DEM-based modelling framework for spray-dried powders in ceramic tiles industry . Part I : Calibration procedure

This work describes a combined experimental-numerical study to characterize fine spray-dried powder used in the ceramic tile pressing process. A DEM-based granular assembly is endowed with a new set of scaling laws that allows for simulating reliably industrial processes using a much lower number of granules. To do it, a calibration strategy relying on three experimental setups is proposed; (i) compression test of bulk for granule stiffness, (ii) dynamic angle of repose and (iii) image analysis of the powder motion in a rotating drum for the intergranular and granular-boundary sliding and rolling friction coefficients. In order to evaluate the powder motion in a rotating drum, a robust method relying on a direct image analysis is proposed. This methodology makes it possible to quantitatively assess the frictional properties of the powder in contact with different surface materials.


Introduction
The procedure of forming ceramic tiles basically consists of three stages: first, the powder is poured in a mould via a transportation system, secondly it is compacted using a uniaxial hydraulic press and finally, the generated "green tile" is moved to a kiln for the firing stage [1,2].
A C C E P T E D M A N U S C R I P T a review of the calibration procedures can be found in [22], where the existing variety of calibration studies is shown. Nevertheless, the morphology and particle size of the powder ultimately determine the calibration testing setup (due to the computational limits and the required small time increment), and in most cases the multiple parameters involved in the constitutive laws and the assumed simplifications lead to design custom calibration tests according to specific applications and conditions [23]. To the best of authors' knowledge and experience, some sectors like those related to ceramic tile production are currently demanding a straightforward calibration procedure, where micrometric granules with a wide granule size distribution are involved. The current state of the art is lacking of a robust and reliable framework to calibrate DEM models. In that sense, this calibration framework to simulate an industrial process must be straightforward in terms of implementability, namely, the costs involved in the experimental setup arrangement and test execution time of the material parameter identification must be as low as possible.
In DEM, the most widely used model to describe the powder dynamics is the linear spring-dashpot (LSD) model [5]. To calibrate the LSD model, confined axial compression tests [18,24,17] and shear cell tests [25,26] are widely used, where intergranular stiffness and friction coefficients can be assessed, respectively. The shear cell test is suitable for coarse materials, such as corn [10] or polyethylene pellets [1], with granules of millimeter size. Unfortunately, when finer granules are involved (  1 mm), the shear cell test simulation is computationally unfeasible if real properties are used [27,28]. As the granule size decreases, not only the number of granule increases, but a smaller integration time step is required to simulate successfully the calibration procedure without adding numerical artifacts. For example, Coetzee et al [18] showed a DEM calibration using the direct shear cell with relatively large particles. However, O'Sullivan et al [26] found that when small particles are involved, stability issues (a consequence of the small particle masses in comparison with the contact stiffnesses) and some discrepancies between the real and simulated tests arise, i.e., in the values of the angle of friction and normal stresses obtained from a direct shear cell test.
Another issue associated with the shear tests is the required time to perform a full test, because the longer the elapsed time to perform a test, the longer the simulation. Table 1 shows the estimated time to perform typical tests used to calibrate DEM parameters with different equipments, including the angle of repose test used in this paper. The pre-conditioning step, which is usually applied to remove the packing history of the powder, is not considered (it is normally A C C E P T E D M A N U S C R I P T ignored in the simulations to reduce the computational cost). The dynamic angle of repose is the shortest test, followed by the FT4 rheometer test. The shear cell test can be significantly longer compared to the others. Regarding the FT4, which is a universal powder rheometer, the typical full test duration takes a few minutes but only short cycles are simulated. The confined compression test is also a long test, but no better alternatives to calibrate the stiffnesses have been found in the literature.
This study presents an alternative, faster and straightforward methodology to calibrate powder models composed of granules with a wide range of sizes. The methodology also relies on scaling laws that make it possible to study big granular assemblies typically used in powder-based industrial applications. This paper is organized as follows: section 2 presents the numerical model used to simulate the powder and the scaling laws. Section 3 addresses the experimental part of this work, where the powder material and the setups used to calibrate the model are described. The rolling and sliding friction coefficients of intergranular and granule-boundary were determined using a rotating drum.
With it, measurements of dynamic angles of repose and powder dynamics can be achieved. Section 4 presents the details of the identification parameter process and the results of the calibration. The influence of using different types of wall surface in the powder response is also addressed. This paper concludes by summarizing the main findings as well as the limitations and basic assumptions required for this type of analysis. Additionally, two appendices are included dealing with the computational validation of the used DEM framework. 7 shows the verification of the implemented constitutive equations for the contact law (Scilab script is provided as Supplementary Material) and 8 presents the study of scaling independence. Further details of validation by simulating real mould filling industrial processes will be presented in a forthcoming publication.

Model formulation
The LSD model [6] was selected due to its well-balanced ratio between simplicity from the computational point of view and reliability of its response from the physical point of view. Despite its simplicity, this model has proved efficient and accurate to simulate the powder dynamics [29, A C C E P T E D M A N U S C R I P T 30,31] and powders under low consolidation stresses [32,33]. Its development results in the well-known differential equation of the damped harmonic oscillator. Fig. 1 shows schematically of the forces involved in the interaction between granules.
When two spherical particles, i and j (with diameters i d and j d , respectively) are close to each other, they can collide generating a force ij F and a moment ij  on the contact point. The collision occurs when there is an interpenetration between the particles. The interpenetration value where i r and j r are the position of the particles center and i R and j R are the radii of the particles i and j , respectively.
A granular system is modelled as a set of spatial coordinates i r and angular coordinates i  with = 1,..., p iN , where p N is the total number of particles in the system. The time evolution of these quantities is governed by: In these equations, the summation is extended to the c N particles (or surfaces) in contact with the particle i. i m and i I are the mass and moment of inertia, respectively, and g is the gravity. In this work, adhesive forces are not considered. Moments occurring in (2) are due to tangential and rolling forces.
In the LSD model, the contact forces , ij n F and , ij s F , which are the normal and tangential forces between two particles, can be formulated as: , , The reduced radius * R is calculated as * = / ( ) The rolling quasi-force , ij r F , is defined as: Newton's third law is applied in order to enforce the correct force direction for each

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A C C E P T E D M A N U S C R I P T particle. The boundary surfaces were considered to be granules of infinite mass, infinite radius, and infinite normal stiffness. It is important to note that the directions of the tangential force and the rolling quasi-force from the previous time step () tt  F must be corrected at the new time step [7]. Additionally, the Coulomb criterion (Eqs. (8) and (13)) is applied to truncate the tangential force and the rolling quasi-force with the maximal possible value, i.e. the product of the friction coefficient and the magnitude of the normal contact force. For further details, see [7,32]. In this work the Verlet integration scheme [34] was used, and the time increment t  must be smaller than the critical time increment in order to guarantee numerical stability. For the LSD model, the critical time step [35] is defined as: where m is the mass of the lightest granule and n k is the normal spring elastic constant. In this work, the selected time step was 0.6 crit t  .

Scaling laws
The computational cost of DEM simulations increases with the number of particles in the system.
Unfortunately, many industrial processes of interest typically involve a huge number of particles (more than 10 millions) which cannot be simulated even using the highest current computational resources. For this reason, the application of scaling laws is essential to reduce the number of particles in the system with the aim of simulating industrial processes realistically. To do this, the coarse granule model approach is widely used [8,36]. In this scaling method, the number of particles is reduced by increasing their size, but trying to keep the overall dynamic response unaltered. Recently, Lommen et al. [37] presented another approach of the coarse granule model, which is applied to the Hertz physical model. This novel approach conserves the character of the contact, making it possible to scale correctly particle assemblies. The scaling laws proposed in the present work are fundamentally based in the coarse granule model proposed by Hilton et al. [36].
A real system with r N particles can be reduced to s N particles using the following equation: where  is the scale factor, V and R stand for the volume and radius of the particle, respectively, and the superscripts "r" and "s" refer to "real" and "scaled" variables, respectively. One way to apply the coarse grain model is to keep the mass of the coarse granule constant. In that case, the following relation must hold: where  is the density of the particle. Comparing Eq. (15) with Eq. (16), the following relationship can be obtained: This expression corrects the density of every particle when their volumes change, what leads to the same coarse granule model approach presented by Hilton et al. [36]. Notice that this way enables us to obtain the coarse granule model by changing just the size of the granules and its density.
Another scaling law must be applied in order to keep constant the average coordination number in the system. As it can be observed in the Fig. 2, when the particle size increases while keeping its mass unaltered, the relative overlap (defined as / ij hR ) will decrease, which in turn might decrease the coordination number.
In order to keep the relative overlap constant, the relationship between  and the stiffness coefficient n k is: Therefore, two scaling laws are required to obtain an appropriate similarity between the scaled and the real system. Nevertheless, the scale factor cannot be increased indefinitely and, for each application, it is necessary to determine the minimum number of particles that reproduce the studied effect, since its influence in some experiments, like the angle of repose tests, has been proved [38,39]. This situation would be analogous to what happens during the process of mesh convergence required in simulations based on finite element method. Therefore, when this type of scaling is applied, a preliminary analysis is crucial to determine the maximum applicable scale factor (Appendix B).

Spray-dried powder characterization
A standard porcelain tile powder (Grupo EUROATOMIZADO ® ) was selected. The powder was dried to avoid cohesion effects due to moisture presence, which ranges between 4 and 8 % on a dry basis. Drying was performed in a laboratory oven at 110 °C for 24 hours. A sieve analysis was used to extract the granule size distribution (GSD) of the spray-dried powder. Fig. 3 shows the granule morphology and the GSD. It can be observed that the spray-dried powder is quite spherical, therefore, it was considered appropriate to approximate the shape of the granules to perfect spheres. The density of the granules was measured in laboratory tests, estimating an average value of 1800 kg/m 3 . The GSD was fitted to a log-normal distribution with a number-median distribution of 200 µm and a geometric deviation of 1.43 .

Calibration strategy
Calibration is necessary to approximate the rheological behaviour of simulated powder to the real one. Several experiments were selected to calibrate the model, which ideally should maximize the influence of one or two parameters and minimize the others. They should be short experiments, because DEM simulations require a high computational effort to simulate the necessary amount of particles with small time steps for numerical stability. Despite the use of scaling laws, the simulated macroscopic properties are usually not independent of the scaling factor, therefore, this factor must be reduced until convergence is achieved. Furthermore, experiments must be reproducible. It is worth mentioning that the calibration procedure outlined in this section is intentionally aimed at being straightforward, flexible and computationally less demanding. Therefore, although more complex calibration strategies can be found in [23,18,19], they rarely deal with small particles ( <1 mm) which are relatively common in industrial scenarios and they imply a much higher computational effort, scaling laws and a high variability of the material properties.
For the sake of simplicity, in all simulations the three types of stiffnesses were assumed to be equal to each other ( == n s r k k k ) and the damping coefficient was set to 70 % of the critical damping coefficient, assuming quasi-static conditions [9].
First, the confined compression test was used to evaluate the granule stiffness value. Next, the measurement of the dynamic angle of repose and the powder motion inside a rotating drum was ). All tests were recorded with a video capture system. A color digital Camera (Canon PowerShot S90) was used for image acquisition. The camera was attached to a tripod completely perpendicular to the ground.

Confined compression test
To determine the stiffnesses, compression tests were quasistatically conducted at low pressures [9,24]. A vertical load is applied to the bulk powder confined in a cylindrical container and the bulk material is compressed along the vertical axis. Bulk material strain is associated with the stiffness parameter in DEM simulations. However, in the last cycles when the particle movement was limited, stable hysteresis loops were obtained. Confined Young's modulus E , obtained from stable cycles, can be calculated as: where max  is the maximum axial compression stress, max  is its associated strain, min  the minimum axial compression stress and min  its associated strain.
The pressure limits of the compression cycles were selected in a series of preliminary trials such that, at maximum pressure, no breakage of the spray-dried granules occurred, whilst at minimum pressure the granules were still in direct contact with each other.
The load application rate was very low (1 mm/min). Consequently, the test was conducted under quasi-static conditions implying that the forces were exclusively governed by the intergranular elastic contacts.

Dynamic angle of repose
The dynamic angle of repose or flowing angle is a widely used measure for the flowability characterization of powders by using rotating drums [40,41].
The equipment for measuring the dynamic angle of repose is shown in Fig. 5. The assembly consists of a rotating drum and a variable DC power supply in order to control the drum rotational speed. The drum was constructed with polycarbonate and had an inner diameter of 100 mm and a depth of 44 mm. The powder was inserted into the drum through a movable end plate.
Moreover, sheets of different materials were prepared to cover the inner drum wall in order to analyse the motion and the dynamic angle of repose with different wall materials. In this test, the rotation rate remained constant at 4 rpm with a filling degree of 43 %, which produced a rolling motion with a steady flow. In this type of motion, the dynamic angle of repose can be measured as the angle formed between the horizontal and the inclined plane formed by the particles.
The dynamic angle of repose was determined through the open source image processing software ImageJ [42]. The same procedure was used for both experimental and simulated results.

The area method
The aforementioned rotating drum can be used to obtain more valuable information about the powder, as for example how the powder motion occurs into the drum at different rotational speeds.
With this purpose, an additional methodology called "the area method" is presented here to achieve the powder calibration. The area method consists in tracking the evolution of the cross-sectional area (CSA) of the drum occupied by the powder as a function of the rotational speed of the drum. It must be noticed that the higher the rotational speed, the higher the CSA of the drum occupied by the powder, until centrifugation occurs. Likewise, as long as centrifugation does not occur, the higher the CSA of the drum occupied by the powder, the higher the porosity of the powder bed. In this test the filling degree was also 43 %.
This method brings two advantages over other calibration tests such as the static angle of repose [43,44,45]: firstly, the methodology is fast, because the physical simulation time takes less than 3 seconds; second, this calibration test is purely dynamic, and therefore very suitable to calibrate the powder models undergoing highly dynamic situations (very common for DEM simulations aimed at industrial environments).
In this test, 5 different rotational speeds for the area method were studied: 4, 40, 80, 105 and 116 rpm, which cover a wide range of speeds. Fig. 6 shows the evolution of the powder flow in the drum for every rotation speed. Fig. 7b shows a red circumference, that encloses the area corresponding to the CSA of the drum (CSAdrum), and a black area corresponds to the CSA occupied by the powder. Therefore, the CSA occupied by the powder (CSAoc) can be obtained by the following relationship:

Preparing the cylindrical surfaces
In order to evaluate the coefficients of friction of the granules with different surfaces, cylindrical plates of different materials were collected. Fig. 8 shows four different cylindrical surfaces made of aluminium, polypropylene (PP), polytetrafluoroethylene (PTFE) and granules. Fig. 9 shows a zoomed view of the surface covered by granules.
Among all surfaces, the surface coated with granules has a great interest because it makes possible to obtain the intergranular friction coefficients. The preparation consisted in covering one side of a plastic surface with double-face adhesive tape. Then, the porcelain tile powder was sprinkled over the surface. Finally, the surface was vibrated to homogenize and spread the granules uniformly.
This coating of granules neutralizes the effect of the plastic inner surface of the drum on the behaviour of the powder, in such a way that each granule always interacts with another granule.
For the sake of simplicity, it is assumed that in this drum the inner surface has a major impact on the powder motion than the end plates. Notice that some researchers have identified that, depending on the diameter to depth ratio of the drum, the end plates can exhibit a significant influence on the powder dynamics [46,47].

Simulation details
The DEM simulations were performed on an in-house software developed. The software was implemented using the C++ programming language. A brief computational verification of the

A C C E P T E D M A N U S C R I P T
software is included in Appendix A, which will be extended in a forthcoming paper. Numerical simulations were performed on a cluster with 2 Intel Xeon hexacore E5649 2.53 GHz processors and 48 GB of RAM memory. The operating system was CentOS 6. The code was compiled using g++ 5.2 with the compiler flag -Ofast.

Determination of the stiffnesses
The stiffness of the granules showed in Fig. 3 was determined using the confined compression test described in section 3.2.1. Fig. 10 presents the experimental and numerical force-displacement curves. The first cycle produces a wider deformation range of the granular bed in comparison to the subsequent cycles. This situation is a result of the rearrangement regime of granules. It can be seen that the deformation increases slightly in every applied cycle, until reaching a stationary state.
Once the granular assembly reaches this level of packing, the level of permanent deformation does not increase by applying additional cycles. This means that the deformation produced within a stationary cycle is mostly elastic, and therefore, it should be related to the Young's modulus of the granules. After 3 repetitions, the confined Young's modulus was obtained from the stationary compression cycle. An average value of 45.4 1.5  MPa was measured for the dry spray-dried powder.
This compression experiment was simulated using DEM as described in section 2. A total of six simulations were performed, in which the value of the stiffness was changed between 250 up to 10000 N/m. Fig. 10 shows the curves resulting from the simulations using two extreme stiffnesses. This response agrees very well with the results from other authors [24]. It can be seen that using granules with higher stiffness, the compressibility of the granular assembly decreases accordingly. For all the confined compression test simulations the scale factor was = 27  , simulating a total of 62000 granules. The influence of the intergranular friction coefficients is negligible during this type of test [9]. However, the effect of the granule-boundary frictions had to This assumption implies that the results obtained in systems where the intergranular compressive response plays an important role might not be realistic [29]. Nevertheless, it is expected that the external forces acting on certain applications, like powder dynamics, are small [49,50]. In fact, according with the results observed in Fig. 12, Loomen et al [48] showed that a stiffness reduction can be applied without altering the simulation results as long as only low external forces are involved. However, this reduction should be made cautiously and the model results need to be thoroughly verified against different benchmarks.

A C C E P T E D M A N U S C R I P T
To determine the intergranular friction coefficients ( ,

Determination of the granule-boundary friction coefficients
The same procedure used to obtain , s g g   and , r g g   was performed to determine the pair of (  Similar to section 4.2, these results present again a little variation of the area for a wide range of rotational speeds (from 4 to 80 rpm). Nevertheless, when the rotational speed exceeds 100 rpm (105 and 116 rpm), the differences between the CSA occupied by the powder are noticeable. On the one hand, the difference between using an internal coating of spray-dried powder and aluminium is negligible for all rotational speeds tested. Therefore, the same friction coefficients calibrated previously can be used as friction coefficients for the granule-aluminium contact.
On the other hand, the differences between using PP or PTFE are also very little. The maximum difference is 10 % for a rotational speed of 116 rpm. For the sake of simplicity, the differences were not considered relevant, and the same friction coefficients were assigned for both granule-PTFE and granule-PP contact. Consequently, only the friction coefficients for the polymeric surfaces needs to be determined.
To perform the simulation of the area method in this case the following pairs were selected:  In summary, s,g s   should be increased to be able to reproduce correctly the area method, however, the r,g s   should be decreased to reproduce the dynamic angle of repose (Figs. 17 and  19). As a result, the pair ( r,g s = 0.0001  Table 3 shows the calibrated values of the granule stiffness and the sliding and rolling friction coefficients for the intergranular and granule-boundary contacts. It should be noticed that the stiffnesses for the granule-boundary contact is twice the stiffnesses for the granule-granule. This is because the surfaces are always considered elements infinitely rigid, and the contact stiffness is derived assuming two elastic springs connected in series.

. Discussion of results
On the other hand, the granule-polymer contact involves a drastic reduction of r,g s   , while the effect on s,g s   is, in comparison, negligible. However, as it can be deduced from Figs. 13-19, s,g g   and r,g g   seem to have a higher impact in the model than s,g s   and r,g s   . Finally, the scaling independence study was repeated for the calibrated model, demonstrating the validity of the proposed scaling (Appendix B).

Conclusion
This paper proposes a straightforward methodology to obtain the main parameters of a DEM simulation based on the LSD contact law: the granule stiffnesses and the sliding and rolling friction coefficients of the intergranular and granule-boundary contacts. Currently, DEM simulations cannot handle the real number of particles present in many industrial processes. Therefore, with the aim of making this approach feasible for industrial applications, this paper also proposes a set of scaling laws where the size and the stiffnesses of the granules are conveniently modified. This procedure makes it possible to keep unaltered the dynamic response of the simulated spray-dried powder when the collisional regime dominates over the external confining pressures. This approach demonstrates that only one experimental setup was required to calibrate the powder model: a rotating drum.
To calibrate a spray-dried powder for industrial-oriented purposes, four assumptions have been adopted: (i) the stiffness of all particles in the system is considered equal.
(ii) the damping coefficient is the 70 % of critical damping coefficient assuming quasi-static conditions (no rate-dependency of the restitution coefficient).
(iii)a covered surface of granules is approximately equal to a surface with granular properties.
(iv) the influence of the end plates of the rotating drum is negligible in the powder dynamics compared to the inner surface effect.
This proposal enables the characterization of different types of powders independently of their GSD, just by using a single experimental setup. In this sense, this work not only presents the calibration procedure but also its applicability by testing four types of material surfaces in contact with the powder.
The main advantages of the proposed methodology over others (such as methods based on shear cell tests) to calibrate DEM models are the simplicity of the tests and the short simulation times involved. Furthermore, the presented procedure to calibrate the friction coefficients does not involve external loads, as the shear cell tests do. This is an advantage if the real stiffnesses cannot be used in the simulations as with the tested spray-dried powder, whose real stiffness involves too small time steps to perform feasible simulations. Additionally, the presented procedure is specially A C C E P T E D M A N U S C R I P T suitable to calibrate powder models to be used for simulating highly dynamic processes. This is because the area method presented makes it possible to characterize the powder in a dynamic regime, which can also be adjusted depending on the final application of the model.
Regarding the limitations, the proposed methodology uses a manual image treatment, which involves an inherent error in the measurements depending on the researcher who performs it. It produces, inevitably, less accurate results than the one obtained using a ring shear test, for example. In the future, a way to automate the measurement of the dynamic angle of repose and the image analysis should be investigated. Additionally, other calibration test could be investigated, such as the use of a FT4 rheometer. The authors encourage readers to assess more accurate tests to determine the friction coefficients, but meeting the requirements of easiness and quickness (highly demanded by industrial environments). Furthermore, the proposed methodology does not provide a calibration test for viscous damping, which is fixed at its theoretical value in quasi-static conditions. A customized test should be addressed to properly calibrate this parameter before the calibration of the friction coefficients.
Finally, it is worth mentioning that the proposed scaling laws as well as the simulation strategy are also valid for simulating any powder-based process, independently of their size.
Therefore, it has an immediate applicability in the modelling of large granular flows and in the design of powder equipment.

Acknowledgements
The authors of this paper wish to thank MACER S.L and the CDTI Ministry of Science and Appendix A.1.

Model verification
The purposed model detailed in section 2 was included in a DEM framework developed using the C ++ programming language. To verify the model implementation, a simple test was executed and compared with the same model implemented in Scilab.
The verification test consisted in dropping two vertically aligned particles on a flat surface.
A schematic of the test is depicted in Fig. A.1, where 1 R and 2 R are the radii of the particles 1 and 2, respectively, 1 r and 2 r are the positions, 1  and 2  are the densities, and 1  is the initial angular velocity of the particle 1. Initial conditions and the model parameters used in the verification test are depicted in

Appendix A.2. Benchmarking
DEM framework implementation was verified by comparing it with one of the most widely used software packages for DEM simulations, LIGGGHTS [51]. The verification was made comparing the number of contacts and the total kinetic energy of the particles involved during a silo discharge.
The discharge of the silo consisted in dropping the particles from the silo in a vessel (Fig.   A.3). It is also worth emphasizing that LIGGGHTS does not include exactly the same contact model used in this paper. In order to perform a fairy comparison and use the same contact model in both implementations, some model parameters such as damping coefficient and rolling friction were set to 0 (note that LIGGGHTS considers the tangential damping coefficient, which was also set to 0). Table A.2 includes all model parameters used in the simulation of the silo discharge. On the other hand, Fig. A.5 shows the evolution of the total kinetic energy of the particles during the silo discharge. When the discharge begins, the total kinetic energy increases rapidly, and it gradually reduces as the discharge progresses. The differences between both implementations are small, which are attributable to the different integration schemes used (LIGGGHTS uses the velocity Verlet scheme, while the DEM framework developed uses the basic Verlet scheme).

Appendix B. Scaling independence study
DEM simulations performed in this paper required a granule upscaling to be computationally feasible to simulate realistic industrial processes. Although several granule properties were corrected to keep constant the macroscopic response of the powder bulk, it is essential to ensure that the solution is not affected by the scaling applied. After calibrating the model, the scaling independence study was repeated for each experiment, in order to increase the confidence in the calibrated values and the scaling applied.  found very small (notice that with the calibrated friction coefficients, the resulting coordination number is lower than expected according to the Fig. 12). This proves that, for the values of  tested, the structure of the scaled powder bulk represents very well the unscaled one.
The scaling effect of the calibrated model in the dynamic angle of respose and in the CSA of the drum occupied by the powder are shown in is observed between a model where the diameter of the granules is scaled twice and another one in which it is scaled four times, although the granule distribution pattern remains the same (Fig. B.3).
The influence of the scale factor in the dynamic angle of repose may be related to the nature of the measure, which depends on the size of the powder [40]. Nevertheless, according to the Table B Table 3. Calibrated parameters of the model.

Granule-Granule Contact
Granule density, g

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Research highlights ► A novel methodology to calibrate DEM simulations is proposed.
►The methodology is focused on systems with low particle size (Φ<1mm).
►Scaling laws required to reduce the number of particles to simulate are shown.
►Spray-dried powder behaviour with several surfaces is investigated.