Powder Flow
This collaboration project was created to use the experimental facilities available in the lab of Karen Daniels (North Carolina State University) to test a nonlocal rheological model by Prabhu Nott (Indian Institute of Science), beyond the work already presented in FRR-12-07. The experiments and image analysis were carried out during July 2022 by graduate students Gautam Vatsa (IISc), Ravi Gautam (IISc), and Farnaz Fazelpour (NCSU) during a month-long visit of the students from IISc, supported by the collaboration funds. The open question is to address the formulation of reliable and robust continuum models for the slow, dense flow of cohesionless granular media. Of particular interest is to examine the interrelation between shear dilatancy (change in packing fraction caused by shear) and the kinematics, which is incorporated in a model recently developed by Nott and collaborators. In this final report, we present the results of successful validation of the model and interpret the significance of these findings.
Our experiments are performed in a 2D cylindrical Couette device (rheometer) developed by Fazelpour & Daniels [1], in which particle-scale measurements of both kinematics and stress as possible through image-processing of digital movies of the single layer of particles. By video imaging the flow in the dense, slow flow regime, we extract the radial variation of the azimuthal velocity and the packing fraction in the steady state. We find that the velocity decays roughly exponentially and the packing fraction increases with radial distance from the rotating inner cylinder. We make a quantitative comparison to the non-local rheological model of Dsouza & Nott [2], and find the model predictions to be in excellent agreement with the experimental data for several different boundary roughness imposed at the outer wall of the rheometer. Moreover, by considering initial states of different packing fraction profiles (but having the same average), we show a coupling between the velocity and density fields, as predicted by the model. Our results establish the importance of shear dilatancy even in systems held at constant volume.
Despite the widespread use of screw feeders in industry for transporting, metering, and processing powders, scientific understanding of their functioning is far from satisfactory. This is primarily due to the complexity of the mechanical response of powders and the complex geometry of screw feeders. In this project we have developed two models for the kinematics and mechanics of non-cohesive powders.
The first model
relies on several simplifying approximations, but makes the interesting prediction that the feed rate is maximum for a specific value pitch to diameter ratio of the screw.
The second model
is a more detailed continuum model that predicts the variations of velocity, packing fraction and stress within the feeder.
To validate the model predictions, we have conducted DEM simulations and gathered experimental data using a custom-built screw feeder apparatus. Overall, we find good agreement between the experimental data, DEM simulations, and model predictions for non-cohesive powders (such as glass beads). In particular, the simulations and experiments verify the model predictions of the feed rate being maximum at a certain ratio of pitch to diameter of the screw. The experiments and simulations also throw light on the variability of the feed rate, an aspect that is of concern to industry.
We have conducted some experiments and DEM simulations for cohesive powders commonly used in the pharmaceutical industry. We find that the main source of variability in the feed rate is not within the feeder but at the inlet to the feeder. More detailed investigation of cohesive powders, including extension of the model to account for cohesion, remains to be done, and are the primary goals of our endeavours in the next 3 years of the project.
The 2023 IFPRI Powder Flow Workshop was attended by approximately 70 live participants and 40 online registrants. It consisted of seven academic keynote presentations and two industrial talks aimed at inspiring brainstorming discussions on the subject of solids handling, which remain one of the major industrial challenge of our time [1]. To suggest which speakers, discussion leaders and panelists to invite, and to draft questions that the audience should address, the organizers conducted a survey on the interests of IFPRI members.
This report begins with results of the survey. After summarizing keynote presentations and their significance, we provide a synopsis of discussions, and we identify knowledge gaps that should elicit future grants from IFPRI or other funding agencies. The workshop schedule and talks are attached to this document.
This annual report presents key advances made during year 2 moving towards year 3. Building upon the experimental study from the previous report period, comprehensive work was done towards validation of the contact mechanics based predictive models for the selection of flow aids (silica) type and amount. This significant component of the outcomes is reported as detailed in a recently published paper; “Selection of Silica Type and Amount for Flowability Enhancements via Dry Coating: Contact Mechanics Based Predictive Approach”, see Appendix A.
In the area of modeling, the previous year’s report reviewed the available particle contact models for smooth and rough particles. During the current reporting period, advancement was made by accounting for the intrinsic macro-roughness of the particle on its cohesion and subsequent reduction after dry coating. A Manuscript, in preparation, will be submitted in Spring 2024.
Another major accomplishment is a comprehensive study to account for the entire PSD of the powder sample via the size class dependent Bond number approach as a promising tool to account for different cohesion amongst fine powders with similar d50 but varying size distributions. That work can help develop a decision tool to identify which component of a powder blend to dry coat while minimizing cohesion yet using the lowest possible flow aid amounts in the blend. A manuscript in preparation will be ready and submitted by the end of Spring 2024.
Another effort towards fulfilling a major deliverable examined four industry relevant silicas, including three hydrophilic and two hydrophobic, detailed in a published Manuscript, “On predicting the performance of different silicas on key property enhancements of fine APIs, blends, and tablets”; see (Appendix B).
In this work, the predictability of the performance of different silica types on cohesion reduction is better explained by combining several models, some of which counter each other for more pragmatic understanding of the nuances involved:
- (1) the Multi-asperity contact model,
- (2) Deng’s stick and bounce model explain the aggregation tendency of nano flow aids (e.g., silica) on the host particle as a function of process intensity and guest-host sizes (Details in recently published paper is attached in Appendix C),
- and the interactive mixture model based on host-guest total surface energy differential (discussed in the paper included in Appendix B).
The results convey that while silica size and its extent are important, silica aggregation is another key parameter governing the performance of dry coating indicating what role is played by the process intensity and time. Interestingly, a major take home message of this work is that while coating of nano-sized flow aids requires high-intensity processing, subsequent processing of the blends in a conventional low intensity mixer may be adequate since it leads to synergistic transfer of flow aids that greatly enhances the blend flowability. This outcome has significant industrial implications in designing of powder blends and processing and will be one major focus of the future work beyond year three.
This synergy along with the effect of blend mixing time were further examined to uncover the effect of mixing time on blend bulk properties when a dry coated component is mixed; detailed in a published manuscript, see Appendix D.
Current work, which will continue through 2024 and beyond will examine applicability of industry relevant, potentially scalable approaches to dry coating. This includes assessing the dry coating performance from a batch device such as LabRAM against using low-intensity batch-mode V-Blender, as well as potentially continuous, higher intensity COMIL while varying the processing parameters. These outcomes will be included in a manuscript which will also form basis to propose additional work beyond year three.
Last, these significant advancements during the current reporting period would not have been possible without regular IFPRI member interactions gained through regular update meetings and additional tutorial style meetings as needed. Such activities will continue and a workshop on this topic will be offered in Fall 2024.
Experimental Approach to Investigate the Rheology of Powders
We propose an experimental approach to investigate the rheology of powders and their behavior during compaction and aeration processes. The first step is to develop protocols to synthetize and characterize model cohesive granular materials. The aim is to synthetize particles with tailored properties (stiffness and adhesion) using two technics (micro-polymer particles, or polymer coated silica particles).
Steps Involved
- The first step involves developing protocols to synthetize and characterize model cohesive granular materials.
- The second step involves developing tools to characterize particle properties and their bulk rheology.
- The third step will involve studying different flow configurations encountered in packaging processes.
- The final step concerns the coupling with air.
Discrete Element Method (DEM) consists in solving the equations of motion of a collection of rigid particles by accounting for their contact interactions [32, 137, 60, 29, 120]. Over the last 40 years, DEM has matured into a general-purpose tool for the simulation of industry-related particulate processes and for the investigation of the complex behavior of granular materials. With rising computational power and inclusion of realistic particle characteristics, both the accuracy and the computational efficiency of DEM simulations have continuously increased, but the level of expectations of DEM has considerably grown at the same time.
This report attempts to outline the horizons of granular modeling beyond the current practice of DEM. It is not meant to be a review of DEM and its recent numerous achievements or alternative methods to DEM, but to serve as an objective description of the issues and new resources that may lead to a paradigm shift in near future. The seminal report of P.W. Cleary for IFPRI, entitled “Review of DEM for Industrial Applications", in 2010 provides a clear and rich background of DEM together with the breadth of industrial applications that are possible with DEM [29]. Despite huge progress accomplished during the last decade, most themes and issues developed and exemplified in that report about discrete modeling and its applications are still relevant. The present report may be considered as a complement to that one, with the somewhat different goal of highlighting the shortcomings of the current practice of DEM and the novel trends that can allow us to identify the most promising future developments. Several examples of coupled DEM-CFD (Computational Fluid Dynamics) simulations are cited in this report, but the focus will be on the particles and their interactions in DEM.
Section 1
In section 1, we discuss the role of DEM as an original approach for gaining knowledge on particulate systems alongside theory and experiment. We argue that DEM is an inherently bottom-up approach and the adequate definition of numerical material is as much important as the mathematical algorithm used for the prediction of cooperative dynamics. We also describe the three levels of DEM with increasing complexity of the numerical material and the scope of a data-driven approach with the potential power of providing tools to improve accuracy and efficiency. We underline the interpretive use of DEM in connection with theory and the origins of its general trustworthiness in connection with experiment.
Section 2
In section 2, we highlight the role of contact interactions and their implementation in DEM. The focus will be on several ambiguities and shortcomings which need to be resolved, such as normal force positivity and memory of tangential displacements. We develop the difference between force laws and contact laws and the prospect of a shift from the hard-particle soft-contact approach to a soft particle hard-contact approach. We also consider different models of adhesion and recent models of elastoplastic contacts and discuss their applicability and consequences for granular dynamics. Finally, we focus on parametric randomness and more specifically polydisperse input parameters as a major ingredient of physics fidelity that has been so far ignored in DEM simulations.
Section 3
Section 3 is devoted to the representation and implementation of particle shape with its variants as a key input of DEM. In particular, we discuss arbitrary particle shapes and their extraction from image data as a step towards data-driven DEM and the contact detection issues. We underline the role of shape polydispersity and discuss the issue of reducing particle shape to a small number of descriptors or through its effect in connection with dissipation.
Section 4
In section 4 we describe different modeling strategies for particle breakage at the sub-particle and particle levels. The realism and efficiency of sub-particle methods are discussed, such as breakage criteria with regard to fracture mechanics, finite size effects, shapes of the generated fragments, and recently developed hybrid methods. We discuss how the higher physics-fidelity of sub-particle models can be combined with the computational efficiency of particle level models.
Section 5
Section 5 is devoted to DEM models of soft particles, i.e. particles undergoing large deformations without breakage. We briefly present the surface deformation methods based on material points or nodes at the particle surface, and volume deformation methods based on continuum field description of the particle behavior.
Section 6
In section 6 we discuss several computational issues. The important role of parallel computing, specially on General-Purpose GPUs, for the applicability of new models of high physics fidelity and for speedup of simulations is underlined. The limits of particle coarsening are discussed. We also recall new developments in original multiscale hybrid models and the benefits of concurrent use of discrete and continuum simulations of granular materials. Finally, we discuss the ways Machine Learning models can be used with DEM simulations and a data-driven approach allowing expensive calculations of contacts, forces and velocities in DEM algorithms to be replaced by a Machine Learning-enabled framework.
Section 7
In section 7 we consider the issues of verification and validation and discuss the methods of uncertainty quantification as an asset to reinforce the reliability of DEM in application to real-world processes. We use examples of rigorous uncertainty quantification to illustrate the treatment of uncertainties related to the input data and model approximation. We also present the concept of validation metric for optimal use of experimental data for the evaluation of model form errors.
Section 8
Finally, we present an outlook of future directions around and beyond DEM in section 8. Recent algorithmic developments are qualified according to their contributions to physics fidelity, data fidelity, computational efficiency, and game-changing nature. We discuss the developments beyond the hard-particle approximation and the scope of a data-driven DEM.
In the field of granular rheology, one of the most promising advances of the past decade has been the development of various nonlocal rheologies [1–7]. These constitutive models hold the promise of permitting the determination of a small number of empirical parameters for a particular set of particles, which then can be used to predict flow fields and stresses over a large range of intermittent, creeping, quasi-static, and intermediate flows. In order for these models to be useful, the aim is to make a set of flow measurements for a set of particles in one geometry, and then determine the constitutive parameters for use in predicting flows in other geometries (for the same particles). Doing this requires a quantitative understanding of which properties are set by both the particle properties, and the boundary conditions at the walls.
In Years 1-3, we established that NLR successfully models granular flows across different packing densities, particle sizes and shapes, and shear rates, using just 3 constitutive properties (A, b, μs), but that we must know the amount of slip at the wall from geometry-dependent measurements. During Years 4-7, we extended these measurements to compare which flow properties are set by the particle properties, versus by the wall properties. We performed experiments in both the original annular rheometer, as well as in a vertical hopper, using six different boundary conditions. We found that the roughness and compliance of the boundary strongly controls the amount of wall slip. Nonetheless, we find that we can successfully capture the full flow profile using a single set of empirically determined model parameters, with only the wall slip velocity set by direct observation. Through the use of photoelastic particles, we observed how the internal stresses fluctuate more for rougher boundaries, corresponding to lower wall slip, and connected this observation to the propagation of nonlocal effects originating at the wall. Our measurements indicate a universal relationship between dimensionless fluidity and velocity. The measurements in the annular rheometer are echoed by less-quantitative measurements performed in the vertical hopper. These results have been published in one paper [22] and one preprint [25]. Two graduate students received their PhDs, and one undergraduate gained research experience.
Three IFPRI collaborations have been supported during this seven year period, with Nathalie Vriend, Karen Hapgood, Prahbu Nott and their research groups. With Vriend, we extended our efforts into a chute flow which provided us data at higher inertial number than was possible in the annular rheometer. We defined a quantitative measure for the rate of generation of new force chains and found that fluctuations extend below the boundary between dense flow and quasi-static layers, as well as evaluating several existing definitions for granular fluidity [8]. With Hapgood, we performed stress visualization within 3d printed particles with realistic shapes, using photoelasticity. We characterized the importance of controlling the relative orientation of the print layers and the loading force, and observed that semi-quantitative measurement of internal stresses is possible, with some caveats [9]. With Nott, we performed laboratory tests of an additional nonlocal model [10] that incorporates dilatancy as a model variable, and found good agreement. This effort is ongoing, and will continue into the remaining years of his project. More details are provided in IFPRI ARR-106-03.
In the first year of this project, we had derived a mechanics-based model for the feed rate in a single-screw feeder, making several simplifying assumptions. The model makes the prediction that the feed rate is maximum at a particular value of the ratio of pitch to diameter p/2R of the screw. This prediction matches exactly with the results obtained by DEM simulations under the same conditions. When the simplifying assumptions are relaxed in the DEM simulations, the dependence of the feed rate on p/2R was found to be qualitatively similar, suggesting that the simple model captures the essential physics of the problem.
In the second year, our work was extended in several directions:
- experimental measurement of the feed rate for different p/2R, the stress at the barrel surface using sensitive force sensors, and the velocity profile adjacent to the (transparent) barrel surface by flow imaging;
- application of a newly developed non-local constitutive model to the screw feeder problem and solving the governing equations to obtain the velocity and stress fields;
- DEM simulations to study the effect of particle cohesion on the feed rate and obtain the detailed spatial variation of the stress and velocity in the particulate medium.
Overall, we found good agreement between results of the DEM simulations, model predictions, and experimental data. The important conclusion was that combination of the three components of our investigation, namely theoretical analysis, DEM simulations and experiments, led to substantial insight.
In the third year (for which this report is written) we have further extended our experimental studies in some directions: we first completed the determination of the feed rate for a larger range of p/2R for glass beads and confirmed the existence of a maxima in the feed rate at an optimum value of p/2R. We then measured the feed rate for two cohesive powders – though measurements for sufficient large p/2R are yet to be made, the data strongly suggest the presence of the maximum in the feed rate. The experiments also throw light on the feed rate fluctuations, which are quite different for non-cohesive and cohesive powders. Our earlier DEM simulations restricted the feeder length to one pitch and assumed periodic inlet and outlet conditions. We have now conducted simulations for the full feeder, from the inlet hopper to the feeder exit. The results show a gradual fall in the fill level with axial distance from the inlet, as observed in the experiments.
Our ongoing work is to obtain solutions of the non-local model for the more general cases of finite screw friction in the presence of gravity. We are measuring the feed rate of cohesive powders for a large range of p/2R to confirm the presence of the maxima. We will soon conduct DEM simulations for cohesive powders for the full length of the feeder.
In this report, we provide an update on the progress of the second part of the IFPRI Robin. In our Part 1 report, we quantitatively assessed the effectiveness of discrete element method (DEM) calibration methods utilised by 8 industrial DEM practitioners for a number of differing experimental geometries, particulate media, and combinations thereof. The accuracy of the methods was assessed by comparing the outputs of simulations performed following the procedures of 8 industrial participants with detailed experimental data produced using Positron Emission Particle Tracking (PEPT), a technique which allows the dynamics of particulate systems to be imaged, in three dimensions, with sub-millimetre spatial resolution and sub-millisecond temporal resolution. Strikingly, of all the participants surveyed, no two institutions adopted the same practices, highlighting the need for a more standardised approach and best practice. Our results showed that while most contemporary calibration methods were able to successfully capture the dynamics of simple, free-flowing, spherical particles under low-shear conditions, and a reasonable percentage of participants could correctly predict the dynamics of angular particles, the majority of procedures tested were unable to correctly reproduce the behaviours of smaller, more cohesive particles, or higher-shear environments. For the latter case, though qualitative agreement and visual similarity between simulated and experimental systems could be observed, deeper and more quantitative analysis using PEPT revealed significant disparities. Of the calibration methods examined, the most effective – indeed the only one to consistently reproduce the experimentally-measured dynamics of the cohesive systems tested – involved the combination of both static and dynamic powder characterisation tests, suggesting this to be the best practice for multi-parameter DEM calibration.
In the second part of the project, we will assess the ability of DEM, and the practitioners thereof, to handle a series of still more complex particles, including binary systems whose components possess strongly differing PSDs; fine particles (both free-flowing and cohesive); and highly elongated particles. We will also explore additional industryrelevant test systems (a Resodyn acoustic mixer and a Pascall mixer), and create additional digital twins of characterisation tools used by our industrial project partners (a Granutools GranuPack, Granutools GranuFlow. aerated Freeman FT4, and Anton Paar powder rheometer). We will also use detailed sensitivity analysis to assess the suitability and efficacy of all characterisation tools explored for the determination of different DEM parameters. This brief report highlights progress made so far toward these aims, and showcases a selection of the new tools developed and data obtained. All tools and data are available, free and open source, to IFPRI members upon request.
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This annual report presents key advances made during year 2 of which, a major component is a concise treatise on our key advances in model-guided dry coating-based enhancements of poor flow and packing of fine cohesive powders, included in Appendix A. The report also includes a review of the available particle contact models for both smooth and rough particles and presents a database of industry relevant materials and their key properties. In terms of IFPRI Member interactions, we have held regular update meetings and worked with a member company on their powder characterization device. We plan to prepare a manuscript on that and include that in the report next year.
Major Accomplishments
Major accomplishments include a review of the existing van der Waals force-based particle contact models to elucidate the main mechanism of flow enhancement through silica dry coating. Our multi-asperity model explains the effect of the amount of silica, insufficient flowability enhancements through conventional blending, and the predominant effect of particle surface roughness on cohesion reduction. Models are presented for the determination of the amount and type of guest particles, and estimation of the granular Bond number, used for cohesion nondimensionalization, based on particle size, particle density, asperity size, surface area coverage, and dispersive surface energy.
Processing Conditions
Selection of the processing conditions for LabRAM, a benchmarking device, is presented followed by key examples of enhancements of flow, packing, agglomeration, and dissolution through the dry coating. Powder agglomeration is shown as a screening indicator of powder flowability (Appendix B). The mixing synergy is identified as a cause for enhanced blend flowability with a minor dry coated constituent at silica <0.01%. The analysis and outcomes presented in this paper are intended to demonstrate the importance of dry coating as an essential tool for industry practitioners.