Effect of Microscopic Properties on Flow Behavior of Industrial Cohesive Powder

Abstract

The characteristics of powders on a bulk scale are heavily influenced by both the material properties and the size of their primary particles. Throughout the stages of storage and transportation in the powder processing industry, various forms of deformation and stress, such as pressure and shear, impact these materials. Recognizing the point at which a powder undergoes yielding becomes particularly significant in numerous applications. There are also times when the level of stress needed to maintain it must be understood. The measurement of powder yield and flow properties remains a challenge and is addressed in this study. As part of the European collaborative project, a number of shear experiments were performed using two shearing devices: the Schulze ring shearing device and the Anton Paar Powder Cell (APCC). These experiments have three purposes: (i) test reproducibility/consistency between two shear devices and test protocols; (ii) relate bulk behavior to microscopic particle properties, focusing on bulk density and thus the effect of cohesion between particles; and (iii) investigate the influence of the temperature of heated powders on the powder’s flow properties, which is important for industrial reactors. Interestingly, for samples with small particle sizes, bulk cohesion increases slightly, but bulk friction increases significantly because of particle interaction effects. The experimental data not only provide useful insight into the role of microscopically attractive van der Waals gravitational and/or compressive forces on the macroscopic flow behavior of bulk powders but also have industrial relevance. We also provide robust data of cohesive and attritional fine powder for silo design used for calibration and validation of silos, models, and computer simulations.

1. Introduction

Granular materials are ubiquitous in our daily lives and extensively employed across a spectrum of industries such as food, pharmaceutical, agricultural, and mining industries. Granular phenomena like yielding and jamming [1,2,3,4], dilatancy [5,6,7], shear-band localization [8,9], history-dependence [10], and anisotropy [11,12] have attracted significant scientific interest over the past decades [13,14,15,16,17,18,19,20,21,22]. The bulk behavior of granular materials is investigated by using a variety of laboratory element experiments [23]. One of the important purposes of conducting an element test is to understand particle characteristics, such as size, shape, and size distribution. In addition, it can help analyze the particle characteristics in the macroscopic bulk response level. These assessments of the particle characteristics are used in industrial storage and production, for example, in the design of silos, reactors, etc. [24,25,26]. Throughout the test, the element test (macroscopic test) regulates the force (stress) and/or displacement (strain) paths. The most important element test used in both academia and industry is shear testing, where the sample of a granular material is sheared until the yield point is reached and the materials start to flow. Shear testers are divided into two groups based on the shear zone: direct and indirect shear testers [23,25]. The most widely used indirect shear testers are the uniaxial compression tester [10,27,28] and the bi-axial shear box [29,30,31].

For accurate material characterization, the quality and repeatability of results are essential. Despite the substantial development and study of shear testing methods, significant measurement scatter still exists when evaluating the flowability of powders in various labs and conditions [32,33,34,35,36]. Prior research has focused on this issue by comparing various devices [37] and conducting round-robin experimental tests on the Jenike tester [38], Schulze ring shear tester [32], and Brookfield powder flow tester [36]. The first round-robin investigation [38] led to the development of a certified material (CRM-116 limestone powder) and a consistent experimental testing process for identifying the yield locus.

On one batch of limestone powder (CRM-116), Schulze [32] gathered 60 yield loci using the small Schulze shear tester RST-XS (21 laboratories) and 19 yield loci using the big Schulze shear tester RST-01 (10 labs). Each of these was compared with the results of the reference Jenike test tester. While there was strong agreement between the RST-01 and RST-XS findings, the Schulze ring shear tester and Jenike shear tester results showed a significant difference (up to 20%). When yield loci from the Brookfield powder flow tester, Schulze ring shear tester, FT4 powder rheometer, Anton Paar Shear cell [39], and Jenike shear tester were compared, additional studies [36,37,39] discovered similar results.

Other investigations [40,41] only used one instrument to compare several industrially relevant powders. Furthermore, the stresses used in these comparative investigations are often mild. There is still a lack of knowledge on the flow behavior of powders in various shear devices across a broad stress range. Beyond the scope of earlier initiatives, our collaboration network, EU/ITN CALIPER (https://caliper-itn.org/ accessed on 10 December 2023), provides the one-of-a-kind opportunity to shed light on the complicated subject of powder yielding and flow. There are 16 partners in the network from both academia and business across Europe. This work was carried out in the Solid Handling Lab in BASF SE, Ludwigshafen am Rhein, Germany.

Over the last thirty years, a plethora of testers has been devised to assess the flow characteristics of bulk solids. This development has progressed from semi-automated to fully automated systems. The range of testers now accommodates diverse materials, including powders and granules, while the evolution toward automation has significantly improved efficiency and accuracy in the testing processes. The current study has a number of objectives. First, we aim to examine the accuracy and reproducibility of yield loci measurements among widely utilized shear testers.

This can offer a solid foundation for determining the validity of the testing approach and processes. Second, we aim to evaluate powders for studying the effect of cohesion and bulk density. Understanding the effects of cohesion on powder flowability is important. Finally, a change in the cohesive flow properties of the powder at high temperatures is observed in many industrial applications, such as fluidized bed reactors in hot gas filtration, granulators, and dryers. A modified ring-shaped Schulze shear cell was used in this work to measure the flow properties of a powder at elevated temperatures.

To understand the flow properties of a powder, a methodical study was carried out by testing an industrial cohesive powder (Powder A with a mean particle diameter of 2.02 μm) in two shear testers (the Schulze Ring shear Tester and Anton Paar Powder Cell) at our partner location: BASF SE, Germany. In order to maintain the data privacy of the company, the powder name will be referenced in the entire article as Powder A. Powder A (BASF SE, Ludwigshafen am Rhein, Germany) is extensively used in different fields to produce chemical products such as paints, coatings, petroleum industry catalysts, pigments in ceramics, etc. The structure includes an introduction to Powder A samples, followed by device details and experimental procedures. The conclusion focuses on discussing experimental results, particularly in relation to shear devices.

2. Materials Description and Characterization

Powder A is light yellow in color and is insoluble in water, soluble in alkali, and slightly soluble in acid. The median particle size (d₅₀) ranges from 2.02 μm and are cohesive, sticky primary particles that form clumps. The particle size distributions were measured in BASF SE by using laser diffraction (BASF SE) with the dry dispersion unit. The span of the particle size distribution is 14.48, and the average particle size (SMD) is 0.981 μm. The initial bulk density (bulk density measured directly after filling) is 1258 Kg/m³. The tapped density was measured using two different levels of tapping (1250 taps and 2500 taps). For 1250 taps, the bulk density is 2238 Kg/m³, and for 2500 taps, the bulk density is 2276 Kg/m³. The angle of repose (48.2°) and sliding angle test were conducted to learn more about the powder flow and concerns for a variety of applications. The sliding angle test was carried out using two materials: hot-rolled steel (HRS) and cold-rolled steel (CRS). The reason for selecting these materials was that hot-rolled steel has a scaly surface finish, and cold-rolled steel has a semi-rough surface. In addition, these two materials are widely used in industrial applications. The test was carried out using two methods, one with (2.5 Kpa) stress and another without stress. For both methods, the sliding angle for HRS is close to 90 degrees. For CRS, it was 43 degrees without stress and 80 degrees with stress. Based on the value of the angle of repose and sliding angle, Powder A exhibits poor flow behavior (flow function (ffc) within the range of 2 to 4).

3. Experimental Setup

In our study, we present a comparison between measurements of two shear devices, specifically rotation devices (the Schulze Ring Shear Tester and the Anton Paar Shear Cell). Two main characteristics of these devices are the degree of automation and normal stress regime. Both of these devices are completely automated in most of the operational stages, which strongly reduces the operator influence.

3.1. Schulze Ring Shear Tester—RST-XS.s and RST-01

The Schulze ring shear tester is a widely used shear device for powder characterization. Schulze ring shear testers are linked to a computer running control software, allowing users to obtain data on yield loci, wall yield loci, attrition, and compression, providing insights into the material’s flow properties and mechanical behaviors. A smaller version of the ring shear tester, which works on the exact same principle, is the so-called RST-XS.s with specimen volumes of 30 mL (RST-XS.s) and 200 mL (RST-01).

The bottom ring of the shear cell, which is ring-shaped (annular) for both testers, contains the bulk solid sample. The bulk solid sample is covered with an annular-shaped lid that is attached at a cross-beam. The cross-beam in the shear cell’s rotating axis experiences a normal force, F_N, which is then transferred through the lid to the sample (Figure 1). As a result, the bulk solid is subjected to normal stress. The counterbalance force, FA, acts in the middle of the cross-beam, formed by counterweights and directed upward, counteracting the gravity forces of the lid, the hanger, and the cross-beam in order to permit small confining stress.

The bottom ring is rotated at an angle to shear the sample, while the lid and the cross-beam are restrained from rotation by two tie-rods attached to the cross-beam. To measure the forces, F1 and F2, acting on the tie-rods, each tie-rod is fastened to a load beam. To stop the bulk solid from sliding over these two surfaces, the shear cell’s bottom and the lower side of the lid are both rough. As a result, shear deformation occurs inside the bulk solid when the bottom ring is rotated in relation to the lid. The deformation of the solid bulk is a consequence of the shearing forces acting on the tie-rods (F1 + F2), resulting in shear stress directly proportional to these forces. The ASTM standard [42] is followed for every test carried out in this study.

3.2. Anton Paar Shear Tester

The powder shear cell is a tool used for evaluating the time-dependent flow behavior of consolidated powders. Additional attachments offer complete control over humidity and temperature. When creating the Anton Paar Powder Cell (APPC), the Anton Paar firm used a similar idea to assess the powder flow characteristics using Anton Paar MCR rheometers. A cutting-edge and scientific technology for characterizing powders that offer a variety of test procedures is the powder flow cell. Powder performance can be analyzed via simulations and adjustments, with a focus on optimization and other relevant conditions. In this study, we used an 18 mL Anton Paar powder shear cell for the test. It employs standardized test loops and very accurate readings for powder analysis. The method involves applying the Mohr–Coulomb failure envelope theory [42,43,44], where the measured shear stress is compared to the applied normal stress. This theory is commonly used to elucidate materials exhibiting a substantial difference between compressive and tensile strength, particularly applicable to brittle materials.

3.3. Test Procedure

The Schulze ring shear tester and Anton Paar require one single pre-shear cycle before the first shear point and the steady state are reached (Figure 2). The primary elements addressed in this study, namely the linearized effective yield locus and yield locus, are illustrated. The depicted values correspond to the measured points at both pre-shear and shear stages.

Then, in Figure 2, during a steady flow, a straight line passing through the origin of the σ − τ illustration by receding toward the large Mohr circle is the effective yield locus as defined by Jenike [46]. The slope of the effective yield locus is called the effective angle of internal friction, φe. The largest Mohr stress circle represents the steady-state flow behavior; the angle φe can be considered a measure of internal friction at steady-state flow. This angle is necessary for silo design, according to Jenike’s theory. The remaining quantities from the yield locus test are the angle of internal friction, which is approximated by the slope angle of linearized yield locus (φ_lin) [47]. These are all the parameters that describe the flow properties, which can be obtained from the yield locus diagram in Figure 2 [45]. We chose pre-shear normal stress values between 3.9 and 19.6 kPa.

4. Results

We evaluate the measurements from two shear devices and provide a comprehensive overview of the test findings’ repeatability and reproducibility. When comparing the yield loci from various tests, Powder A, which was introduced in the above section, is used as a reference powder. We analyze the previously mentioned powder based on parameters such as bulk density, the angle of internal friction, cohesive strength, the steady-state angle of internal friction, the effective angle of internal friction, and the flow function.

For both devices, repeatability is very high, with the standard deviation found within the symbol size. Despite using the same pre-shear normal stresses, the yield loci recorded by the two devices for powder A show an average deviation (standard deviation of 0.23 and Coefficient Of Variation (COV) of 0.06). Results from the APPC are consistently lower than results from the RST-Xs.s. The instruments do not display a linear increase in slope or a decreasing slope as the normal stress increases (Figure 3).

Our findings indicate that the powder response in the case of cohesive material may be impacted by the system size, as the sole distinction between RST-XS and APPC is the size of the shear cell.

To validate the consistency of results from both shear devices, we extrapolate the linearized yield loci and compare the angle of internal friction, as well as the cohesive strength (intersection of the linearized yield locus on the y-axis), for reference powders (Figure 4 and Figure 5) with a standard deviation of 1.8, 0.6 and Coefficient Of Variation (COV) of 0.6, 0.02, respectively.

Data from different shear testers are interpreted in diverse ways. Using the default software and the pro-rating procedure, RST-XS.s and APCC results are both linearized. For Powder A, we obtain a good agreement between the RST-XS.s and APCC for the cohesive strength, c. In Figure 4, we plot the cohesive strength against pre-shear normal stress. As expected, the cohesive strength values at a given stress level are higher for Powder A. In theory [45], smaller particles with higher densities may exhibit stronger cohesive forces on each other. A similar observation is also found for the angle of internal friction, as shown in Figure 5. The angle of internal friction is plotted against normal stress using RST.XS.s and APCC, but the value of φ obtained from the APCC is lower than that of RST-XS.s but still within the fluctuation range. In addition to the internal friction angle, it is necessary to check the cohesivity, which is the coordinates at the origin extrapolated from the linearized yield locus that gives an indication of the resistance/strength of the powder under zero confining stress (σ_n).

The angle of internal friction describes how the powder can withstand applied shear stress before undergoing plastic flow, which is inferred from the linearized yield locus, as shown in Figure 5. Generally, for the cohesive powders, the yield locus is non-linear, but the linearized yield locus can still be used to evaluate the angle of internal friction for the studied stress ranges. Utilizing the assessed values given above, a predominant property is identified that governs the maximum bulk friction of the powder based on a specific pre-consolidation history. All internal friction angles are derived from the linearized yield loci.

In Figure 5, we plot the angle of internal friction versus normal stress at three different pre-shear normal stresses. Within the stress studied, there is no clear dependence of the angle of internal friction on the normal stress. To check whether there is any impact on the devices, we tested the RST.XS.s and APPC. The flow characteristics results of Powder A are very similar in both devices. The agreement suggests that the observed behavior is attributed to material properties (Powder A) rather than being dependent on the specific shear device used. The possible explanation for this interesting behavior on bulk friction is that particles of different sizes have the same shape but different surface roughness/asperity, but this needs to be studied. Another possibility is the battle between inter-particle cohesion and inter-particle friction (influenced by shape). In this case, the particles are small in size; and the inter-particle cohesion between the particles governs the flow behavior and increases the shear resistance. Moreover, when the sample is subjected to confinement below a specific stress level, a low inter-particle cohesion can result in a higher bulk density. This, in turn, reduces the available free space for particle movement. In such cases, the significance of geometrical interlocking becomes crucial.

We examine how the bulk density of powder A varies with respect to normal stress and particle size. Figure 6 (Coefficient Of Variation (COV) of 0.03) displays data and shows the increasing trend in bulk density for normal stress.

The bulk density of Powder A increases with an increase in normal stress at varying ranges. When the level of normal stress ranges increase, the range of bulk density also steadily increases for both devices. We attribute this tendency to the wider particle size distribution, as indicated by the large span value of 14.48. A wider particle size distribution allows for the easy rearrangement of the packing structure when applying an external load. The presence of cohesive forces, such as van der Waals forces, in elementary particles is widely acknowledged, and additional gravitational forces may also contribute to this phenomenon. Since liquid bridging and other forces are anticipated to be minimal in Powder A’s comparatively dry state, the bulk density will be high due to the formation of clusters and many voids caused by the dry cohesive interaction.

The effective angle of internal friction influences the positioning of the Mohr circle, providing insights into the shear strength and stress conditions within the material. The relationship between these two concepts is crucial for analyzing and predicting the mechanical behavior of materials under various loading scenarios. Additionally, this characteristic is important for designing the hopper angle to achieve high flow rates in the silo. In Figure 7 (standard deviation of 3 and Coefficient Of Variation (COV) of 0.05), the effective angle of internal friction is plotted versus the normal stress. Within the stress investigated, the effective angle of internal friction decreases with increasing normal stress.

We analyze the results to assess powder flowability by examining the flow function. The flow function is defined as ffc = (σ₁/σ_c), whereas σ₁ is the major consolidation stress and σ_c is the unconfined yield stress. This evaluation helps us understand how a specific powder would behave or flow under a given major consolidation stress (Figure 8 (standard deviation of 2.19 and Coefficient Of Variation (COV) of 0.12) and Figure 9 (standard deviation of 0.07 and Coefficient Of Variation (COV) of 0.05)). This is also significant for designing the outlet diameter of a silo [48]. In Figure 8, we plot the unconfined yield strength against the major principal consolidation stress. As can be seen, our powder flowability values lie in the range of cohesivity (flow function (ffc) within the range of 2 to 4). In the stress range we investigated, unconfined yield strength increases for all stress ranges with increasing principal consolidation stress.

As can be seen from Figure 6, bulk density is plotted against normal stress using RST.XS.s and APCC (bulk density); the bulk density increases in a large range when the normal stress rate is increased. In order to obtain deeper insights into this interesting behavior, we tested the shear cell experiments in a heated chamber with different temperatures. A Schulze ring shear cell was placed inside the closed heated chamber with a temperature monitor. 5.4 kPa was applied as a normal stress for all the shear cell experiments. As can be seen in Figure 10 (standard deviation of 5.3 and Coefficient Of Variation (COV) of 0.002), the graph is plotted against bulk density and normal stress for different temperatures (room temperature, 40, 120, 200, and 280 °C). When the temperature increases, the bulk density continuously decreases. This is due to a lot of reasons, such as shape, size, environmental conditions, and the mechanism behind chemistry. Normally, cohesive powder, in which attractive inter-particle force outweighs its particle weight, tends to produce an open structure supported by the inter-particle force. This result is therefore a relatively low bulk density. Because the chemical structures formed are not robust, they are prone to collapse under low pressure.

In order to verify the decreasing trend of bulk density for different temperatures, we conducted the same ring shear test in a heated chamber for a single temperature (200 °C), maintained for two different time ranges. One was maintained at 200 °C for 2 h, and the other was maintained at 200 °C for 5 h. The graph (Figure 11) is generated by plotting bulk density against normal stress for a normal stress rate of 5.4 kPa with (a standard deviation of 4.1 and a Coefficient Of Variation (COV) of 0.002).

In both tests, the bulk density shows the anticipated decreasing trend. This pattern indicates an increase in aggregation content, resulting in decreased bulk density at a normal stress rate of 5.4 kPa. Tillage operations, such as plowing, typically decrease bulk density and increase pore space, impacting the structure of the material. Another contributing factor may be the small size and wider particle size distribution of powder A, reducing the likelihood of breakdown and fresh face formation (reduction process) and consequently leading to a long-term reduction in bulk density at a constant temperature.

5. Conclusions and Outlook

In this investigation, we methodically investigated the powder flow behavior of Powder A samples in two shear testers at various confining stress levels. The main objective was to comprehend the relationship between macroscopic bulk properties like bulk density, cohesive strength, and shear resistance (characterized by the effective angle of internal friction and the internal friction at steady-state flow) and microscopic bulk properties like particle size and contact cohesion. Two shear testers gave highly reproducible and good results with a deviation in the range of 20%. The APCC gives a higher standard deviation than the Ring shear tester. The yield loci obtained from the Schulze ring shear tester (RST-01) remain consistently slightly higher than results from the Anton Paar Powder Cell. From a practical perspective, this conservative tendency is safer for silo design. In summary, automated devices reduce operator influence, and correct interpretation of results is crucial. Protocol differences can significantly affect deviations in operator and material response. However, if established qualitative trends are consistent across different testers, it enhances the reliability of the outcomes.

Powder A is tested over a wide range of normal loads (5, 20, and 35 kPa). Size and stress factors, bulk density, and cohesion are recognized for their substantial influence on bulk flow. Typically, an increase in load results in a higher power, indicating a more delicate and pronounced effect on particle behavior. On the other hand, the internal friction angle does not seem to be affected by normal stress (at least within the range considered here); the effective interior angle of friction and internal friction show a decreasing trend for different normal stress. Bulk density increases monotonically for Powder A in both shear devices. Interlocking between particles due to surface roughness and shape dominates the bulk behavior of Powder A, while cohesion is a key factor in determining the shear strength of fine powders. The geometric interlocking effect is enhanced by increasing the bulk density in the case of powder samples. For a deeper study, we tested the shear cell experiments for a powder with a different range of temperatures. For heated cases, bulk density is steadily decreasing, which is due to the reduction process.

For the sake of completeness, powder flow behavior is also considered as it relates to silo design. Overall, for smaller-sized particles (Powder A), the flowability increases as the normal stress increases (the powder flows more easily). For larger particles, the fluidity tends to be more pronounced. The current study marks the beginning of the collection of experimental data, which could be further enriched in the future using data from many other materials of industrial and academic interest. Our speculation about the interesting aggregation and frictional behavior of the bulk with increasing particle size requires further investigation. Additionally, this experimental database serves as a foundation for designing methods, such as silo methodologies, and stands as a benchmark for future experimental research endeavors. Last but not least, the experimental data presented here are required for particle modeling and simulation, especially for Discrete Element Method (DEM) contact model development, calibration, validation, and element test (shear test) simulation.