume Rate (MVR) of the different polymeric materials under the conditions described in Table 6 Table 6. The final density values were then averaged and used at any temperature for the processing simulations.

Screw-Freezing Experiments
The EAM melting model predictions were validated through a series of screw-freezing experiments that were conducted through rapid water cooling of the operating microextruder (Ghent University, Gent, Belgium). This was performed through water-cooled aluminum bands that were positioned along the extruder barrel, as visible in Figure 2a. After a screw-freezing experiment was completed, the extruder was disassembled. Then, the solidified polymer channel was extracted from the barrel and cut into sections to validate the model predictions on SBP.
The screw freezing technique was first introduced by Maddock for conventional extruders [23]. This technique starts with the extruder running in steady state. The screw rotation is then stopped, and the barrel is air cooled to solidify the polymer in the screw channel. The screw with the solidified polymer is extracted and the cross-sections of the solidified polymer are polished and investigated. In the present work on micro-extruders, the same approach was applied, although some modifications were made. In greater detail to highlight the regions where the polymer was molten, a small amount of PE pigmented feedstock polymer was introduced at a mass ratio of 0.5:100. The solid bed still showed the natural color of the pellets, while the regions where the polymer had melted were strongly colored by the pigment, according to the same principle described in Maddock's study [28]. Additional water-cooling rings were added to the compression and metering sections of the extruder barrel to improve the cooling behavior. The cooling rings were assembled to promote the cooling of the lower section first and then the upper section. The cooling curves for the two sections after EAM competition are depicted in Figure 2b, with the positions of the thermocouples visible in Figure 2d. It follows that a relatively efficient cooling is realized.
For most of the tests with ABS, the solidified polymer channel had a negligible deformation during the extraction process, which allowed for epoxy embedding to better showcase the melting mechanism and the SBP. The embedded samples were finally polished, and a high-resolution scanner was used for the image acquisition, with the results depicted in Figure 2 for three selected screw frequencies. For the tests with PLA, SEBS, and two specific ABS tests, due to the deformations or fractures of the channel during the extraction process, it was impossible to replicate the methodology used for the previous samples mentioned. After cutting and polishing of the sections, the image was acquired through a camera. Examples of sections for the non-embedded samples are visible in Figure S3 of the Supporting Information. The screw freezing technique was first introduced by Maddock for convention truders [23]. This technique starts with the extruder running in steady state. The s rotation is then stopped, and the barrel is air cooled to solidify the polymer in the s channel. The screw with the solidified polymer is extracted and the cross-sections o solidified polymer are polished and investigated. In the present work on micro-extru the same approach was applied, although some modifications were made. In greate tail to highlight the regions where the polymer was molten, a small amount of PE mented feedstock polymer was introduced at a mass ratio of 0.5:100. The solid bed showed the natural color of the pellets, while the regions where the polymer had m were strongly colored by the pigment, according to the same principle described in dock's study [28]. Additional water-cooling rings were added to the compression and tering sections of the extruder barrel to improve the cooling behavior. The cooling were assembled to promote the cooling of the lower section first and then the uppe tion. The cooling curves for the two sections after EAM competition are depicted in F 2b, with the positions of the thermocouples visible in Figure 2d. It follows that a relat efficient cooling is realized.
For most of the tests with ABS, the solidified polymer channel had a negligibl formation during the extraction process, which allowed for epoxy embedding to b Similarly to what was observed by Maddock and Tadmor [28][29][30][31] for conventional extrusion, the polymer melt appears at first sight as a film in between the hot barrel and the compacted pellets, as conceptually shown in Figure 3a. Advancing along the channel, however, the recorded behavior departs from what Maddock and Tadmor observed [28][29][30][31], due to the clear presence of an outer recirculation zone, as conceptually depicted in Figure 3b. This can be explained by the different geometry of the micro-extruder, in particular the conical shape of the screw and barrel that leads to a substantial variation in the velocity profiles, as pointed out in our previous work [38].
Due to the presence of such outer recirculating flow, the width of the molten phase was not constant along the solid bed (in a given screw element), and the percentage of unmolten area over the total area was selected to represent the ratio of the solid bed width and screw width for comparison with the numerical model predictions. The area (A) analysis was executed using the IMAGEJ image processing and analysis software (Version Similarly to what was observed by Maddock and Tadmor [28][29][30][31] for conventional extrusion, the polymer melt appears at first sight as a film in between the hot barrel and the compacted pellets, as conceptually shown in Figure 3a. Advancing along the channel, however, the recorded behavior departs from what Maddock and Tadmor observed [28][29][30][31], due to the clear presence of an outer recirculation zone, as conceptually depicted in Figure 3b. This can be explained by the different geometry of the micro-extruder, in particular the conical shape of the screw and barrel that leads to a substantial variation in the velocity profiles, as pointed out in our previous work [38]. Due to the presence of such outer recirculating flow, the width of the molten phase was not constant along the solid bed (in a given screw element), and the percentage of unmolten area over the total area was selected to represent the ratio of the solid bed width and screw width for comparison with the numerical model predictions. The area (A) analysis was executed using the IMAGEJ image processing and analysis software (Version 1.8.0, U. S. National Institutes of Health, Bethesda, MD, USA) for the different sections. For the non-embedded samples, a different image acquisition interpretation was found to be related to the separation of the two phases, due to the lack of a very clear separation in the color distributions in contrast to the very clear color contrast for the embedded samples. The threshold for these cases was selected based on visual feedback, in coherence with the melting mechanism. Too high or low values of the threshold would, for example, show the presence of molten or solid particles in positions not consistent with the expected melting mechanism.

SEM Analysis of Extruded and Solidified Samples
A Phenom Pro X Desktop Scanning Electron Microscope (SEM) from ThermoFisher Scientific (Waltham, MA, USA) was used to investigate the surfaces of extruded filament samples at different screw frequencies. The images were acquired using a backscatter electron detector (BSD) technique with a beam energy of 15 keV with a magnification of 490:1.
The scope of the analysis was to investigate the presence of surface defects caused by prolonged residence times, or by the presence of solid particles in the metering section. The selected frequencies were 0.5, 5 and 20 rpm, based on model screening, allowing us

SEM Analysis of Extruded and Solidified Samples
A Phenom Pro X Desktop Scanning Electron Microscope (SEM) from ThermoFisher Scientific (Waltham, MA, USA) was used to investigate the surfaces of extruded filament samples at different screw frequencies. The images were acquired using a backscatter electron detector (BSD) technique with a beam energy of 15 keV with a magnification of 490:1.
The scope of the analysis was to investigate the presence of surface defects caused by prolonged residence times, or by the presence of solid particles in the metering section. The selected frequencies were 0.5, 5 and 20 rpm, based on model screening, allowing us to identify the position of the point of melt finalization. Two filament samples were always collected from the extrusion under steady state conditions, at a 15 min interval. The process was repeated using 2 nozzles with 0.8 and 1.5 mm final opening diameter, for a total of 12 samples.

Tensile Testing of the Extruded Filaments
An Instron 5566 tensile machine (Instron, Norwood, MA, USA) was used to investigate the tensile properties of filaments of ABS extruded at different screw frequencies. The method used for the tensile test was based on a previous work [62]. A constant velocity of 10 mm·min −1 was used to evaluate the stress-strain relationship. The gauge length was set at 50 mm. Again, the selected screw frequencies were 0.5, 5 and 20 rpm.

Model Validation Regarding the Point of Melt Finalization for Three Polymeric Materials
Three screw-freezing experiments were first performed for the ABS polymer at a nominal screw speed of 5 rpm, and the results after data analysis are reported in Figure 4a (symbols with connections). The average (mean) values of these experimental results are compared in Figure 4b with the model predictions, inputting the rheological data from Figure 1a (parameters in Table 3). For completeness, these modeled data are also reported in Figure 4a. It follows from Figure 4b  in Figure 4a. It follows from Figure 4b that the melting is performed in the compression section at ca. 250 mm and the decrease in the solid fraction is gradual and sufficiently captured by the model. The details of the image processing steps are provided in Figures  S4-S6 (Table 3).
For ABS, two additional experiments were performed at 2 and 8 rpm to evaluate the effect of an increment and a decrement in the screw speed. The results are depicted in Figure 5a,c directly as average experimental results, also including the model predictions. For the sake of comparison, the ABS results from before at 5 rpm are also repeated in Figure 5b. The details of the image processing are visible in Figure S7 of the Supplementary Materials for the 2 rpm test and in Figure S8 of the Supplementary Materials for the 8 rpm test. In Figure 5, a good agreement is observed between the experimental results and the numerical model prediction for all three screw frequencies, also realizing that a model can wipe out experimental issues, in the present work due to non-embedding.  (Table 3).
For ABS, two additional experiments were performed at 2 and 8 rpm to evaluate the effect of an increment and a decrement in the screw speed. The results are depicted in Figure 5a,c directly as average experimental results, also including the model predictions. For the sake of comparison, the ABS results from before at 5 rpm are also repeated in Figure 5b. The details of the image processing are visible in Figure S7 of the Supplementary Materials for the 2 rpm test and in Figure S8 of the Supplementary Materials for the 8 rpm test. In Figure 5, a good agreement is observed between the experimental results and the numerical model prediction for all three screw frequencies, also realizing that a model can wipe out experimental issues, in the present work due to non-embedding. Closer inspection reveals that the observed final differences between the 2 and 5 rpm results are still safely within the limits of the envisaged melting zone (but with 50 mm difference), while for 8 rpm, a shift in the melting profile to higher values is observed, even up to 300 mm, which is outside the envisaged melting zone.
A further interpretation of Figure 5a-c also enables a better assessment of the experimental errors and the relevance of the melting model. For example, for 2 rpm, the observed difference between the position of the point of melt finalization in the numerical model and the experiments is around 17.9% for the ninth experimental point. Focusing on the eighth experimental point at which the image processing delivers an estimate of 98.89% of molten material, the difference drops to about 8.2%. For 5 rpm, in turn, the observed difference is around 9.2% for the 9th experimental point. Considering the eighth experimental point, at which the molten fraction is estimated as 97.5%, the difference now increases to 18.8%. For 8 rpm, the observed variation is around 1.5% for the 10th experimental point, with the next point exhibiting about 96.4% of solid material and a 0.8% distance from the experimental profile. Hence, one can indeed state that the model filters out natural experimental errors and is a more reliable tool to fully extrapolate the final point of melting.
As shown in Figure S9a of the Supplementary Materials, the accuracy of the simulations' results depends on the correctness of the input parameters. Employing the Q 0 values from Table 3, the modeling outcome is in good agreement with the experimental results (full lines). Instead, the use of ballpark Q 0 values, as considered in previous theoretical work [38], is too approximate (dashed lines). The need of benchmarked input parameters is further highlighted in Figure S11 of the Supplementary Materials, showing that for the ABS case, the use of the PLA and SEBS Q 0 and n values from Table 3 are incorrect. Furthermore, in a previous study on SSEs [63], Mount and Chung also highlighted the importance of the method used to evaluate the solid bed velocity. Closer inspection reveals that the observed final differences between the 2 and 5 rpm results are still safely within the limits of the envisaged melting zone (but with 50 mm difference), while for 8 rpm, a shift in the melting profile to higher values is observed, even up to 300 mm, which is outside the envisaged melting zone.  (Table 3).
A further interpretation of Figure 5a-c also enables a better assessment of the experimental errors and the relevance of the melting model. For example, for 2 rpm, the observed difference between the position of the point of melt finalization in the numerical model and the experiments is around 17.9% for the ninth experimental point. Focusing on the eighth experimental point at which the image processing delivers an estimate of 98.89% of molten material, the difference drops to about 8.2%. For 5 rpm, in turn, the observed difference is around 9.2% for the 9th experimental point. Considering the eighth experimental point, at which the molten fraction is estimated as 97.5%, the difference now increases to 18.8%. For 8 rpm, the observed variation is around 1.5% for the 10th experimental point, with the next point exhibiting about 96.4% of solid material and a 0.8% distance from the experimental profile. Hence, one can indeed state that the model filters out natural experimental errors and is a more reliable tool to fully extrapolate the final point of melting.
As shown in Figure S9a of the Supplementary Materials, the accuracy of the simulations' results depends on the correctness of the input parameters. Employing the Q0 values from Table 3, the modeling outcome is in good agreement with the experimental results (full lines). Instead, the use of ballpark Q0 values, as considered in previous theoretical work [38], is too approximate (dashed lines). The need of benchmarked input parameters is further highlighted in Figure S11 of the Supplementary Materials, showing that for the ABS case, the use of the PLA and SEBS Q0 and n values from Table 3 are incorrect. Furthermore, in a previous study on SSEs [63], Mount and Chung also highlighted the importance of the method used to evaluate the solid bed velocity.  (Table 3).
In view of extra model validation, a single screw freezing experiment has been additionally performed for the PLA and SEBS polymeric materials at the nominal screw speed of 5 rpm. The experimental (symbols) and modeling (lines) data are depicted in Figure 6a,b, again displaying the average experimental results. The corresponding results from the image processing are now visible in Figures S9 and S10 of the Supplementary Materials. It is worthwhile mentioning that while the color distribution for ABS and PLA clearly shows in most cases a bimodal distribution, allowing for a clear separation between the different phases, for SEBS, the threshold for separation between the two phases could only be obtained based on visual feedback. As shown in the Supplementary Materials, the SEBS distribution is not clearly bimodal, and thus this somewhat more arbitrary approach for melt efficiency determination is the most recommended.
It follows from Figure 6a,b that the numerical model predictions are again in good agreement with the experimental data, showing a good overall reliability, taking into account the different morphology of the materials in Table 1 and a wide range of viscosities, as expressed in Figure 1 and Table 3. For PLA, a difference in the position of the experimental and simulated point of melt finalization of about 12.3% is observed, while for SEBS, this difference is about 6.9%. Hence, the model is capable of tackling different material morphologies, highlighting the model's efficacy in preventing experimental errors. Closer inspection shows that the melting for PLA is slightly slower and takes place for longer than the envisaged melting zone, while SEBS melting is still within the envisaged melting zone and is performed at a similar position as for ABS (Figure 5b). Overall, it can thus be concluded that the processing temperature variation in Table 3 allowed us to create similar global behavior in melting. Hence, this operating condition is crucial in the overall design. the image processing are now visible in Figures S9 and S10 of the Supplementary Materials. It is worthwhile mentioning that while the color distribution for ABS and PLA clearly shows in most cases a bimodal distribution, allowing for a clear separation between the different phases, for SEBS, the threshold for separation between the two phases could only be obtained based on visual feedback. As shown in the Supplementary Materials, the SEBS distribution is not clearly bimodal, and thus this somewhat more arbitrary approach for melt efficiency determination is the most recommended.  (Table 3).
It follows from Figure 6a,b that the numerical model predictions are again in good agreement with the experimental data, showing a good overall reliability, taking into account the different morphology of the materials in Table 1 and a wide range of viscosities, as expressed in Figure 1 and Table 3. For PLA, a difference in the position of the experimental and simulated point of melt finalization of about 12.3% is observed, while for SEBS, this difference is about 6.9%. Hence, the model is capable of tackling different material morphologies, highlighting the model's efficacy in preventing experimental errors. Closer inspection shows that the melting for PLA is slightly slower and takes place for longer than the envisaged melting zone, while SEBS melting is still within the envisaged melting zone and is performed at a similar position as for ABS (Figure 5b). Overall, it can  (Table 3).
A detailed model-driven approach is thus within reach if more rheological data and Arrhenius parameters regarding rheology are available, facilitating automated model screening. In this context, the potential of the model is further highlighted in Figure 6c by comparing at different rpm the melting behavior for the three polymeric materials. It follows that the relative trend (melting faster for the order PLA, SEBS and ABS) is always respected but a different rpm threshold can exist for each material type to obey the melting zone idea of the original micro-extruder design.

The Impact of the Polymer Material Type on the Melting Mechanism
Combining the modeled data in Figures 5 and 6, the melting behavior can also be studied at a fixed rpm, varying the material type. This is conducted in the present subsection, specifically at 5 rpm. While the position of the point of melting finalization at 5 rpm moves, e.g., by 8% between ABS and PLA, as shown in Figure 7b, the underlying melting mechanism, as included in Figure 7a, shows a very different behavior. In this subplot, focus is on the variation of Br, with lower values of this number indicative of a higher share of the thermal energy being supplied by the external heater bands compared to the viscous heat generated by friction.
It follows from Figure 7a that the Br values show a very large difference in the heating mechanism for the different materials. While for the ABS material the viscous heat generated is initially still higher than the conduction heat (Br > 1), for the SEBS material, the viscous heat always represents a small fraction, and for the PLA material, it appears to be negligible. The reason for the difference in the melting mechanism can be explained by the differences in the viscosity profiles highlighted in Figure 1, and again highlights the relevance of the rheological curves.

The Impact of the Polymer Material Type on the Melting Mechanism
Combining the modeled data in Figures 5 and 6, the melting behavior can also be studied at a fixed rpm, varying the material type. This is conducted in the present subsection, specifically at 5 rpm. While the position of the point of melting finalization at 5 rpm moves, e.g., by 8% between ABS and PLA, as shown in Figure 7b, the underlying melting mechanism, as included in Figure 7a, shows a very different behavior. In this subplot, focus is on the variation of Br, with lower values of this number indicative of a higher share of the thermal energy being supplied by the external heater bands compared to the viscous heat generated by friction. It follows from Figure 7a that the Br values show a very large difference in the heating mechanism for the different materials. While for the ABS material the viscous heat generated is initially still higher than the conduction heat (Br > 1), for the SEBS material, the viscous heat always represents a small fraction, and for the PLA material, it appears to be negligible. The reason for the difference in the melting mechanism can be explained by the differences in the viscosity profiles highlighted in Figure 1, and again highlights the relevance of the rheological curves.

Impact of Melting Efficiency on 3D Printed Properties
To evaluate the impact that bad melting can have on the final 3D printing applications, the surface of the extruded filament, selecting first a nozzle diameter of 0.8 mm, was analyzed with SEM. For a meaningful comparison, sufficiently different frequencies were selected so that the point of melt finalization is located early in the compression section (0.5 rpm case), at the end of the compression section (5 rpm case; reference case from before), and at the end of the metering section (20 rpm case). This is further confirmed by

Impact of Melting Efficiency on 3D Printed Properties
To evaluate the impact that bad melting can have on the final 3D printing applications, the surface of the extruded filament, selecting first a nozzle diameter of 0.8 mm, was analyzed with SEM. For a meaningful comparison, sufficiently different frequencies were selected so that the point of melt finalization is located early in the compression section (0.5 rpm case), at the end of the compression section (5 rpm case; reference case from before), and at the end of the metering section (20 rpm case). This is further confirmed by the model lines in Figure 8. For the 20 rpm case, in particular, the solid bed at the end of the metering section still accounts for about 0.9% of the section area. The SEM images, always recorded based on data in replicate format, are presented as subplots with the arrows highlighting the rpm value. While the SEM images for both a screw frequency of 0.5 and 5 rpm show a similar surface roughness, the surface for the filament extruded at 20 rpm presents a higher number of defects and a higher roughness. As shown in Figures S15-S17 in the Supplementary While the SEM images for both a screw frequency of 0.5 and 5 rpm show a similar surface roughness, the surface for the filament extruded at 20 rpm presents a higher number of defects and a higher roughness. As shown in Figures S15-S17 in the Supplementary Materials, the same differences in roughness are observed in case the nozzle diameter is equal to 1.5 mm instead of 0.8 mm. It is worthwhile mentioning that no substantial variation in Q 0 was observed after the modification of the nozzle diameter. Hence, limitations exist regarding the melting efficiency to enable good material properties. In other words, the model can be used to identify suited operating conditions, saving experimental screening time and material usage.
Furthermore, the tensile curves in Figure S18 of the Supplementary Materials do not show substantial differences among the different frequencies. It is worthwhile mentioning that the amount of solid material predicted by the numerical model for the micro-extrusion at 20 rpm was under 1% and, due to the high temperature, the melting should have been completed in the filament after the extrusion. A slight increment in the yield strain and a decrement in the modulus with increasing frequency was observed, as shown in Figure 9a,b. These variations can be attributed to the variations in the average diameters of the filaments, caused by the different die swell, as visible in Figure 9c and coherent with previous extrusion work [64]. For higher frequencies, the larger diameters cause an increment in the cooling time, allowing the molecules to partially lose orientation, causing the drop in modulus. During the tensile test, the molecules can then be re-oriented, leading to a higher strain at yield for the larger diameters, and therefore higher frequencies.  Table 3.

Conclusions
Once rheological data are available, an EAM melting model, based on the drag removal principle and accounting for both conduction and heat dissipation, can be utilized  Table 3.

Conclusions
Once rheological data are available, an EAM melting model, based on the drag removal principle and accounting for both conduction and heat dissipation, can be utilized to predict melting efficiencies. This has been confirmed by acceptably describing screwfreezing experiments for ABS under various screw frequencies and for two other polymeric materials, SEBS and PLA, for a fixed screw frequency. Notably, the model can wipe out natural experimental discrepancies, due to the impossibility to sometimes embed screwfreed samples. In any case, reliable model parameters on physicochemical parameters are needed, although sometimes well-measured averages suffice. The EAM melting model can also be employed to perform the design, and here the material type plays a role. A sufficiently high processing temperature is needed to ensure sufficiently low viscosities. The model also allows us to establish the melting mechanism of the studied materials; for ABS only, a short period of a dominant contribution from heat dissipation was observed. The screw-freezing experiments further showcase that under several conditions, an outer circulation flow is present related to the geometry and dimensions of the micro-extruder.
The SEM analysis of the extruded filaments for a set of operating conditions that have a predicted point of melt finalization outside of the envisaged melting zone presents a higher amount of surface defects compared to the filaments obtained via operating conditions with a melting point well within the extruder's limits. These defects can be attributed to the presence of unmolten material within the extruder, confirming the importance of the melting model in the process design of polymeric AM applications. Furthermore, the screw frequency also has an impact of the die swell and the tensile properties.
Hence, the current work highlights the relevance of controlling the melting in the overall process and the need for further material-oriented research to fully design the printing process.
Supplementary Materials: The following are available online at https://www.mdpi.com/article/10 .3390/ma14195566/s1, Figure S1: Definition of x and z direction for the general equations for melt removal by drag, Figure S2: DSC for the PLA pellets and PLA injection molded hot disk sample. The melting temperature was defined as the onset temperature of the melting peak for pellets, Figure S3: Examples of sections of the solidified extruder channel in the micro extruder for a) PLA; b) SEBS, Figure S4: Image processing for ABS 5RPM (not embedded sample 1), Figure S5: Image processing for ABS 5RPM (not embedded sample 2), Figure S6: Image processing for ABS 5 RPM (embedded sample), Figure S7: Image processing for ABS 2RPM (embedded sample), Figure S8: Image processing for ABS 8RPM (embedded sample), Figure S9: Image processing for PLA 5 RPM (not embedded sample), Figure S10: Image processing for SEBS 5RPM (not embedded sample), Figure S11: (a) Relevance of the Q0 parameter; (b) Relevance of the n parameter, Figure S12: SEM Images for ABS extruded filament at 0.5 rpm, 0.8 mm nozzle, Figure S13: SEM Images for ABS extruded filament at 5 rpm, 0.8 mm nozzle, Figure S14: SEM Images for ABS extruded filament at 20 rpm, 0.8 mm nozzle, Figure S15: SEM Images for ABS at 0.5 rpm, 1.5 mm nozzle, Figure S16: SEM Images for ABS at 5 rpm, 1.5 mm nozzle, Figure S17: SEM Images for ABS at 20 rpm, 1.5 mm nozzle, Figure S18: Tensile curves for ABS filament extruded at a) 0.5 rpm; b) 5 rpm; c)20 rpm. Other operating conditions in Table 3 of the main document.

Conflicts of Interest:
The authors declare no conflict of interest.