# Cohesive Powder Flow: Trends and Challenges in Characterisation and Analysis

Mojtaba Ghadiri, Mehrdad Pasha, Wenguang Nan, Colin Hare, Vincenzino Vivacqua, Umair Zafar, Saeid Nezamabadi, Alejandro Lopez, Massih Pasha, Sadegh Nadimi

► To cite this version:

Mojtaba Ghadiri, Mehrdad Pasha, Wenguang Nan, Colin Hare, Vincenzino Vivacqua, et al. Cohesive Powder Flow: Trends and Challenges in Characterisation and Analysis. KONA Powder and Particle Journal, 2020, 37, pp.3-18. 10.14356/kona.2020018. hal-02370183

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# Cohesive Powder Flow: Trends and Challenges in Characterisation and Analysis†

Mojtaba Ghadiri<fnref n="1" />*, Mehrdad Pasha<fnref n="1" />, Wenguang Nan<fnref n="2" />, Colin Hare<fnref n="3" />, Vincenzino Vivacqua<fnref n="1" />, Umair Zafar<fnref n="1" />, Saeid Nezamabadi<fnref n="4" />,<fnref n="5" />, Alejandro Lopez<fnref n="6" />, Massih Pasha<fnref n="1" />,<fnref n="7" /> and Sadegh Nadimi<fnref n="8" />

## Abstract

Powder processing and manufacturing operations are rate processes for which the bottleneck is cohesive powder flow. Diversity of material properties, particulate form, and sensitivity to environmental conditions, such as humidity and tribo-electric charging, make its prediction very challenging. However, this is highly desirable particularly when addressing a powder material for which only a small quantity is available. Furthermore, in a number of applications powder flow testing at low stress levels is highly desirable.

Characterisation of bulk powder failure for flow initiation (quasi-static) is well established. However, bulk flow parameters are all sensitive to strain rate with which the powder is sheared, but in contrast to quasi-static test methods, there is no shear cell for characterisation of the bulk parameters in the dynamic regime. There are only a handful of instruments available for powder rheometry, in which the bulk resistance to motion can be quantified as a function of the shear strain rate, but the challenge is relating the bulk behaviour to the physical and mechanical properties of constituting particles. A critique of the current state of the art in characterisation and analysis of cohesive powder flow is presented, addressing the effects of cohesion, strain rate, fluid medium drag and particle shape.

**Keywords:** cohesive powder, bulk flow, characterisation, flowability, spreadability, additive manufacturing

## 1. Introduction

Particulate solids are ubiquitous in many manufacturing industries, ranging from pharmaceuticals, foods, chemicals and minerals to additive manufacturing, which is the fastest growing sector in high value manufacturing and depends critically on powder spreading. Powder pro-

cessing and manufacturing operations are rate processes for which the bottleneck is cohesive powder flow. Diversity of material properties and sensitivity to environmental conditions, such as humidity and tribo-electric charging, make the prediction of powder flow very challenging. However, such prediction is highly desirable particularly when addressing a powder material for which only a small quantity is available or when flow testing at low stress levels is required.

Characterisation of bulk powder failure for flow initiation (quasi-static) is well established, although empiricism is still the order of the day. There are in fact a large number of commercial devices as well as some developed in-house, which can apply a compressive and shearing or a tensile load to a powder bed and provide information on bulk density, bulk cohesion, internal and wall angles of friction, unconfined yield stress and tensile failure stress, all of which can be obtained as functions of applied load and consolidation time. Examples of such instruments

<footnote n="1">¹ School of Chemical and Process Engineering, University of Leeds, UK</footnote>

<footnote n="2">² School of Mechanical and Power Engineering, Nanjing Tech University, China</footnote>

<footnote n="3">³ Department of Chemical and Process Engineering, University of Surrey, UK</footnote>

<footnote n="4">⁴ LMGC, Université de Montpellier, CNRS, France</footnote>

<footnote n="5">⁵ IATE, CIRAD, INRA, Montpellier SupAgro, Université de Montpellier, France</footnote>

<footnote n="6">⁶ University of Deusto, Spain</footnote>

<footnote n="7">⁷ The Chemours Company, Wilmington, Delaware, USA</footnote>

<footnote n="8">⁸ School of Engineering, Newcastle University, UK</footnote>

<footnote>† Received 28 August 2019; Accepted 24 September 2019
J-STAGE Advance published online 19 October 2019</footnote>

<footnote n="1">¹ Leeds LS2 9JT, United Kingdom</footnote>

<footnote n="2">² Nanjing 211816, China</footnote>

<footnote n="3">³ Guildford, Surrey GU2 7XH, United Kingdom</footnote>

<footnote n="4">⁴ 860 Rue de St - Priest, 34090 Montpellier, France</footnote>

<footnote n="5">⁵ 2 place Pierre Viala, 34060 Montpellier, France</footnote>

<footnote n="6">⁶ Avenida de las Universidades 24, Bilbao, 48007, Spain</footnote>

<footnote n="7">⁷ 1007 Market Street, Wilmington, Delaware, United States</footnote>

<footnote n="8">⁸ Merz Court, Newcastle upon Tyne NE1 7RU, United Kingdom</footnote>

<footnote>* Corresponding author: Mojtaba Ghadiri;
E-mail: m.ghadiri@leeds.ac.uk
TEL: +44(0)113-343-2406 FAX: +44(0)113-343-2384</footnote>
include: Schulze Ring Shear Tester (Schulze, 1994), Brookfield Powder Flow Tester (Berry et al., 2014), Jenike and Peschel Powder Testers, as reviewed by Schwedes and Schulze (1990), Salerno Unconfined Compression Tester (Parrella et al., 2008), Edinburgh Powder Tester (Bell, 2007), Environmental Caking Tester (Calvert et al., 2013), Ball Indentation Method (Hassanpour and Ghadiri, 2007), SSSpin Tester of Material Flow Solutions Inc. (Johanson, 2019), the shear cell of FT4 Powder Rheometer (Freeman Technology), Sevilla Powder Tester (Castellanos et al., 2004), and the Calabria Raining Bed method (Girimonte et al., 2018). These testers all produce different quantitative values of the bulk parameters, as the powder response depends on the residual stress history and bulk structure. Cohesive powders readily form clusters, the size and packing density of which depend on the stress history (Li et al., 2018; Ku et al., 2015). Moreover, beyond the quasi-static regime the bulk flow parameters are all sensitive to shear strain rate (Tardos et al., 2003), but in contrast to quasi-static test methods, there is no shear cell that can characterise the bulk parameters at high strain rates, i.e. in the dynamic regime. There are only a handful of instruments available for powder rheometry, the most prominent ones being the FT4 Rheometer of Freeman Technology, the powder cell of Anton Paar Modular Compact Rheometer and a Couette device, as described later below. In these devices the bulk resistance to motion can be quantified as a function of speed of shearing (strain rate) and is reviewed here. However, a challenge remains to relate the bulk rheological characteristics, i.e. bulk friction and viscosity, to the physical and mechanical properties of constituting particles in order to predict the bulk flow behaviour.

For free flowing (cohesionless) granular materials, the dimensionless group inertial number, $I$, has been proposed to account for the dependence of bulk internal friction coefficient, $\mu_b$, and apparent shear viscosity of flowing powder, $\eta$, on the shear strain rate:

$$I = \gamma d_p \sqrt{\frac{\rho_p}{P}} \qquad (1)$$

where $\gamma$ is shear strain rate (1/s), $d_p$ is particle size (m), $\rho_p$ is particle density (kg/m³), and $P$ is hydrostatic pressure (N/m²). It is noteworthy that the dimensionless shear strain rate, $\gamma^0$, proposed by Tardos et al. (2003), is a special case of inertial number, where the pressure is approximated by the stress exerted by the weight of a single particle distributed over its projected area:

$$\gamma^0 = \gamma \sqrt{\frac{d_p}{g}} \qquad (2)$$

where $g$ is gravitational acceleration (m/s²). For cohesionless particles, Jop et al. (2006) propose the following form for the bulk internal friction coefficient:

$$\mu_b = \frac{\tau}{P} = \mu_1 + \frac{\mu_2 - \mu_1}{I_0 / I + 1} \qquad (3)$$

where $\tau$ is the shear stress, $\mu_1$ is the bulk friction coefficient in the quasi-static regime, $\mu_2$ is the asymptotic value corresponding to large inertial numbers and $I_0$ is a fitting constant. Chialvo et al. (2012) propose a similar functional form with slightly different constants in the above equation.

The apparent shear viscosity, $\eta = \tau/\gamma$, generally follows a typical shear-thinning Non-Newtonian trend, but the influence of particle shape, adhesive interactions and medium fluid drag has not yet been extensively analysed.

Rognon et al. (2008) modelled shear deformation of dense cohesive granular material by Discrete Element Method (DEM) using a simple cohesive force, which approximates the DMT theory (Derjaguin et al., 1975), together with a linear spring model for the normal force and Coulombic friction condition for the tangential direction. Various features of the macroscopic bulk behaviour such as bulk friction, microstructure, anisotropy and void fraction were analysed. More recently, Berger et al. (2015) propose an extension for cohesive powders by defining a cohesive inertial number:

$$I_c = \frac{I}{\sqrt{1 + \alpha\beta}} \qquad (4)$$

where $\beta$ is the ratio of cohesive contact force over the normal stress and particle size, i.e. $f_c/(\sigma_n d_p)$ for a two-dimensional geometry, $\alpha$ is a coefficient accounting for the structure of the packing or the details of dissipation mechanisms during flow. Its equivalence for bulk powder materials is the modified Bond number, describing the ratio of the adhesive force over the particle weight, i.e. $f_c/mg$. For a wide range of conditions, their simulation predictions for the dependence of bulk cohesion, following Coulomb's law, are unified against the cohesive inertial number. Their analysis prescribes the dependence of bulk cohesion as well as bulk friction coefficient on the shear strain rate. A method and device are therefore required for validation of such simulation trends. As mentioned above, there is no shear cell which can characterise the bulk parameters in the dynamic regime. There are only three instruments available for powder rheometry: the Couette device (Tardos et al., 2003), the FT4 Powder Rheometer of Freeman Technology (Freeman, 2007), as analysed recently by a large number of workers, see e.g. Bharadwaj et al. (2010), Hare et al. (2015), Nan et al. (2017a-c), Wilkinson et al. (2017) and Vivacqua et al. (2019) and the powder cell of Anton Paar Modular Compact Rheometer, as recently analysed by Salehi et al. (2018). There are of course other instruments, such as GranuDrum of GranuTools (Lumay et al., 2012), Hall Flow Tester (ASTM B213-17) and Hosokawa Micron Powder Tester (ASTM D6393-08), with the latter integrating
several test methods into one instrument, giving indirect measures of bulk behaviour under flowing conditions. Recently, Ogata (2019) has reviewed the latest works on the evaluation of flowability and floodability of powders with a focus on the experimental methods. In the work reviewed here, we provide a complementary critique of current trends and challenges in the characterisation methods and instruments, and analysis of dynamics of cohesive powder flow with a focus on the rheological properties and methods for their characterisation. The effects of particle size and shape, fluid drag, cohesion and strain rate are covered.

## 2. Instruments for powder rheometry

Powders exhibit extreme dynamic flow behaviour from highly frictional to almost inviscid, as influenced by particle properties, the drag of the fluid medium and the strain rate. We first review the state of the art in measurement of the bulk rheological response of cohesive powders, subjected to shear straining, followed by a critique of current understanding of the effects of particle properties and process conditions. The dynamic flow testers may conveniently be classified into two categories: (i) those which address powder rheometry by measuring the powder resistance to shearing as a function of shearing speed by a rotating impeller or surface, and (ii) other dynamic flow testers in which the flow behaviour and characteristics are indirectly inferred. In the first category the Couette device, powder cell of the Anton Paar Modular Compact Rheometer and FT4 Powder Rheometer of Freeman Technology are placed. The rotating drum and Ball Indentation Method (BIM) at high strain rates, are placed in the second category. We also include here a review of powder spreadability testing by a blade in view of its increasing importance in additive manufacturing and its relation with powder flowability.

### 2.1 Powder rheometers

#### 2.1.1 Couette device

This is a simple device based on the design of a classic liquid rheometer, consisting of two co-axial vertical cylinders in which powder is sheared in the annular gap between the two cylinders by rotating the inner cylinder whilst keeping the outer cylinder stationary (Lun et al., 1984; Tardos et al., 1998). Such a device is common for rheological measurements of liquids, though was first reported for powders by Savage and Sayed (1984). It is necessary to ensure the powder is gripped at the wall to provide a no-slip boundary condition and therefore ensure that the entire bed is sheared, as such sandpaper is typically glued to the cylinder walls (Tardos et al., 2003). The

normal stress is adjusted simply by varying the mass of powder above the sheared bed, referred to as the ‘overburden’. Sensors are placed at the outer wall that enable measurement of normal and shear stresses across the height of the sheared region.

A Couette device can be operated in ‘batch’ or ‘continuous’ mode; with a slow, downward axial flow of powder being introduced in the latter, with the removed powder being recirculated to the top, whilst no such axial flow is induced in the former. Batch mode (no axial flow) results in a near constant packing fraction regardless of the shear rate induced by the Couette (Vidyapati, 2012), and consequently leads to shear stress remaining constant across the range of shear rates (Langroudi et al., 2010). It should be noted that the reported work is for large, granular media, and for fine, cohesive powder it could be expected that packing fraction would still vary with strain rate in batch mode. In continuous mode, at low shear rates the packing fraction is lower than that in the batch mode operation, and consequently so is the shear stress, however an increase in shear rate results in dilation and a subsequent increase in shear stress as the flow approaches the collisional regime. Experimental work reported by Savage and Sayed (1984), Qin (2000), Klausner et al. (2000) and Tardos et al. (2003) show the dependency of the shear stress on the strain rate for a number of materials in the quasi-static, intermediate and dynamic regimes, where there is a general agreement that the shear stress increases with strain rate in the intermediate and dynamic regimes. Tardos et al. (2003) defined approximate boundaries of the dimensionless shear strain rate for the quasi-static to intermediate ($\gamma^0$ = 0.15 to 0.25) and intermediate to rapid ($\gamma^0$ = 3) granular flow regimes, based on the dimensionless strain rate given by Eq. (2). Vidyapati et al. (2012) carried out DEM simulations of this device and showed agreement with these boundaries, and indicated that the number of enduring contacts reduces with increasing strain rate, and increases with solid fraction and particle friction.

Langroudi et al. (2010) expressed the bed stress ratio using Eq. (5).

$$ \frac{\tau}{\sigma} = a + b\gamma^n \qquad (5) $$

where $\tau$ and $\sigma$ are shear and normal stresses, respectively, and $a$, $b$ and $n$ are constants. This can be further generalised by substituting $a = \tan(\phi)$, where $\phi$ is the internal angle of friction, thus at zero shear rate Eq. (5) reduces to the Coulomb yield condition with no cohesion.

The vertical force due to gravity compressing the powder is not constant throughout the bed; varying significantly with depth since the cylinders are tall (Tardos et al., 1998). Contradictory trends of vertical and radial stress variations throughout the bed height have been
shown, with Tardos et al. (1998) finding the stress varied with ρgz, Tardos et al. (2003) finding stress scaling with 3tan(φ)ρgz, and Gutam et al. (2013) showing an exponential growth of stress with z. Furthermore, Gutam et al. (2013) show that the direction of σ<sub>rz</sub> switches at the onset of shearing, and that the stress variation across the powder bed is dependent on the gap width. It is suggested that this could be driven by a downward flow of particles near the outer wall, due to the anisotropic bed fabric; an observation that shows that the strain field is not as simple as that intended by the Couette design. Anisotropy of the bed fabric has been shown for much simpler systems of static sand piles (Vanel et al., 1999) and during shear (Howell et al., 1999), and hence it is expected that this would indeed also be the case in the more complex Couette flow. Furthermore, Gutam et al. (2013) state that Couette is one of the few devices where gravity is perpendicular to the shear direction, which may have significant effects on the rheology, however this is also true of blade-driven powder rheometers that are discussed further below. Another drawback of the Couette device is the potential for wall slip at the rotating inner cylinder, and steps should be taken to mitigate it. This device also requires a large quantity of powder, so it is not suitable for instances where the powder quantity is scarce.

## 2.1.2 Powder cell of the Anton Paar modular compact rheometer

The Anton Paar powder rheometer measures the torque required by an impeller blade to rotate at a fixed height inside a powder bed. Different impeller shapes are available (cylindrical, including one having grooved surfaces, blade, and a ring with radial fins) to investigate the resistance to shearing and influence of wall friction. The powder cell is a 50 mm diameter glass cylinder, having a porous base plate for aeration. The torque sensor can measure a wide range (10<sup>-8</sup> to 0.3 Nm), making it possible to accurately measure the torque whilst the powder is flui-dised and sheared. In a standard test procedure the blade is placed at 10 mm above the bottom of the cell and can be rotated from a very slow speed of 0.001 to 500 rpm. The powder bed can also be conditioned prior to torque measurement to remove any residual vertical friction due to insertion of the impeller in the bed. Recently, Salehi et al. (2017), evaluated the Anton Paar powder cell for characterising flowability at low stresses using glass beads, sand and alumina powder. They reported that the minimum torque necessary to rotate an impeller in a powder bed depends on material properties, air flow rate, impeller depth and shape of the impeller. Furthermore, Salehi et al. (2018) compared torque measurements between different sizes of glass beads and different impeller geometries and used DEM to analyse the dynamic behaviour of the powder. Differences between the temporal profiles of torque

of different impeller shapes are reported which might be attributed to the differences in shearing surfaces and the formation of instantaneous high magnitude force chains. Moreover, as the flow response is measured at a fixed position of the rotating component in the powder bed, the results may not be representative for the whole powder bed (e.g. due to a number of factors such as segregation, local aeration, slipping, etc.). On the other hand, the vertical stress is constant throughout the measurement, which is advantageous for analysis.

### 2.1.3 FT4 powder rheometer of freeman technology

This instrument (referred to as FT4 herein) measures the mechanical work done by a twisted-shape impeller while penetrating into a powder bed at given rotational and downward translational speeds (Freeman, 2007). The expended work is taken as a measure of flowability under dynamic condition. Two types of test can be carried out: a downward test and an upward test. In the downward test the impeller rotates anticlockwise with its blade surface facing downward, thus compressing and shearing the powder bed. The work expended in this test has been termed ‘Basic Flow Energy (BFE)’. In the upward test, once the downward traverse is complete and the impeller is close to the bottom of the bed, the rotation direction is reversed (clockwise) and the impeller cuts and lifts the powder bed i.e. a dominant tensile and shearing action. The work associated with this action per unit mass of the material is known as ‘Specific Energy (SE)’.

Nowadays, FT4 is used extensively in industry to provide a relative measure of the ease with which powder flows. For example, Fu et al. (2012) reported that FT4 could be used to identify the importance of the effect of particle size and shape of three grades of lactose particles. Li et al. (2018) attributed the torque fluctuation of highly cohesive powders to breakage of cohesive clusters. Wilkinson et al. (2017) carried out a parametric evaluation of flowability as indicated by FT4 through statistical and sensitivity analyses using DEM. A question which naturally emerges is how the work expended on both penetrating and withdrawing the impeller is influenced by particle properties, and whether it can actually reflect bulk rheological properties, such as bulk friction and shear viscosity. In recent years, a good number of attempts have been made to elucidate the correlation between the expended work and the bulk mechanical and rheological features of cohesive powders. Using silanisation to provide controlled bulk cohesion for otherwise free flowing glass ballotini, Hare et al. (2015) showed that the expended work can be simulated by Discrete Element Method (DEM). Several attempts have been made to link the measured flow energy from FT4 to processes that the powder experiences at high strain rates (Goh et al., 2018; Mellin et al., 2017). However, no direct correlation has
been consistently found. In another study, Li et al. (2018) showed that cohesive powders exhibit cyclic torque in FT4, and as cohesion increases, the cycle time increases, whilst free-flowing powders act like liquids with no periodic response. It is noteworthy that powder flow in industrial operations is not necessarily actuated by a moving impeller, and therefore the influence of the presence of the impeller on the powder rheology cannot be ignored, due to the potential of slip on the impeller tip and containing walls, and the local aeration or jamming of particles in the impeller-wall clearance. Nevertheless, to use FT4 and Anton Paar instruments as powder rheometers, it is clearly necessary to analyse the mechanics of powder flow induced by the impeller and relate the expended work to the bulk powder rheological characteristics. For this purpose, Ghadiri and co-workers have carried out a systematic study of the effects of cohesion, air drag and strain rate, and particle shape on bulk powder rheology by analysing the stress and strain fields within FT4 using numerical simulations by a combined DEM-CFD approach (Nan et al., 2017a, b, c; Vivacqua et al., 2019). With current computer power and memory, it is too challenging to use fine cohesive powders with a complex shape in such simulations. For this reason, each effect of cohesion, air drag, and particle shape has been analysed separately as a function of strain rate using large particles for which experimental validation can be made. Salient features of the outcomes of their analysis are summarised in section 3 on the analysis of cohesive powder flow.

## 2.2 Other dynamic flow testers

### 2.2.1 Rotating drum

One of the most practical geometries used to study the flow properties of powders, or more generally granular materials, is the rotating drum (e.g. GranuDrum of GranuTools and Revolution Powder Analyzer of Process-technik). It is a free surface flow test under dynamic avalanching condition, contrary to shear testers, where a powder bed is subjected to a compressive load and the resistance to shearing is measured (Nalluri and Kuentz, 2010; Lumay et al., 2012; Yang et al., 2016). The free dynamic flow inside the rotating drum is similar to many industrial processes such as mixers, granulators, and heap formation. The non-cohesive (or mildly cohesive) powder flow inside the rotating drum is commonly defined as a function of the Froude number $Fr = R\Omega^2/g$ (where $\Omega$ is the rotational speed and $R$ is the drum radius). It can take on one of a number of regimes such as slumping, rolling, cascading, cataracting and centrifuging. By measuring the flowing angle or speed, all of these regimes can be characterised (MiDi, 2004; Fischer et al., 2008; Morrison et al., 2016). For cohesive powders, determining these parameters is difficult due to the irregular surface of the

flow and the lack of a continuous regime. In this context, some authors propose to measure the standard deviation of the fluctuations of the flow interface in order to characterise the cohesive powders (e.g. Alexander et al., 2006; Lumay et al., 2012, 2016). However, such dynamic tests are generally very challenging to interpret, as adhesive contacts cause clump formation, and adhesion and particle friction have a coupled effect on flow. Although more relevant to free-flowing powders, rotating drums are very effective in causing segregation, adversely affecting the homogeneity of the powder and hence rheological response.

### 2.2.2 Ball indentation method (BIM) at high strain rates

This test method was initially developed for quasi-static testing of the flow resistance of a powder bed against the penetration of a spherical indenter, which promotes shearing of the bed without further compression (Hassanpour and Ghadiri, 2007). The flow resistance, expressed as hardness, can be related to unconfined yield strength by the constraint factor—a material dependent property—which can be established by carrying out measurements of hardness and unconfined yield strength under identical consolidation conditions. Zafar et al. (2017) have shown the constraint factor to be independent of consolidation stress for a given material. This technique has the advantages of being applicable at low consolidation stresses and requiring only a very small quantity of powder, whilst the disadvantage is measuring hardness rather than unconfined yield strength directly.

The BIM has recently been extended to the dynamic range by dropping a ball onto a powder bed and measuring its penetration depth (Zafar et al., 2019). The dynamic flow resistance expressed by the dynamic hardness of the powder bed surface, $H$, is determined by

$$H = \frac{1}{2} \frac{MV^2}{U} \qquad (6)$$

where $M$ is the mass of the indenter, $V$ is the indenter velocity at impact and $U$ is the volume of the crater formed by the indentation (Tirupataiah and Sundararajan, 1990). On the face of it, dynamic indentation appears to be a relatively quick and simple approach for assessing powder flowability under a wide range of strain rates. However, as well as the disadvantages listed above, this technique is also challenging to apply in practice and requires further development. Moreover, dependence of the constraint factor on strain rate needs to be established if the powder yield stress, rather than the flow resistance, is desired.

Since the indenter is fired at the sample at a given velocity (or released from a given height), the depth to which it penetrates the powder bed is not directly controlled. It has been shown for quasi-static indentation that the
hardness should be measured in a given acceptable range of the penetration depths (Pasha et al., 2013; Zafar et al., 2017). So iterative refinement of test conditions may be required in order to generate reliable flow measurement results at higher strain rates. If the quasi-static hardness is known *a priori*, then the penetration depth can be estimated for an indenter of given size, density and velocity, and hence a maximum velocity which enables reliable measurement can be determined. However, since the expectation is that flow resistance will vary with strain rate, this approach can only provide an estimate of the upper operational range. Other practical considerations of the dynamic indentation test are the requirement to measure penetration depth (to determine the crater volume) and the indenter velocity. A high-speed camera can serve both functions. In order to explore a wider range of strain rates, a variety of indenters of differing material and size can be applied from a range of drop heights, as shown by Tirapelle et al. (2019)

### 2.2.3 Powder spreadability testers for additive manufacturing

Characterisation of bulk cohesive powder flow has recently attracted increased attention for powder spreading in additive manufacturing (AM). However, there is no standard method for testing whether a given powder can produce the required spread uniformity for further processing. Across the community, every possible characteristic of bulk mechanical properties is being analysed in an attempt to characterise features of powder properties which give uniform spreading (e.g. Nguyen et al., 2017; Carrozza, 2017; Han et al., 2019). However, the recent work of Nan et al. (2018) shows that uniform spreading is affected by transient jamming and arching. Therefore, spreadability and flowability are two different measures of powder bulk flow characteristics, albeit inter-related. The former refers to flow of powders in narrow gaps, whilst flowability is more a measure of bulk behaviour, i.e. not having boundary constraint. Nan et al. (2018) characterised the physical and mechanical properties of gas-atomised stainless steel powders for DEM simulation of powder spreading. They show that for spreading gaps typically used in metal AM applications, empty patches/spaces could be found within the spread particle layer, as shown in **Fig. 1**, which adversely affects the uniformity of the spread powder layer. They find that the characteristic particle size, *D*, for which 90 % particles by number have a diameter less than *D*, best describes the transient jamming condition. By using Eq. (7) for diagnosing the empty patches, the transient jamming is found to have a frequency in the range 10–100 Hz, as shown in **Fig. 2**. In Eq. (7) $\Sigma V_p$ is the total volume of spread particles and the denominator is the volume swept by the spreader blade. A gap size, $\delta$, that is less than about 3D causes transient

Discrete Element Method Simulations

Experimental

<figure><img src="image_2.png" /><figcaption>**Fig. 1** Discrete Element Method simulation and experimental validation of spreading of gas-atomised metal powders by a blade, showing empty patches and size segregation in the spread layer as a function of spreader gap height. Narrow gaps cause transient jamming, as evident by empty patches. The frequency of formation and size of empty patches can also be inferred, as shown in **Fig. 2**. The particles are coloured based on their projected area equivalent circle diameter, blue (15–25 µm), dark grey (25–35 µm), light grey (35–45 µm), and red (45–55 µm). The number density of the largest particles (shown in red) is the lowest for the smallest gap, as predicted by Nan et al. (2018). The simulation results are for four gap heights and the experimental one is a scanning electron micrograph for the smallest gap, courtesy of Mr M.T. Hussein. Gap heights are normalised with respect to the characteristic particle size below which 90 % of particles by number lie ($D_{90}$).</figcaption></figure>

<figure><img src="image_3.png" /><figcaption>**Fig. 2** Frequency of empty patches for each patch length as a function of gap height (Nan et al. (2018), https://doi.org/10.1016/j.powtec.2018.07.030. Copyright: (2018) Elsevier B.V. under https://creativecommons.org/licenses/by/4.0/.</figcaption></figure>
jamming, leading to empty patches.

$$ \frac{\sum V_p}{\Delta x \times \Delta y \times (\delta - \delta_c)} < 0.1 \qquad (7) $$

Nan and Ghadiri (2019) identify a critical spreading speed above which the mass flow rate of powder through the gap is independent on the blade spreading speed. Haeri (2017) identified the optimum blade tip shape to produce a spread particle layer with volume fraction and surface roughness comparable to a roller at the actual operation conditions. Geer et al. (2018) and Han et al. (2019) measured the repose angle and pile bulk density of metal powders, and then used DEM simulations to calibrate and characterise the sliding and rolling friction coefficient and surface energy of the powder to be used in their simulations of the spreading process. Desai et al. (2019) also developed a DEM calibration method based on angle of repose testing and powder rheometry for AM, which was designed around multiple characterization experiments applicable to the spreading step. However, particle adhesion and sliding friction influence the repose angle in a complex way, which is not yet fully understood and hence calibration methods should be treated with caution. More work is needed to identify and characterise factors which influence spreadability of powders in AM and develop appropriate instrument for its characterisation.

# 3. Analysis of cohesive powder flow

## 3.1 Effect of cohesion

The relative cohesivity of a powder is most commonly described by the granular bond number, Bo, the ratio of the attractive force (adhesive or cohesive) over particle weight (Castellanos, 2005). Cohesion is commonly due to van der Waals, liquid bridge and/or electrostatic forces. There are extensive analyses of bulk cohesion reported in the literature, but its influence on the dynamic flow behaviour has not been as widely investigated. Recently, Hare et al. (2015) made large spherical glass beads (1.7–2.1 mm) cohesive by silanising their surfaces and measured their surface energy by the Drop Test Method (Zafar et al., 2014). They measured the work (basic flow energy) required to penetrate the rotating impeller into the cohesive powder bed, and showed that this could also be quantitatively predicted by DEM using the elasto-plastic adhesive model of Pasha et al. (2014). Bulk cohesion simply lifts up the baseline of powder resistance to bulk motion and the functional dependence on the shear strain rate has the same trend, as recently analysed by Vivacqua et al. (2019). They simulated the FT4 test using DEM for both cohesive (two levels) and cohesionless contacts, using Luding's contact model (Luding, 2008) and calculated

<figure><img src="image_4.png" /><figcaption>**Fig. 3** DEM prediction of shear stress on the impeller blade of the FT4 rheometer as a function of impeller blade tip speed for glass beads for three adhesive indices according to the contact model of Luding (2008). Simulation data are from Vivacqua et al. (2019): https://doi.org/10.1016/j.powtec.2018.10.034. Copyright: (2019) Elsevier B.V. under https://creativecommons.org/licenses/by/4.0/.</figcaption></figure>

the shear stress on the impeller blade as a function of the impeller tip speed, as shown in **Fig. 3**. Clearly, at low speeds the lines are parallel with the intercept with ordinate being a function of cohesion, and interestingly at high speeds interparticle cohesion has little influence on the shear stress acting on the impeller blades.

The above experimental observations are consistent with the recent numerical analysis of Berger et al. (2015), who used contact dynamics simulations to investigate cohesive shear flows at a wide range of strain rates. Their simulation predictions for the dependence of bulk cohesion, following Coulomb's law, on the shear strain rate shows a logarithmic decrease for a wide range of conditions. This effect was attributed to the reduction in the coordination number with increasing shear strain rate, expressed in terms of inertial number.

## 3.2 Effect of shear strain rate and medium fluid drag

As the particles become finer, the effect of air drag becomes more pronounced at large shear strain rates. So, this has to be taken into account in the analysis of fine cohesive powder dynamics. Guo et al. (2011a, 2011b) propose a dimensionless number made of the product of the Archimedes number and the ratio of particle envelop density over the fluid density (i.e. an air sensitivity index) to account for the influence of air drag in die filling. They define a critical value of this group below which the fluid drag effect is notable. However, this approach is more relevant to lean particle-fluid systems. Nan et al. (2017a, 2017b) used large particles (for faster simulation) with air
permeation from the base of the FT4 rheometer to provide
notable drag. In this way the effect of air drag and strain
rate could be analysed in reasonable time for glass beads
of 0.3–0.35 mm and polyethylene spheres of 0.5–0.6 mm
for permeating gas velocities ranging from no gas flow to
near fluidisation. The expended work for penetrating the
rotating impeller into the bed and gas pressure drop could
be both measured and predicted, thus providing further
validation of the simulations. In the absence of air, the ex-
pended work increases with the speed of the impeller, as
intuitively expected. An interesting outcome of their anal-
ysis is that the expended work scales with the potential
energy of the bed above the impeller height, except for the
top 10 mm, where the entrance effect of the blade is very
strong.

Nan et al. (2017a, 2017b) also analysed the stress and
strain fields in cells in front of the blade of FT4 rheometer.
Their work reveals the sensitivity of powder rheology to
both the strain rate and gas velocity. Their simulation re-
sults show that the normalised expended work (with re-
spect to the potential energy of the bed mass above the
mid-position of the impeller blade) for all conditions in-
cluding permeating air is actually a linear function of the
prevailing normalised shear stress, with the latter in turn
being a function of the strain rate and the prevailing pres-
sure, as the latter changes with height. The most notable
outcome of their analysis is the prediction of the bulk
friction coefficient as a function of the inertial Number.
The effect of permeating air simply modifies the prevail-
ing pressure on the particles, whereby increasing the per-
meating air speed reduces the pressure and therefore
increases the inertial number. By introducing the perme-
ating air, the powder flow, which is initially in the quasi-
static state, could transform into the intermediate or even
dynamic state, where the bulk friction coefficient is
shown to increase almost linearly with the inertial num-
ber.

Bruni et al. (2007, 2005) and Tomasetta et al. (2012)
used a mechanically stirred fluid-bed rheometer to study
the rheology of aerated and fluidised powders, which was
followed by Salehi et al. (2017, 2018). To keep the bed in
quasi-static state, the rotational speed of the impeller and
gas superficial velocity were chosen to have low values.
Based on the method of differential slices (Janssen's ap-
proach) and the Mohr-Coulomb description of the powder
failure, they developed a model to describe the applied
torque. In their model, the effect of air drag on the powder
stress was considered by subtracting the pressure gradient
force from the gravity force. The most interesting out-
come of their work is that the applied torque of the impel-
ler could be linked to the stress state of the powder.
However, as the powder bed was in quasi-static state,
their analyses did not reveal the response of powder rhe-
ology to the variation of the strain rate or flow regimes. In

conclusion, the dynamic behaviour of fine cohesive pow-
der affected by the fluid medium drag is still a very chal-
lenging task to analyse, but based on the above
observations, the trend shown in **Fig. 3** for large cohesive
particle should also prevail for fine powders, subject to
taking account of fluid drag effects.

3.3 Effect of particle shape

Granular flow is highly affected by particle shape due
to interlocking of the particles. High fidelity simulation of
particle shape provides a complexity which is ill-afforded
by the DEM approach, from the viewpoint of contact me-
chanics. Therefore, approximating to simple shapes is the
order of the day. There are a good number of approaches
for consideration of shape of particles in DEM simula-
tions; clumped spheres, (Favier et al., 1999), elliptical
(Rothenburg and Bathurst, 1991), polygonal (Cundall,
1988), bonded assemblies of polygons (Potapov and
Campbell, 1996), spherosimplices (Pournin et al., 2005),
super-quadrics (Williams and Pentland, 1992), and digi-
talisation of particles of arbitrary shapes by voxel packing
(Jia and Williams, 2001). For particles with a rounded
shape, the clumped sphere approach of Favier et al. (1999)
is commonly used. For example, Hare et al. (2013) used
this approach to show that the stress ratio in a shear box is
greater for rods than for spheres, though decreases as as-
pect ratio is increased from 1.25–2, remaining constant
beyond this due to alignment of the particles. Pasha et al.
(2016) simulated mixing of corn kernels by this method,
showing that an adequate description of the effect of par-
ticle shape on particle velocity profile in a mixer could be
achieved. Alizadeh et al. (2017) used X-Ray tomograms
of spray dried particles to construct clumped spheres and
obtained reliable prediction of the repose angle and segre-
gation of binary mixtures. Nan et al. (2017c) simulated the
rheological behaviour of rod-like particles in the FT4 rhe-
ometer, using the clumped-sphere approach. They re-
ported the flow energy required for the FT4 impeller
penetrating the powder bed is much larger for rod-like
particles than for spheres. This was attributed to the com-
bined effect of the coordination number and excluded vol-
ume. They also proposed an empirical correlation for the
binary mixture of rodlike particles with aspect ratio
AR = l<sub>max</sub>/l<sub>min</sub> – 1 (i.e. AR = 1.5 and 3.0) and spherical par-
ticles (i.e. AR = 0.0). The flow energy was larger for
non-spherical particles than that of spherical particles,
due to interlocking between particles.

For crystalline solid structures with faceted shapes,
sharp edges and corners, it is inappropriate to use
clumped spheres. Recently, Vivacqua et al. (2019) used
bonded Polyhedra to construct faceted shapes in the DEM
simulation software package ROCKY-DEM, ESSS,
Brazil, and followed the same approach as Hare et al.
<table><caption>**Table 1** Polyhedra used by Vivacqua et al. (2019) for simulating faceted shapes. https://doi.org/10.1016/j.powtec.2018.10.034. Copyright: (2019) Elsevier B.V. under https://creativecommons.org/licenses/by/4.0/.</caption><thead><tr><th>Name</th><th>Number of faces</th><th>Number of corners</th><th>3D shape</th></tr></thead><tbody><tr><td>Deltahedron</td><td>16</td><td>10</td><td></td></tr><tr><td>Faced cylinder</td><td>12</td><td>20</td><td></td></tr><tr><td>Actual paracetamol shape</td><td>25</td><td>44</td><td></td></tr><tr><td>Dodecahedron</td><td>12</td><td>20</td><td></td></tr><tr><td>Truncated polyhedron</td><td>14</td><td>16</td><td></td></tr></tbody></table>

(2015) and Nan et al. (2017c) to analyse the effect of faceted particle shape on the powder flow rheology for both adhesive and non-adhesive particles using the FT4 rheometer. They investigated the effect of the shapes as illustrated in **Table 1**. The results obtained by Vivacqua et al. (2019) are shown in **Figs. 4 and 5**. They agree qualitatively with the trend shown previously by Nan et al. (2017a); the average shear stress is initially independent of the strain rate, corresponding to the quasi-static value, but starts increasing at large strain rates. The notable point is that faceted shapes present much larger shear stresses, with vertices and edges influencing the resistance, but follow the same trend as that of the spheres, with the base line shifted to larger values of shear stress (as with the effect of cohesion discussed above). A similar trend also prevails when the interparticle adhesion is increased for these faceted shapes. In both cases the normalised shear stress ($\tau/\rho_p d_p^2 \gamma^2$) obeys the following relationship with the inertial number for spheres (Eq. 8) and all faceted shapes, shown in **Table 1**, unified and given by Eq. (9):

$$ \frac{\tau}{\rho_p d_p^2 \gamma^2} = 0.481 I^{-1.743} \qquad (8) $$

$$ \frac{\tau}{\rho_p d_p^2 \gamma^2} = 0.918 I^{-1.754} \qquad (9) $$

Thus, two rheological models with roughly the same power index, but with different pre-exponential constants, are obtained for cohesive spheres (Eq. 8) and faceted particles (Eq. 9). These equations point toward the possibility of obtaining a unified rheological model incorporating the effect of cohesion, strain rate and shape.

In a subsequent study by Lopez et al. (2019), powder flow of faceted particles in screw feeders was analysed. Analysis of the stresses in the screw based on the same

<figure><img src="image_5.png" /><figcaption>**Fig. 4** DEM prediction of expended work to penetrate the impeller blade of FT4 rheometer into a bed of faceted particles in the standard test method. Simulation data are from Vivacqua et al. (2019): https://doi.org/10.1016/j.powtec.2018.10.034. Copyright: (2019) Elsevier B.V. under https://creativecommons.org/licenses/by/4.0/.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>**Fig. 5** DEM prediction of shear stress on the impeller blade of FT4 rheometer as a function of impeller blade tip speed for spherical and deltahedra shape particles. Simulation data are from Vivacqua et al. (2019): https://doi.org/10.1016/j.powtec.2018.10.034. Copyright: (2019) Elsevier B.V. under https://creativecommons.org/licenses/by/4.0/.</figcaption></figure>

approach as Vivacqua et al (2019) showed a linear relationship in a logarithmic plot between the non-dimensional shear stress and the inertial number for different cohesion and strain rate levels. When both analyses are plotted in the same graph, an overlap between the lowest shear rates of the FT4 and the highest shear rates of the screw feeder exists. This shows the close relationship between the flow regimes in both devices for the same shear rates.

The apparent viscosity ($\eta = \tau/\gamma$) follows a linear trend with the inertial number on a log-log plot, with a negative slope for both spheres and faceted particles indicating a shear thinning behaviour. The slope obtained for cohesive particles, however, deviates from the behaviour of
non-cohesive particles for some strain rates. Lopez et al. (2019) attributed the trend to transient jamming and clustering of the particles. Recently Macaulay and Rognon (2019) analyse the dynamics of cluster formation under shear deformation and concluded that cluster diffusivity increases up to two orders of magnitude with increasing cohesion. In their work, they proposed a new relationship between cluster size, its lifetime and cohesion for two dimensional flows under shear induced deformation.

Cohesion level and shape of the particles have a prominent effect on the regime transition. In the case of the latter, transition between the quasi-static regime and the intermediate regime occurs for smaller values of the shear rate and higher stress values. On the other hand, if cohesion is first introduced and then increased for spherical particles, the average level of stress increases for the same system, while the regime transition between the quasi-static and the intermediate flow regimes gradually disappears for increasing cohesion levels. Transition to the rapid flow regime occurs for the same shear rate.

In conclusion, particle shape influences the angle of friction in bulk failure of particles and the presence of vertices and edges in faceted shapes strongly influences the resistance to shear deformation. Approximating real crystal shapes by truncated polyhedron shapes provides a close match in the shear deformation behaviour between the two shapes, as shown for Paracetamol crystals by Vivacqua et al. (2019). It appears that cohesion affects the incipient yield but does not influence bulk shear viscosity.

## 3.4 Powder mixtures

Formulated powder mixtures have long been used in industry to provide product innovations as well as overcoming poor product performance due to segregation, powder flow problems, tabletting issues and instabilities. For example, multi-component detergent powders containing bleach activator and enzymes are prone to segregation. Issues related to tabletting and tablet strength prevail in the pharmaceutical industry and are commonly resolved by formulating the powder. Individual powder components have their own flow characteristics and their mixing ratio not only affects the product performance but also the flow behaviour of the powder mixture. When the overall mixture is too cohesive, the powder mixture flows poorly and could be very difficult to handle in the required processes (e.g. discharge from silo). On the other hand, if it is very free flowing, powder segregation could result in non-uniformity of the product from batch to batch. To address extreme cohesivity, the surfaces of cohesive active ingredients may be coated with very fine powder, acting as spacers to improve the overall flow behaviour of the powder (Fulchini et al., 2017).

There have been several studies looking at improved

flowability of pharmaceutical active ingredients (APIs) using dynamic powder flow testers. Qu et al. (2015) reported that coating the surface of cohesive ibuprofen with flow aids (i.e. silica or magnesium stearate) improves the flowability, as measured by the FT4 rheometer aeration test. In their investigation, the total energy measured by the rheometer for raw cohesive ibuprofen was considerably higher than for those coated with flow aids, for a wide range of air velocities (0 to 30 mm/s).

In recent years, the interest in predicting the flow behaviour of multi-component mixtures has been increased. In a recent work for example, Capece et al. (2015) developed a methodology for averaging the granular Bond number for a powder mixture and linking that to the flow function coefficient as measured by shear cell testing. Their approach is applicable to the onset of flow. However, most of the reported works in the literature for dynamic powder flow are based on empirical approaches. In an ongoing research programme entitled Virtual Formulation Laboratory, supported by the Engineering and Physical Sciences Research Council, UK, (https://gow.epsrc.ukri.org/NGBOViewGrant.aspx?GrantRef=EP/N025261/1), the dynamic flow behaviour of cohesive powder mixtures is under investigation based on the single particle properties of the formulation components. Following a similar approach to that of Capece et al. (2015) it is shown that by averaging the Bond numbers of individual components with different cohesion/ adhesion, size and density, the rheological characteristics of the mixture, i.e. bulk friction coefficient and apparent bulk viscosity can be predicted as a function of the shear strain rate, expressed in the non-dimensional form by the inertial number.

## 4. Conclusions

For characterisation of cohesive powder flow under dynamic conditions only a handful of devices are available, namely the FT4 Powder Rheometer, Anton-Paar Powder Cell and Couette device. They act as a rheometer for powders, measuring the rheological response of powder under varying shear strain rates. Experimental classification of the flow regime has so far been established with the Couette device, but wall slip and the presence of secondary flows pose a challenge to its use, in addition to lack of commercial availability. For rheometers the underlying relationship between the torque and bulk rheological properties, such as bulk friction and apparent shear viscosity, is imperative and has yet to be established.

Other dynamic testers include the rotating drum and ball indentation method. The rotating drum is applicable to free surface flows and does not have the versatility to control applied stresses; furthermore, it is difficult to
interpret a relevant cohesion parameter from such tests. Ball indentation is a relatively new test method which allows stress to be controlled and a range of strain rates to be applied by manipulating indenter properties. However, its operating range is narrow, due to the limited acceptable indentation depth.

An increasingly important sector dealing with powders operated at high strain rates is additive manufacturing (3D printing). There is currently great effort being put into relating the spreading performance in additive manufacturing to various flow testers. However, in contrast to flow resistance in shear flows, additive manufacturing processes utilise a very thin powder layer in close proximity to wall boundaries. As such the flow behaviour is strongly influenced by transient jamming/arching. A different approach is needed to describe the rheology of spreading of thin powder layers for the increased demand of powder spreading in additive manufacturing.

The prediction of bulk rheological characteristics of fine cohesive powders is still a grand challenge. Such powders are in dynamic cluster forms, the size and packing density of which depends on the stress history that the powder has experienced. The current research effort is aimed at addressing the influence of particle properties on bulk rheological behaviour in a systematic way, but there is still a long way to go to develop fully predictive tools.

## Acknowledgments

The support of the following research programmes is gratefully acknowledged: (i) Virtual Formulation Laboratory Grant of the EPSRC Future Formulation Programme (EP/N025261/1); (ii) Advanced Manufacturing Supply Chains Initiative (AMSCI) and the Medicines Manufacturing Industry Partnership (MMIP), UK, through the funding of the ‘Advanced Digital Design of Pharmaceutical Therapeutics’ (Grant No. 14060); (iii) the EPSRC Programme Grant: Friction: The Tribology Enigma (EP/R001766/1) ; (iv) Project ID 1502-607 funded through ANR (the French National Research Agency) under the “Investissements d'avenir” programme with the reference ANR-10-LABX-001-01 Labex Agro and coordinated by Agropolis Fondation, France, under the frame of I-SITE MUSE (ANR-16-IDEX-0006).

## References

Alexander A.W., Chaudhuri B., Faqih A., Muzzio F.J., Davies C., Tomassone M.S., Avalanching flow of cohesive powders, Powder Technology, 164 (2006) 13–21. DOI: 10.1016/j.powtec.2006.01.017

Alizadeh M., Hassanpour A., Pasha M., Ghadiri M., Bayly A., The effect of particle shape on predicted segregation in binary powder mixtures, Powder Technology, 319 (2017) 313–322. DOI: 10.1016/j.powtec.2017.06.059

ASTM B213-17, Standard Test Methods for Flow Rate of Metal Powders Using the Hall Flowmeter Funnel.

Bell A.T., Evaluation of Edinburgh Powder Tester, Proceedings of PARTEC, Nuremburg, Germany, 2007.

Berger N., Azéma E., Douce J. F., Radjai F., Scaling behaviour of cohesive granular flows, EPL (Europhysics Letters), 112 (2015) 64004. DOI: 10.1209/0295-5075/112/64004

Berry R.J., Bradley M.S.A., McGregor R.G., Brookfield powder flow tester – Results of round robin tests with CRM-116 limestone powder, Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering, 229 (2014) 215–230. DOI: 10.1177/0954408914525387

Bharadwaj R., Ketterhagen W.R., Hancock B.C., Discrete element simulation study of a Freeman powder rheometer, Chemical Engineering Science, 65 (2010) 5747–5765. DOI: 10.1016/j.ces.2010.04.002

Bruni G., Barletta D., Poletto M., Lettieri P., A rheological model for the flowability of aerated fine powders, Chemical Engineering Science, 62 (2007) 397–407. DOI: 10.1016/j.ces.2006.08.060

Bruni G., Colafigli A., Lettieri P., Elson T., Torque measurements in aerated powders using a mechanically stirred fluidized bed rheometer (msFBR), Chemical Engineering Research and Design, 83 (2005) 1311–1318. DOI: 10.1205/cherd.05092

Calvert G., Curcic N., Redhead C., Ahmadian H., Owen C., Beckett D., Ghadiri M., A new environmental bulk powder caking tester, Powder Technology, 249 (2013) 323–329. DOI: 10.1016/j.powtec.2013.08.037

Capece M., Ho R., Strong J., Gao P., Prediction of powder flow performance using a multi-component granular bond number, Powder Technology, 286 (2015) 561–571. DOI: 10.1016/j.powtec.2015.08.031

Carrozza A., Characterization of powders to be used in a laser powder bed machine: Analysis of the critical parameters and relationship with powder flowability, MSc Thesis, Politecnico di Torino (2017).

Castellanos A., Valverde J.M., Quintanilla M.A.S., The Sevilla Powder Tester: A tool for characterizing the physical properties of fine cohesive powders at very small consolidations, KONA Powder and Particle Journal, 22 (2004) 66–81. DOI: 10.14356/kona.2004011

Castellanos A., The relationship between attractive interparticle forces and bulk behaviour in dry and uncharged fine powders, Advances in physics, 54 (2005) 263–376. DOI: 10.1080/17461390500402657

Chialvo S., Sun J., Sundaresan S., Bridging the rheology of granular flows in three regimes, Physical Review E, 85 (2012) 021305. DOI: 10.1103/PhysRevE.85.021305

Cundall P.A., Formulation of a three-dimensional distinct element model—Part I. A scheme to detect and represent contacts in a system composed of many polyhedral blocks, International Journal of Rock Mechanics and Mining Sci-
ences & Geomechanics Abstracts, 25 (1988) 107–116. DOI: 10.1016/0148-9062(88)92293-0

Derjaguin, B.V., Muller, V.M., Toporov, Y.P., Effect of contact deformations on the adhesion of particles, Journal of Colloid and Interface Science, 53 (1975) 314–326. DOI: 10.1016/0021-9797(75)90018-1

Desai P.S., Mehta A., Dougherty P.S.M., Higgs C.F., A rheome-
try based calibration of a first-order DEM model to gener-
ate virtual avatars of metal Additive Manufacturing (AM)
powders, Powder Technology, 342 (2019) 441–456. DOI:
10.1016/j.powtec.2018.09.047

Favier J.F., Abbaspour-Fard M.H., Kremmer M., Raji A.O., Shape representation of axi-symmetrical, non-spherical particles in discrete element simulation using multi-element model particles, Engineering computations, 16 (1999) 467–480. DOI: 10.1108/02644409910271894

Fischer R., Gondret P., Perrin B., Rabaud M., Dynamics of dry granular avalanches, Physical Review E, 78 (2008) 021302. DOI: 10.1103/PhysRevE.78.021302

Freeman R., Measuring the flow properties of consolidated, conditioned and aerated powders – a comparative study using a powder rheometer and a rotational shear cell, Powder Technology, 174 (2007) 25–33. DOI: 10.1016/j.powtec.2006.10.016

Fu X., Huck D., Makein L., Armstrong B., Willen U., Freeman T., Effect of particle shape and size on flow properties of lactose powders, Particuology, 10 (2012) 203–208. DOI: 10.1016/j.partic.2011.11.003

Fulchini F., Zafar U., Hare C., Ghadiri M., Tantawy H.,
Ahmadian H., Poletto M., Relationship between surface
area coverage of flow-aids and flowability of cohesive parti-
cles, Powder Technology, 322 (2017) 417–427. DOI:
10.1016/j.powtec.2017.09.013

Geer S., Bernhardt-Barry M.L., Garboczi E.J., Whiting J., Donmez A., A more efficient method for calibrating discrete element method parameters for simulations of metallic powder used in additive manufacturing, Granular Matter, 20 (2018) 1–17. DOI: 10.1007/s10035-018-0848-4

Girimonte R., Bernardo P., Minnicelli A., Formisani B., Experi-
mental characterization of the cohesive behaviour of fine
powders by the raining bed test, Powder Technology, 325
(2018) 373–380. DOI: 10.1016/j.powtec.2017.11.038

Goh H.P., Heng P.W.S., Liew C.V., Investigation on the impact of powder arching in small die filling, International Journal of Pharmaceutics, 551 (2018) 42–51. DOI: 10.1016/j.ijpharm.2018.09.005

Guo Y., Wu C.Y., Kafui K.D., Thornton C., 3D DEM/CFD analysis of size-induced segregation during die filling, Powder Technology, 206 (2011a) 177–188. DOI: 10.1016/j.powtec.2010.05.029

Guo Y., Wu C.Y., Thornton C., The effects of air and particle
density difference on segregation of powder mixtures
during die filling, Chemical Engineering Science, 66
(2011b) 661–673. DOI: 10.1016/j.ces.2010.11.017

Gutam K.J., Mehandia V., Nott P.R., Rheometry of granular materials in cylindrical Couette cells: Anomalous stress caused by gravity and shear, Physics of Fluids, 25 (2013) 070602. DOI: 10.1063/1.4812800

Haeri S., Optimisation of blade type spreaders for powder bed preparation in Additive Manufacturing using DEM simulations, Powder Technology, 321 (2017) 94–104. DOI: 10.1016/j.powtec.2017.08.011

Han Q., Gu H., Setchi R., Discrete element simulation of powder layer thickness in laser additive manufacturing, Powder Technology, 352 (2019) 91–102. DOI: 10.1016/j.powtec.2019.04.057

Hare C., Ghadiri M., The influence of aspect ratio and roughness on flowability, API Conference Proceedings, 1542 (2013) 887–890. DOI: 10.1063/1.4812074

Hare C., Zafar U., Ghadiri M., Freeman T., Clayton J., Murtagh M.J., Analysis of the dynamics of the FT4 powder rheometer, Powder Technology, 285 (2015) 123–127. DOI: 10.1016/j.powtec.2015.04.039

Hassanpour A., Ghadiri M., Characterisation of flowability of loosely compacted cohesive powders by indentation, Particle & Particle Systems Characterization, 24 (2007) 117–123. DOI: 10.1002/ppsc.200601111

Howell, D., Behringer, R.P., Veje, C., Stress fluctuations in a 2D granular Couette experiment: A continuous transition, Physical Review Letters, 82 (1999) 5241–5244. DOI: 10.1103/PhysRevLett.82.5241

Hosokawa Micron Powder Tester PT-X, Standard Test Method for Bulk Solids Characterization by Carr Indices, ASTM International Designation: D 6393-08.

Jia X., Williams R.A., A packing algorithm for particles of arbitrary shapes. Powder Technology, 120 (2001) 175–186. DOI: 10.1016/S0032-5910(01)00268-6

Johanson K., SSSpinTester-X Powder Strength Tester, Material Flow Solutions, Inc., https://www.matflowsol.com/images/PDF/products/SSSpinTester/Full%20Brochure.pdf, (2019).

Jop P., Forterre Y., Pouliquen O., A constitutive law for dense granular flows, Nature, 441 (2006) 727–730. DOI: 10.1038/nature04801

Klausner J.F., Chen D., Mei R., Experimental investigation of cohesive powder rheology, Powder Technology, 112 (2000) 94–101. DOI: 10.1016/S0032-5910(99)00310-1

Ku N., Hare C.L., Ghadiri M., Murtagh M.J., Oram P., Haber R.A., Auto-granulation of fine cohesive powder by mechanical vibration, Procedia Engineering, 102 (2015) 72–80. DOI: 10.1016/j.proeng.2015.01.108

Langroudi M.K., Turek S., Ouazzi A., Tardos G.I., An investigation of frictional and collisional powder flows using a unified constitutive equation, Powder Technology, 197 (2010) 91–101. DOI: 10.1016/j.powtec.2009.09.001

Li M., Leturia M., Saleh K., Analysis of the periodic motion in a powder rheometer and development of a new Flowability testing method, KONA Powder and Particle Journal, 35 (2018) 160–171. DOI: 10.14356/kona.2018002

López A., Vivacqua V., Hammond R., Ghadiri M., Analysis of screw feeding of faceted particles by discrete element method, Personal Communication (2019).

Luding S., Cohesive frictional powders: contact models for tension, Granular Matter, 10 (2008) 235–246. DOI: 10.1007/s10035-008-0099-x

Lumay G., Boschini F., Traina K., Bontempi S., Remy J.-C., Cloots R., Vandewalle N., Measuring the flowing properties
of powders and grains, Powder Technology, 224 (2012) 19-27. DOI: 10.1016/j.powtec.2012.02.015

Lumay G., Traina K., Boschini F., Delaval V., Rescaglio A., Cloots R., Vandewalle N., Effect of relative air humidity on the flowability of lactose powders, Journal of Drug Delivery Science and Technology, 35 (2016) 207-212. DOI: 10.1016/j.jddst.2016.04.007

Lun C.K.K., Savage S.B., Jeffrey D.J., Chepurniy N., Kinetic theories for granular flow: inelastic particles in Couette flow and slightly inelastic particles in a general flow field, Journal of Fluid Mechanics, 140 (1984) 223-256. DOI: 10.1017/S0022112084000586

Macaulay M., Rognon P., Shear-induced diffusion in cohesive granular flows: Effect of enduring clusters, Journal of Fluid Mechanics, 858 (2019) R2. DOI: 10.1017/jfm.2018.861

Mellin P., Lyckfeldt O., Harlin P., Brodin H., Blom H., Strondl A., Evaluating flowability of additive manufacturing powders, using the Gustavsson flow meter, Metal Powder Report, 72 (2017) 322-326. DOI: 10.1016/j.mprp.2017.06.003

MiDi G.D.R., On dense granular flows, The European Physical Journal E, 14 (2004) 341-365. DOI: 10.1140/epje/i2003-10153-0

Morrison A.J., Govender I., Mainza A.N., Parker D.J., The shape and behaviour of a granular bed in a rotating drum using Eulerian flow fields obtained from PEPT, Chemical Engineering Science, 152 (2016) 186-198. DOI: 10.1016/j.ces.2016.06.022

Nalluri V.R., Kuentz M., Flowability characterisation of drug-excipient blends using a novel powder avalanching method, European Journal of Pharmaceutics and Biopharmaceutics, 74 (2010) 388. DOI: 10.1016/j.ejpb.2009.09.010

Nan W., Ghadiri M., Numerical simulation of powder flow during spreading in additive manufacturing, Powder Technology, 342 (2019) 801-807. DOI: 10.1016/j.powtec.2018.10.056

Nan W., Pasha M., Bonakdar T., Lopez A., Zafar U., Nadimi S., Ghadiri M., Jamming during particle spreading in additive manufacturing, Powder Technology, 338 (2018) 253-262. DOI: 10.1016/j.powtec.2018.07.030

Nan W., Ghadiri M., Wang Y., Analysis of powder rheometry of FT4: Effect of air flow, Chemical Engineering Science, 162 (2017a) 141-151. DOI: 10.1016/j.ces.2017.01.002

Nan W., Vivacqua V., Ghadiri M., Wang Y., Numerical analysis of air effect on the powder flow dynamics in the FT4 Powder Rheometer, EPJ Web of Conferences, 140 (2017b) 03036. DOI: 10.1051/epjconf/201714003036

Nan W, Ghadiri M, Wang Y, Analysis of powder rheometry of FT4: Effect of particle shape, Chemical Engineering Science, 173 (2017c) 374-383. DOI: 10.1016/j.ces.2017.08.004

Nguyen Q.B., Nai M.L.S., Zhu Z., Sun C.N., Wei J., Zhou W., Characteristics of Inconel powders for powder-bed additive manufacturing, Engineering, 3 (2017) 695-700. DOI: 10.1016/J.ENG.2017.05.012

Ogata K., A review: Recent progress on evaluation of flowability and floodability of powder, KONA Powder and Particle Journal, 36 (2019) 33-49. DOI: 10.14356/kona.2019002

Parrella L., Barletta D., Boerefijin R., Poletto M., Comparison between a uniaxial compaction tester and a shear tester for

the characterization of powder flowability, KONA Powder and Particle Journal, 26 (2008) 178-189. DOI: 10.14356/kona.2008016

Pasha M., Hare C., Hassanpour A., Ghadiri M., Analysis of ball indentation on cohesive powder beds using distinct element modelling, Powder Technology, 233 (2013) 80-90. DOI: 10.1016/j.powtec.2012.08.017

Pasha M., Dogbe S., Hare C., Hassanpour A., Ghadiri M., A linear model of elasto-plastic and adhesive contact deformation, Granular Matter, 16 (2014) 151-162. DOI: 10.1007/s10035-013-0476-y

Pasha M., Hare C., Ghadiri M., Gunadi A., Piccione P.M., Effect of particle shape on flow in discrete element method simulation of a rotary batch seed coater, Powder Technology, 296 (2016) 29-36. DOI: 10.1016/j.powtec.2015.10.055

Potapov A.V., Campbell C.S., A three-dimensional simulation of brittle solid fracture, International Journal of Modern Physics C, 7 (1996) 717-729. DOI: 10.1142/S0129183196000594

Pournin L., Weber M., Tsukahara M., Ferrez J.A., Ramaioli M., Liebling T.M., Three-dimensional distinct element simulation of spherocylinder crystallization, Granular Matter, 7 (2005) 119-126. DOI: 10.1007/s10035-004-0188-4

Qin H., Flow behavior of granular materials: quasi-static to inertial transition, Doctoral dissertation, University of Florida, (2000).

Qu L., Zhou Q.T., Denman J.A., Stewart P.J., Hapgood K.P., Morton D.A., Influence of coating material on the flowability and dissolution of dry-coated fine ibuprofen powders, European Journal of Pharmaceutical Sciences, 78 (2015) 264-272. DOI: 10.1016/j.ejps.2015.07.016

Rognon P.G., Roux J.-N., Naaïm M, Chevoir F., Dense flow of cohesive granular materials, Journal of Fluid Mechanics, 596 (2008) 21-47. DOI: 10.1017/S0022112007009329

Rothenburg L., Bathurst R.J., Numerical simulation of idealized granular assemblies with plane elliptical particles, Computers and Geotechnics, 11 (1991) 315-329. DOI: 10.1016/0266-352X(91)90015-8

Savage S.B., Sayed M., Stresses developed by dry cohesionless granular materials sheared in an annular shear cell, Journal of Fluid Mechanics, 142 (1984) 391-430. DOI: 10.1017/S0022112084001166

Salehi H., Barletta D., Poletto M., Schütz D., Romirer R., On the use of a powder rheometer to characterize the powder flowability at low consolidation with torque resistances, AIChE Journal, 63 (2017) 4788-4798. DOI: 10.1002/aic.15934

Salehi H., Sofia D., Schütz D., Barletta D., Poletto M., Experiments and simulation of torque in Anton Paar powder cell, Particulate Science and Technology, 36 (2018) 501-512. DOI: 10.1080/02726351.2017.1409850

Schulze D., A new ring shear tester for flowability and time consolidation measurements, in: 1st International Particle Technology Forum, USA, (1994) 11-16.

Schwedes J., Schulze D., Measurement of flow properties of bulk solids, Powder Technology, 61 (1990) 59-68. DOI: 10.1016/0032-5910(90)80066-8

Tardos G.I., Khan M.I., Schaeffer D.G., Forces on a slowly rotating, rough cylinder in a Couette device containing a
dry, frictional powder, Physical of Fluids, 10 (1998) 335-
341. DOI: 10.1063/1.869525

Tardos G.I., McNamara S., Talu I., Slow and intermediate flow of a frictional bulk powder in the Couette geometry, Powder Technology, 131 (2003) 23–39. DOI: 10.1016/S0032-5910(02)00315-7

Tirupataiah Y., Sundararajan G., The volume of the crater formed by the impact of a ball against flat target materials: The effect of ball hardness and density, International Journal of Impact Engineering, 9 (1990) 237–246. DOI: 10.1016/0734-743X(90)90015-N

Tirapelle M., Santomaso A., Hare C., Characterising powder flowability at high shear rates by the ball indentation method, Chemical Engineering Transactions, 76 (2019) 391–396. DOI: 10.3303/CET1974066

Tomasetta I., Barletta D., Lettieri P., Poletto M., The measure-
ment of powder flow properties with a mechanically stirred
aerated bed, Chemical Engineering Science, 69 (2012) 373-
381. DOI: 10.1016/j.ces.2011.10.056

Vanel L., Howell D., Clark D., Behringer R.P., Clement E., Memories in sand: Experimental tests of construction history on stress distribution under sandpiles, Physical Review E, 60 (1999) R5040. DOI: 10.1103/PhysRevE.60.R5040

Vidyapati V., Kheiripour Langroudi M., Sun J., Sundaresan S., Tardos G.I., Subramaniam S., Experimental and computational studies of dense granular flow: Transition from quasi-static to intermediate regime in a Couette shear device, Powder Technology, 220 (2012) 7–14. DOI: 10.1016/j.powtec.2011.09.032.

Vivacqua V., López A., Hammond R., Ghadiri M., DEM analy-

sis of the effect of particle shape, cohesion and strain rate
on powder rheometry, Powder Technology, 342 (2019) 653–
663. DOI: 10.1016/j.powtec.2018.10.034

Wilkinson S.K., Turnbull S.A., Yan Z., Stitt E.H., Marigo M., A parametric evaluation of powder flowability using a Freeman rheometer through statistical and sensitivity analysis: A discrete element method (DEM) study, Computers & Chemical Engineering, 97 (2017) 161–174. DOI: 10.1016/j.compchemeng.2016.11.034

Williams J.R., Pentland A.P., Superquadrics and modal dynam-
ics for discrete elements in interactive design, Engineering
Computations, 9 (1992) 115–127. DOI: 10.1108/eb023852

Yang H., Jiang G.L., Saw H.Y., Davies C., Biggs M.J., Zivkovic V., Granular dynamics of cohesive powders in a rotating drum as revealed by speckle visibility spectroscopy and synchronous measurement of forces due to avalanching, Chemical Engineering Science, 146 (2016) 1–9. DOI: 10.1016/j.ces.2016.02.023

Zafar U., Hare C., Hassanpour A., Ghadiri M., Drop test: A new method to measure the particle adhesion force, Powder Technology, 264 (2014) 236–241. DOI: 10.1016/j.powtec.2014.04.022

Zafar U., Hare C., Hassanpour A., Ghadiri M., Ball indentation on powder beds for assessing powder flowability: Analysis of operation window, Powder Technology, 310 (2017) 300–306. DOI: 10.1016/j.powtec.2017.01.047

Zafar U., Hare C., Hassanpour A., Ghadiri M., Effect of Strain Rate on Powder Flow Behaviour Using Ball Indentation Method, Personal Communication, 2019.

Authors' Short Biographies

<figure><img src="image_7.png" /></figure>

Mojtaba Ghadiri

Professor of Chemical Engineering at the University of Leeds, UK, with research activities on Particle Technology, and focusing on the link between bulk particulate solids behaviour and single particle properties with the aid of simulations by combined DEM and CFD. Application areas of interest are cohesive powder flow and fluidisation, size reduction and enlargement, environmental effects and electrical phenomena in particulate systems. For details of the current projects, collaborators and publications please see the following web pages: Group's web page: http://ghadiri-group.leeds.ac.uk/.

<figure><img src="image_8.png" /></figure>

Mehrdad Pasha

Mehrdad Pasha is a Research Fellow of Chemical Engineering at the University of Leeds. His research focuses primarily on particle characterisation, powder flow, segregation/mixing, and coating, using state of the art experimental techniques and computational approaches (e.g. Discrete Element Method). Mehrdad has won several prizes including: Award of Excellence in Modelling and Simulation at World Congress on Particle Technology, Brian Scarlet Award at Annual Meeting of International Fine Particle Research Institute. His current research focuses on prediction of flow behaviour of formulated product at high strain rate conditions by consideration of single particle properties of individual components.
Authors' Short Biographies

<figure><img src="image_9.png" /></figure>

Wenguang Nan

Wenguang Nan holds a Lecturer position at Nanjing Tech University, China. He re-
ceived his PhD in 2017 from Xi'an Jiatong University, China. During his PhD studies, he
received a funding from China Scholarship Council (CSC) to spend a year in Leeds
working with Professor Ghadiri as a visiting research student. He was also a visiting re-
searcher in Professor Ghadiri's group in 2018. His current research focuses on the pow-
der spreading in additive manufacturing, and the rheology and constitutive law of
particle flow.

<figure><img src="image_10.png" /></figure>

Colin Hare

Colin Hare is a Lecturer of Chemical Engineering at the University of Surrey, UK. His expertise are in powder flow, mixing/segregation, coating, particle breakage and the Discrete Element Method. His research is primarily funded by industry and addresses secondary processing of powder products, considering the role of particle properties and process conditions on product performance.

<figure><img src="image_11.png" /></figure>

Vincenzino Vivacqua

I graduated in Chemical Engineering from Università della Calabria (Italy), where I
also completed my PhD in 2011. I have carried out postdoctoral research work at several
international institutions, namely the University of Leeds (UoL), Nottingham (UoN),
British Columbia (UBC), Università della Calabria (UNICAL) and Qatar University
(QU). I am currently Particle Engineering Senior Scientist at Johnson Matthey, Billing-
ham, UK. My research interests are related to several areas of particle technology and
multiphase flow, including powder flow, powder compaction, DEM modelling, fluidiza-
tion and electrocoalescence.

<figure><img src="image_12.png" /></figure>

Umair Zafar

Principal Scientist at Novartis, Basel, Switzerland and visiting research scholar at Uni-
versity of Leeds, UK. PhD in Particle Science & Engineering and having experience
across different industries and processes related with powder technology. Area of exper-
tise are material characterisation (i.e. chemical, physical, surface, mechanical and ana-
lytical), establishing a relationship between microscopic and macroscopic properties and
phenomena of particulate system, design, understanding particle-process-environment
interactions and development of novel techniques to mimic lab scale experiments to in-
dustrial conditions.
Authors' Short Biographies

<figure><img src="image_13.png" /></figure>

Saeid Nezamabadi

Associate Professor in the Laboratory of Mechanic and Civil Engineering (LMGC) at the University of Montpellier, France, with research activities on powders and granular materials, and focusing on the link between the rheology of granular media and single particle properties with the aid of numerical simulations by combined continuum and discrete approaches. Application areas of interest are specially compressive and shear behaviours of soft particle materials. For details of research works, please see my personal page (http://www.lmgc.univ-montp2.fr/perso/saeid-nezamabadi/) and our research team in LMGC (http://www.lmgc.univ-montp2.fr/perso/pmmd/).

<figure><img src="image_14.png" /></figure>

Alejandro Lopez

Alejandro Lopez is a Lecturer in Applied Mechanics at the University of Deusto (Bilbao, Spain). His research focuses on CFD and DEM modelling of multiphase flows, erosion processes, cohesive powder flow and manufacturing processes, He worked as a Manager in the service industry in Spain before deciding to pursue an academic career. He received his PhD in Mechanical and Aerospace Engineering from the University of Strathclyde (Glasgow, UK), specifically studying erosion processes with CFD. After his PhD he joined Ghadiri Research Group (http://ghadiri-group.leeds.ac.uk/) before being recruited for his current position.

<figure><img src="image_15.png" /></figure>

Massih Pasha

Massih Pasha is a Particle Technology Consultant at The Chemours Company, providing technical consultation to the industrial and research facilities of Chemours and its key customers in the area of particle science and technology. He received a PhD degree from the University of Leeds working on ‘Numerical Modeling of Cohesive Powder Flow’. Massih is a Visiting Research Fellow at the University of Leeds and currently acts as Vice Chairman of the Board of International Fine Particle Research Institute (IFPRI). His area of expertise includes dry solids handling and processes such as powder flow, mixing, size reduction, and agglomeration.

<figure><img src="image_16.png" /></figure>

Sadegh Nadimi

Dr Sadegh Nadimi is a Lecturer (Assist. Prof) in the School of Engineering at Newcastle University and a Visiting Researcher at the University of Leeds. He holds a PhD in Geotechnical Engineering from City, University of London and an MSc in Geotechnical Engineering from Newcastle University. Following the award of his doctorate, Sadegh moved to the University of Leeds as Post-doctoral Research Fellow to focus on tribology of particulate solids, working with Prof Mojtaba Ghadiri and Prof Anne Neville. Sadegh is committed to advancing fundamental engineering research and teaching.