Analysis of screw feeding of faceted particles by discrete element method

Analysis of screw feeding of faceted particles by discrete element method Alejandro López 1 , Vincenzino Vivacqua 2 , Robert Hammond, Mojtaba Ghadiri⁎ School of Chemical and Process Engineering, University of Leeds, Leeds, UK abstractarticle info Article history: Received 31 July 2018 Received in revised form 19 March 2020 Accepted 30 March 2020 Available online 3 April 2020 Reliable and consistent powder flow in screw feeders is of great interest to a wide range of industries, particularly for continuous manufacturing of pharmaceutical powders. However, analysis of flow of cohesive powders with sharp corners and edges, as commonly found in the case of crystalline solids, presents a great challenge due to complexity of shape and its influence on flow. In the present work, the influence of particle shape and cohesion on phenomena such as cohesive arching in hoppers and screw feeder pitches is analysed by numerical simulations using the Discrete Element Method, and their impact on the outlet mass flow rate is evaluated. Faceted and spherical particles with different cohesion levels are generated and allowed to settle in a hopper on top of a screw feeder. The screw is then rotated, thus feeding the particles through the barrel. Particle interactions are analysed numerically for the hopper region, a predominantly slow-flow regime, and for the pitches of the screw feeder, where a speed-dependent regime prevails. Paracetamol crystal shape is taken as a model faceted shape. Its parameters such as the coefficients of restitution and friction, needed for the simulations, are calibrated by experimental work. Transient arching occurs as the level of cohesion is increased. The frequency of formation and collapse of arches within the hopper region increases, and eventually, permanent arching is observed. Analysis of stress and strain rate in the screw barrel region shows that the shear stress is a weak function of the shear rate with a power index of around 0.3, which is independent of particle shape. The flow rate is influenced considerably by particle shape, whilst increased cohesion causes an increase in void fraction and affects transient arching. © 2020 Elsevier B.V. All rights reserved. Keywords: DEM Screw feeder Cohesion Faceted particles Powder flow 1. Introduction Screw feeders are commonly used in many industries handling and processing powders and grains. This type of feeder is important because it provides a relatively controllable mass flow rate for free-flowing powders [1]. However, fine and cohesive powders tend to cause rat holing and arching [1]. Early studies on the design of mass flow silos and solids handling equipment were carried out by Jenike [2,3], in which stresses at the outlet of hoppers were calculated and the arch span predicted. In his work as well as in Walker's study of pressure distribution and arching [4], the underlying assumption was that powder strength is dependent only on the local stresses in the bulk powder before arching. Based on the same continuum mechanics approach, Enstad [5] analysed arching in hoppers, making a number of assumptions, some of which were not easily verifiable, such as the angle of the footing of the arch on the hopper wall. He developed a model predicting the critical outlet width, for which the powder transitions between arching and flow. His model is more refined than those of previous studies, but still requires bulk powder characterisation. Pharmaceutical powders are highly diverse in bulk properties, and at the early stages of development of new Active Pharmaceutical Ingredients (API), very little powder quantity is available for their bulk characterisation for flowability. Therefore, the ability to predict bulk flow properties from individual particles of an API is highly desirable. This is possible in principle by numerical simulations by the Discrete Element Method, although the use of fine particles in the micrometre size range in the simulations is still very challenging. Nevertheless, by reproducing the conditions leading to arching in hoppers by DEM simulations, a deeper understanding of how transient arching affects the mass flow rate as well as the conditions leading to arching can be achieved. Hou et al. [1] carried out a DEM study of the flow of spherical particles, which were cohesive, in a screw feeder. However, crystals have faceted shapes and are not well represented by spheres. The commercial software Rocky DEM ESSS, Brazil, can model faceted shapes and accounts for the interaction between the sharp edges and corners. The recent analysis by Vivacqua et al. [6] shows that faceted shapes have a strong influence on particle flow behaviour. Thus, this approach is used here to provide a more realistic analysis of flow of particles having such shapes, as relevant to crystalline structures commonly encountered in APIs. Powder Technology 367 (2020) 474–486 ⁎Corresponding author. E-mail address: [email protected] (M. Ghadiri). 1 Current address: University of Deusto, Avenida de las Universidades 24, Bilbao, 48007, Spain. 2 Curent address: Johnson Matthey, Belasis Avenue, Billingham, TS23 1LB, United Kingdom. https://doi.org/10.1016/j.powtec.2020.03.064 0032-5910/© 2020 Elsevier B.V. All rights reserved. Contents lists available at ScienceDirect Powder Technology journal homepage: www.elsevier.com/locate/powtec The system studied in this work is divided into two distinct regions. The first region is that of the hopper on top of the screw feeder, where the flow regime is mainly quasi-static. The second region is the screw feeder, where the flow regime in the screw pitches is more dependent on the rotational speed of the screw. It can fall into the quasi-static flow regime at low speeds, where the shear stress is independent of strain rate [7], and into to the inertial regime if the rotational speed of the screw is high. Here, the powder flow is liquid-like and it has been modelled in a Eulerian frame as a Bingham fluid [8]. The friction coefficient in the rheological model developed by Jop et al. in [8] is a function of a single non-dimensional number called the Inertial number, I,given by Eq. (1). It represents the ratio between the inertial and the macroscopic deformation timescales. I¼ _ γ jj d ffiffiffiffiffi P ρs sð1Þ j_ γjis the second invariant of the strain rate tensor, dis the particle diameter, ρ s is the particle density and Pis the hydrostatic stress, which is calculated as the average of the three principal stresses. The rheology of granular matter under dynamic conditions has been studied both experimentally as well as computationally by Tardos et al. [9]. They analysed granular flow in a Couette device, consisting of two concentric cylinders containing the powder to be analysed in the annular region, with the inner cylinder rotating and the outer one stationary. The shear stress was constant for different rotational speeds in the slow frictional regime. As the strain rate was increased by increasing the speed, the characteristics of the flow moved towards the intermediate and rapid flow regimes, i.e. the shear stress increased more rapidly at large strain rates. More recently, Berger et al. [10] have also studied dense granular cohesive flows under shear strains by means of contact dynamics simulations. They report that the bulk friction, described by the ratio of shear to normal stress, and bulk cohesion represented by a Coulomb-like functional form are both dependent on the strain rate. Also, they proposed a cohesive inertial number to unify the bulk behaviour for different adhesion and strain rate levels. However, validation of the predictions by comparison with experimental measurements has so far not been reported, presumably due to difficulty of testing. For quasistatic bulk powder failure characterisation, there are nowadays a wide range of methods available, such as the unconfined compression test [11], Edinburgh Powder Tester [12], Ball Indentation Method [13], Schulze Shear Cell [14], Jenike powder tester [3] and Environmental Caking Tester [15], Raining Bed Method [16], The Sevilla Powder Tester [17], Brookfield Powder Flow Tester [18], Hosokawa Micron Powder Tester PT-X [19], SSSpinTester-X Powder Strength Tester [20]. In contrast, for dynamic flow characterisation, the commercially available instruments are limited to Freeman Technology FT4 Rheometer [21]and Anton Paar Powder Rheometer [22], as otherwise it is difficult to operate shear cells under dynamic conditions. Recently powder rheometry has been analysed to establish functional relationships between the torque and the work done on the powder and its bulk rheology [22–30]. The aim of the work presented here is to analyse the flow behaviour of cohesive faceted particles inside a screw feeder and explore if its system dynamics can be correlated to the characteristic rheology, i.e. apparent shear viscosity and bulk friction and cohesion as a function of the strain rate, as obtained for example from the FT4 rheometer. 2. Model description 2.1. Discrete element modelling In DEM, the motion of individual particles is obtained through numerical integration of the equations of motion for every individual particle. The forces acting on the particles are calculated accounting for both contact and body forces such as gravity, as Cundall and Strack first proposed in [31]. The translation and rotation of the individual particles are described by Eqs. (2) and (3) [32]: mi dvi dt ¼XFC;iþmigþfpf;ið2Þ dIiωi ðÞ dt ¼RiXMC;iþMpf ;i  ð3Þ where I i : moment of inertia, ω i : angular velocity, m i : particle mass, v i : translational velocity, F C,i : contact force, f pf,i :fluid-particle interaction force, R i : rotation matrix (from global to local coordinate system), M C,i : contact torque, M pf,i : torque due to fluid forces. In the current work, the interaction with the air has been neglected in all cases as the particles are large and hence the influence of air drag is negligible. 2.2. Contact model Amongst the available contact models incorporating adhesion, Rocky DEM has Luding's adhesive contact model [34], which is the one selected in order to account for cohesive forces. This, so called, linear adhesive force model is defined by two parameters [32]: •A minimum adhesive distance for which a force prevails at negative overlap, i.e. when the surfaces of the particles are not touching. It was set to zero in the cases analysed in this work. •A stiffness ratio (or adhesive stiffness, Kadh), which is responsible for the cohesive force. Its effect on the force-overlap graph is shown in Fig. 1. In this adhesive elasto-plastic contact model the force increases with the overlap according to a linear relationship until the maximum overlap is reached. The slope of the unloading part is larger than the loading part and is generally dependent on the maximum overlap. The full original model, as described by Luding in [33]isshowninFig. 2. The corresponding piecewise-linear set of equations describing the model are shown in Eq. (4), where δis the overlap, k 1 and k 2 are the loading and unloading stiffnesses, respectively, and k adh is the adhesive stiffness. Here as well as in [33]f 0 istakenaszeroandthevaluesfornegative overlap (describing the adhesive distance) are neglected, i.e. the value set for the adhesive distance is zero for the simulations carried out here. fhys ¼ k1δif k2δ−δ0 ðÞ ≥k1δ k2δ−δ0 ðÞif k1δNk2δ−δ0 ðÞN−kadhδ −kcδif−kcδ≥k2δ−δ0 ðÞ 8 > < > :ð4Þ Rocky DEM offers the possibility of modelling faceted particles through polyhedral shapes. While for spherical particles, the contact plane is always perpendicular to the line connecting the centres, when non-rounded particles are considered, Rocky DEM calculates one of the following distances in order to assess the contact between them: closest point of two particles, closest point of a particle and a boundary triangle or, if there is physical contact, the points exhibiting the maximum overlap distance [32]. The contact plane will then be perpendicular to the line that connects those points. 3. Simulation parameters As outlined before, faceted particles were chosen for these simulations as the main aim of this research is to simulate the behaviour of API's with crystalline structures with different cohesion levels. In this particular case, the API modelled is paracetamol. However, both spherical particles as well as faceted particles with different values of the 475A. López et al. / Powder Technology 367 (2020) 474–486 adhesive stiffness were simulated. The faceted shape used in the simulations is depicted in Fig. 3(a) and an SEM micrograph of paracetamol crystals is shown in Fig. 3(b) for comparison. The SEM images were taken with the Hitachi Benchtop TM3030 Scanning Electron Microscope. The computational particles are typically defined in Rocky DEM through a series of parameters, which are shown in Table 1. Regarding the simulation parameters, the material properties and interaction coefficients are given in Tables 2 and 3, respectively, while the particle size distribution is shown in Table 4. The coefficient of restitution was calibrated through high speed camera footage. Through image analysis, an average value for the coefficient of restitution was obtained by computing velocities before and after impact for Paracetamol particles. The static sliding friction coefficient was obtained by means of measuring the angle at which Paracetamol particles slide on a plane substrate of the materials of interest, i.e. glass and stainless steel while tilting it at very low speeds. The dynamic sliding friction coefficient was assumed equal to the static value. Since the aim is to compare different cohesion levels and particle shapes made of the same material, Young's modulus was reduced in order to be able to afford a longer time step and considerably increase the computational speed [33]. The geometry chosen for the simulations is that of a typical screw feeder and is shown in Fig. 4. The inlet from which particles are released is situated in the upper part of the hopper and is represented as a red square in Fig. 4. Regarding the cohesive interactions between particles themselves and particles to boundary, the value for the adhesive stiffness was varied between 0 and 0.9. However, it was observed that, due to the nature of the contact model, if the adhesive stiffness was increased over 0.6, the particles were either expelled from the screw feeder as they were generated or stayed inside it indefinitely due to excessively high adhesion forces. Thus, only the simulations with adhesive stiffness values below Fig. 1. Force-Overlap graph for different values of the adhesive stiffness obtained in Rocky DEM for a spherical particle against a wall. Fig. 2. Luding's elasto-plastic adhesive contact model redrawn from [29]. 476 A. López et al. / Powder Technology 367 (2020) 474–486 0.6 were considered. In addition, different screw angular speeds were simulated in order to assess the effect of the strain rate both on the powder flow regime as well as on arching. 4. Results and discussion A series of simulations were set up for the screw feeder geometry shown in Fig. 4 for different values of the adhesive stiffness and rotational speed. In the first part of the results, the rheological characteristics of powder flow of the proposed faceted shapes in the screw feeder is presented in terms of the functional dependence of the shear stress on the strain rate and compared with those obtained from simulations of the Freeman FT4 powder rheometer. Thereafter, an in-depth analysis is carried out of the fluctuations in some of the most important variables of the screw feeder, such as mass flow rate, particle trajectories and velocities and power consumption as a function of adhesive stiffness and rotational speed of the screw. In the last part of the results an analysis is presented of transient arching and how it is affected by properties and conditions used in the simulations. Fig. 3. (a) Shape of the faceted particles selected for the simulations in Rocky DEM and (b) SEM image of paracetamol crystals. Table 1 Parameters used for construction of the faceted particles. Parameter Value Shape type Faceted Vertical aspect ratio 1 Horizontal aspect ratio 1.25 Number of corners 15 Superquadratic degree 5 Table 2 Material properties for paracetamol and stainless steel. Material property Particles Geometry Density (kg/m 3 ) 800 2500 Young's modulus (GPa) 0.1 0.1 Table 3 Interaction coefficients for particles and boundaries. Interaction property Particle-particle Particle-geometry Restitution coefficient 0.8 0.8 Static friction coefficient 0.4 0.5 Dynamic friction coefficient 0.4 0.5 Table 4 Cumulative particle size distribution. Size (Equivalent volume diameter [μm]) Cumulative % undersize 625 100 600 75 550 50 500 30 450 10 400 1 Fig. 4. Geometry of the screw feeder used in the simulations. 477A. López et al. / Powder Technology 367 (2020) 474–486 4.1. Powder flow in the screw feeder In order to calculate the inertial number of the flow within the screw feeder, two measurement regions are considered, as depicted in Fig. 5, for which the stress tensor is calculated. It is composed of two different contributions, one corresponding to the velocity fluctuations of the particles and another being the sum of the contact forces in the measurement bin. Eq. (5) shows the mathematical expression for the averaged stress tensor. σij ¼1 2VX Np∈V 1 2mpδviδvjþ1 VX Nc∈V rc iFc jð5Þ where Vis the measurement bin volume; m p is the particle mass; δv i and δv j are the fluctuation velocities; F j c is the contact force at contact cand r i c is the position vector, N p is the number of particles, N c is the number of contacts and the sub-indices iand jrepresent the axes on which they are referenced. From the stress tensor, its principal components and invariants are obtained by means of exporting the control volume data from Rocky DEM to Microsoft Excel. Once these first and second invariants are obtained for each of the measurement bins, the hydrostatic and deviatoric stresses are defined according to Eqs. (6) and (7),whereσ 1 ,σ 2 and σ 3 are the eigenvalues of the stress tensor (or principal stresses) and I 1 and I 2 are the first and second invariants of the stress tensor, respectively. The hydrostatic and deviatoric stresses can then be calculated as shown in Eqs. (6)–(7) [32]: I1¼σ1þσ2þσ3 I2¼σ1σ2þσ2σ3þσ3σ1 I3¼σ1σ2σ3ð6Þ Deviatoric Stress τD¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi σ1−σ2 ðÞ 2þσ1−σ3 ðÞ 2þσ2−σ3 ðÞ 2 qffiffiffi 6 p¼ffiffiffiffiffiffiffiffiffiffiffiffiffi I2 1 3−I2 sð7Þ Following this step, the Inertial number is calculated according to Eq. (1) once the strain rate is obtained. For simplicity, the latter is defined as the ratio between the average particle velocity inside the volume and the shear band width, which is assumed to be equal to five particle diameters [6,35–38]. The shear stress may be made non-dimensional by dividing it by the inertial stress as done previously by Vivacqua et al. in [6], represented by Eq. (8). The resulting non-dimensional stress is shown in Eq. (9). Inertial stress ¼ρpd2 pγ2ð8Þ Non−dimensional stress ¼τ ρpd2 pγ2ð9Þ The non-dimensional shear stress is expressed as a function of the Inertial number. The results are shown in Fig. 6, where an almost perfect collapse for all the cases of faceted particles with different surface energies and at different rotational speeds is observed. The best fitted line on a logarithmic plot obtained for the points in Fig. 6 is shown in Eq. (10). τ ρpd2 pγ2¼3:024 I−1:80 ð10Þ For values of the Inertial number below 10 −3 the flow is approximately independent of the shear rate independent, being within the quasi-static regime, while for values of 10 −3 bIb0.1 the flow falls inside the dense flow regime [9,10]. It is worth noting that the collapse of the points on to the line is effective not only in the quasi-static regime but also within the intermediate strain rate flow regime, which is defined by the inertial numbers between the two vertical dotted lines in Fig. 6, delineating the flow regime boundaries. This trend points towards a possible unified rheology for faceted particles in the screw feeder as is discussed in the following. 4.1.1. Comparison between the screw feeder and the FT4 rheometer The Freeman Technology FT4 [21]andAntonPaar[22] powder rheometers are nowadays used increasingly to characterise the bulk Fig. 5. Representation of the measurement volumes in the screw feeder. 478 A. López et al. / Powder Technology 367 (2020) 474–486 powder flow behaviour. A question of great interest is whether the characteristic rheological features of powder flow, as measured by these devices are accountable for bulk powder flow in pieces of process equipment, such as screw feeders. An attempt is therefore made here to analyse the dynamic powder flow in a screw feeder in the same way as it has recently been done for the FT4 instrument by Vivacqua et al. [6] for faceted particles. In FT4 powder rheometer a stainless steel blade moves up and down while rotating inside a powder bed enclosed by a glass tube. A conditioning cycle is run first in order to prepare the bed in a reproducible state. In this first cycle, the blade penetrates the bed while moving clockwise and downwards and then upwards. The shape of the blade induces a gentle slicing and lifting flow pattern which allows a reproducible packing state to be created. In the downward test, the movement induces compression and shearing on the bed as the blade rotates downwards. The measurements in the downward test are obtained by measuring the axial force as well as the torque while the blade rotates anti-clockwise. In this work the small glass cylinder vessel size (25 mm diameter) is simulated, for which the distance between the blade tip and the containing glass wall is 750 μm. The work expended by the blade, termed flow energy, is then calculated and is taken as an indication of the ease with which the bulk powder flows. However, for rheological characterisation it is necessary to calculate the stresses as a function of the strain rate. This has been done by Vivacqua et al. [6] using the same non-dimensional stress equation as given by Eq. (9) as a function of the Inertial number. The results are also shown in Fig. 6, where a similar trend prevails, albeit showing different stress levels, illustrating the similarity in the rheological behaviour for the screw feeder and FT4. The slopes of the lines are remarkably similar, whilst the pre-exponential constant differs greatly. The values obtained for the Inertial number also show the screw feeder to be operating in the quasi-static regime for most of the simulated rotational speeds. The fluctuations around the regression line in the FT4 are greater than in the screw feeder, where an almost perfect collapse is obtained. This is partly due to the more constant shear rate and stress state of the particles in the screw feeder, while the FT4 is subjected to a higher degree of variations in the values obtained due, in part, to the way the shear rate is obtained as well as to the differential change in depth as the blade moves down. For particle flow in the FT4 (Fig. 6), the denominator in the expression for the shear rate was calculated as the maximum translational velocity of the particles, while the average of that velocity was taken instead for the screw feeder. The large fluctuations in maximum velocities if compared to the average are expected to create a higher degree of scattering in the measured values. Averaging the velocity values provides a smoother velocity profile, since it filters spikes in the maximum velocities. 4.2. Analysis of fluctuations in the screw feeder with cohesion and rotational speed 4.2.1. Particle trajectories and velocities The trajectories of the particles in the screw feeder are shown in Fig. 7(a) for spherical shape particles with no adhesion and in Figs. 7(b)- (d) for Paracetamol shaped particles with different levels of the adhesive stiffness. Fig. 8 illustrates the effect of the rotational speed on the trajectories for K adh =0.2.AsevidencedbyFig. 7, an increase in the adhesive stiffness results in a higher translational velocity within the screw feeder, presumably as the powder is transported as a packet. In general, the pitches of the screw feeder are filled from the left-hand side of the funnel. As the adhesive stiffness is increased, this trend seems to disappear. This is likely due to the transient arching in the hopper section influencing the way the pitches are filled. Increasing the rotational speed has an effect on the general trend of the velocity magnitudes of the particles without affecting the trajectories so much. As the rotational speed is increased, particles move faster to the left-hand side of the hopper, where the pitches are filled initially, thus creating a slope in the hopper with a rotational speed of 30 rad/s. This effect was investigated previously by Hou et al. [1], where four different simulations of the same bin with different lengths of the screw feeder were analysed. Depending on the length of the screw inside the Fig. 6. Non-dimensional stress as a function of the Inertial number for different values of adhesive stiffness ranging from 0 to 0.5 and screw rotational speed of paracetamol-like faceted particles in the screw feeder compared to FT4. 479A. López et al. / Powder Technology 367 (2020) 474–486 container a different drawdown pattern was encountered. However, in the present work, no recirculation of particles was found in the simulations independent of the velocity of the screw. This might be related to both the faceted shapes of the particles being simulated in this work as well as the adhesion introduced in the system. Additionally, a longer length of the screw underneath the hopper would result in a higher slope of the drawdown pattern [1]. If the length was short, the sign of the slope would be inverted, as the particles would be drawn towards the outlet of the funnel (or the inlet of the tube where screw feeder is placed). These can be considered a consequence of how the pitches of Fig. 7. Trajectories of spheres (a) and paracetamol-shaped particles with different adhesive stiffness values (b)-(f) in the screw feeder at 10 rad/s impeller rotational speed, coloured by translational velocity. 480 A. López et al. / Powder Technology 367 (2020) 474–486 the screw are filled. In the cases analysed here the pitches are filled first on the left-hand side so that, when the material in the pitch is pushed forward, the pitch on the right-hand side is already full, thus having no more room for further drawdown. 4.2.2. Mass flow rate In the simulations, the hopper is first filled with particles and then the rotation of the screw is started. A certain amount of time after that, which varies for each K adh and rotational speed, particles start to come out of the screw feeder. The flow was allowed to stabilise before measurements were taken. The first step in the simulation was the filling of the hopper, after which the screw was set to start rotating. This causes an initial transient state until the particles settle and the stresses stabilise. After around 2 s of simulation the levels of the stresses in the particles started to oscillate around a mean value, following which the measurements were taken. For screw feeders with pitches of equal length the quantity discharged by a single pitch can be defined by the mass that leaves the screw feeder in one rotation of the screw. Once the particles start to exit the screw feeder, the simulation time is expressed in terms of the number of pitch discharged. This method allows monitoring how much material is coming out of the screw feeder and how stable the flow rate is, as well as its dependency on surface energy and rotational speed. This operation was carried out for the performed simulations and the results are shown in Fig. 9. At a glance, the simulation with the highest surface energy for Paracetamol can be easily identified. At an adhesive stiffness of 0.5, the mass discharged is notably lower if compared to the rest of the cases. This may be seen initially to be at odds with trends shown in Fig. 8, where an increase in the adhesive stiffness results in a higher translation velocity within the screw feeder. However, as the results shown in Fig. 9 are on the mass basis, the trend implies incomplete filling of the pitches. In all cases, the mass discharged per screw feeder pitch exhibits a similar degree of variability with a lowering average of discharged mass as the adhesive stiffness is increased. The average mass discharged per pitch, obtained for each of the sequences in Fig. 9 at 10 rad sis shown in Fig. 10. Despite the mentioned variability within the same simulation in terms of the individual mass discharged per pitch, when looking at the averages for each value of the adhesive stiffness, a general trend can be identified. The calculated averages decrease almost linearly as the adhesive stiffness is increased. There is, however, a value of the adhesion for which the mass discharged becomes null (not shown here). For the Luding contact model used in this work [32,33], at a value of the adhesive stiffness of 0.7, no mass flow rate is detected at the outlet. This is due to most of the particles being expelled out of the domain due to the high cohesive forces and interactions withthe walls. The few particles that entered the screw feeder remain attached to the walls of the domain, hence no mass exiting it. This decrease in the average mass discharged is influenced, in part, by a higher void fraction as the adhesion forces become higher. The effect of the adhesion forces on the bed void fraction is highlighted in Fig. 11. The void fraction is monitored in two cuboid volumes (c.f. Fig. 5). The increase in the void fraction for cuboid 1, which is placed directly below the hopper, is notably smaller than for cuboid 2. This difference is due to the weight of particles inside the hopper, resulting in an increase of the packing fraction in cuboid 1. Cuboid 2 instead is observed to have Fig. 8. Particle trajectories coloured by translational velocity for different rotational speeds with K adh = 0.2. 481A. López et al. / Powder Technology 367 (2020) 474–486 a steeper increase in the void fraction as the adhesive stiffness increases, as in this case there is no surcharge. In another analysis, the variation of the average void fraction is analysed as a function of the rotational speed and the results are shown in Fig. 12. The higher rotational speed of the screw allows for less time of the individual pitches to be filled with particles, which results in a higher void fraction as the speed is increased. The particle weight in the hopper appears to have a clear effect on the trend of the voidage. As suggested previously [1], the rotational motion of the screw tends to generate larger voids between particles. These voids are not successfully filled as a result of the cohesive forces in a confined environment, especially inside Cuboid 2 in the screw feeder, where there are no additional compressive forces (such as the hydrostatic pressure induced by the particles inside the hopper for Cuboid Fig. 9. Discharged mass for each individual pitch of the screw feeder for different surface energies and rotational speeds. (a): spheres; (b)-(h): Paracetamol shaped particles with different adhesive stiffness values. Fig. 10. Average discharged mass for each individual pitch of the screw feeder for different surface energies and rotational speeds. Standard deviation for each of the series with increasing adhesion level is 5.55%, 5.60%, 6.50%, 10.45%, 13.83% and 7.21%. 482 A. López et al. / Powder Technology 367 (2020) 474–486