Powder Flow

This report addresses the properties of flow in a funnel or hopper. One aspect of this work is to better understand and interpret results using the Flowdex tester. This device is used to characterize flowability, and in particular to characterize that property for various powders of interest to P&G. This work has benefitted from collaborative interactions with Paul Mort of P&G.

The Flowdex tester consists of a cylinder with a small hole at the bottom. The material to be tested resides in this cylinder. The typical dimensions are a half dozen centimeters for the cylinder diameter, and about 10 cm for its height. A release mechanism provides a rapid opening mechanism for the plug at the bottom of the cylinder.

Powder caking is considered as the undesired aggregation of particles resulting in the transformation of a free-flowing powder into a coherent solid mass. These might simply be large lumps that break down readily into their constituent primary particles. Alternatively caking may result in the complete and irreversible fusion of the entire particulate contents of a silo or other container. Whether mild or extreme, caking is a significant problem for a wide range of process industries in terms of loss of product quality or process performance, and can therefore have substantial impact on the financial health of a business. The aim of this review is to identify the current state of knowledge regarding the phenomenon of powder caking. Of particular concern are the underlying physical and chemical mechanisms, the role of process variables such as temperature, moisture content and consolidation and their dynamics, the range of experimental methods to assess caking and methods to prevent it. The main challenge of the subject is to be able to predict reliably the caking propensity of a powder product at a protracted time scale in the future, and this requires a detailed understanding of the factors listed above.

Throughout the review, areas for further research have been identified that will take us towards meeting this challenge. The role of interparticle forces in caking has been examined. Further work is required to characterise irreversible, non-equilibrium adhesive contact due to molecular rearrangement. The full role of piezoelectric, and pyroelectric charging in caking also requires further investigation.

A review of the formation of solid bridges between particles has identified two main processes; sintering and solvent evaporation. Research into sintering stems from the technologies of powder metallurgy and ceramic manufacture which involve elevated temperature and pressure. The applicability of this research to powder caking has hardly been addressed and its suitability not been examined. It is therefore recommended that further work is directed to develop the established concepts of sintering into the area of powder caking.

A small body of work has provided evidence of metastability in solid bridges causing the morphology of the bridge to evolve over protracted timescales. It is suspected that this condition is endemic in powder caking and therefore more research is recommended in this area. The formation of solid bridges from mixtures of solutes by solvent evaporation is a common phenomenon in caking. There are apparent contradictions regarding the nature of the solid bridge produced from mixed components which would benefit from further work.

The caking of amorphous powders has received a large amount of attention in the literature and models to predict caking kinetics are showing promise. The remaining uncertainty in this area relates to the behaviour of multi-component mixtures of particles. It is recommended that this area is targeted for further work. The published work relating to the dynamics of caking has been reviewed. Attempts at transient heat and moisture transfer modelling have been directed at materials that cake through dissolution and recrystallisation. More theoretical and experimental work is required in the area to develop a universal modelling tool to describe caking by this mechanism. The role of transient heat and mass transfer in caking by viscous flow, creep or sintering has not been addressed. These processes have been shown to be dependent on temperature and moisture content, and therefore it would be worthwhile to focus further work in this area. A review has been conducted of the wide range of tests to measure the strength and extent of powder caking. Of the conventional mechanical test methods, shear cell testing appears to be the most suitable, particularly if a cell was developed that had full humidity and temperature control by air percolation, and was instrumented to give changes in sample volume during time consolidation. For materials that cake by creeping, it is possible that creep testing could be reliably extrapolated to predict future caking propensity as long as the various creep mechanisms are adequately understood and accounted for. Recent developments in the application of indentation to measure powder flow could be applied to diagnose the early stages of caking. The method is sensitive, and requires very small amounts of material. It is recommended that the suitability of this technique for caking is considered in future work. The application of NMR measurements to caking looks a strong candidate for further investigation. It is recommended that the technique is coupled with more rigorous cake strength measurements. So far only amorphous materials have been studied. It would be interesting to apply NMR to the caking of crystalline or multi-component systems.

Finally the published work relating to anti-caking agents has been reviewed. The mechanisms by which these reportedly operate are various including:

• competing with the host powder for available moisture,
• acting as a surface barrier between the host particles, (preventing the formation of liquid bridges, decreasing inter-particle friction, dissipating electrostatic forces, or inhibiting crystal growth of solid bridges),
• increasing the Tg of an amorphous phase, or
• forming a moisture-protective barrier on the surface of hygroscopic powders using e.g. lipids.

All of these mechanisms could potentially be deployed to reduce caking in multi-component formulations, and therefore further research in this area is strongly recommended.

Executive Summary

The research is focused on the Mechanics of Powders and the ultimate goal of the work is to develop a quantitative description of active flows of fine powders. The study is centered on the “intermediate” regime of flow where both frictional and inertial effects are important. The main application is in the area of small-size, rough and/or cohesive powders that are industrially relevant.

The novelty of the project is to study a relatively large range of materials and flow geometries to gain meaningful insight. We report on a series of materials from simple (round beds) to complex (fine, odd-shaped and elastic), used in an axial-flow Couette and in two Jenike-type shearing devices to measure stresses and their fluctuations as a function of geometry and shear rate.

From stress transmission tests in the Jenike-type devices, we found that a layer of granules (powder) transmits normal stresses only if sheared and large fluctuations are introduced for the case of large particles. When the particles are small, of the order of hundreds of microns or less, or are cohesive and form a cake upon compression, the fluctuations are diminished and stresses are transmitted without significant alteration.

The further goal to develop constitutive equations for the intermediate regime of flow was also undertaken. The axial-flow Couette device was used as a “rheometer” to characterize the flowability of powders, develop a constitutive equation and use it in a continuum-type theoretical model to predict flow patterns, velocity distributions and forces on boundaries such as stationary walls and moving pedals. The PI is collaborating with several groups of simulators (DEM and MDS) and mathematicians to implement these models and compare theoretical results to computations. The best results so far, were obtained for a relatively fast moving Jenike-type cell where large, spherical particles where sheared against a smooth wall. Further results in the Couette device using a continuous-type theory (on the lines proposed by the work of Tardos, 1997) are also very promising.

The mixing of powders and granular materials is of central importance for the quality and performance of a wide range of products. However, process design and operation are very difficult, being largely based on judgment rather than science. There are not even tabulated data to tell how the quality of mixtures depends on mixer selection. Design depends on experience, not science.

There are no sound scale-up laws for a given equipment type, largely because particle size needs to be included in any dimensional analysis. Design is not possible by applying physical principles. There is no reliable equation to describe the flow of single component powders nor an equation for predicting the structure of multi-component mixtures. In most cases, measurement has been difficult because the materials are optically opaque. Much work in the research literature has been questionable because sampling results are affected by sample size.

Modern experimental techniques and modeling work have provided a good deal of information on the behaviour of many of the pieces of equipment, though these have been small in size. The focus has also been restricted to single and two components. However, the studies have enhanced knowledge of physical behaviour. For example, for a wide range of equipment when operating at lower velocities, mixing is determined by the number of revolutions of the mixer, not the time. Observations of flow structure have led to a few specific models that should scale with equipment size. Measurement techniques are becoming more effective in giving internal flow patterns and in measuring powder composition.

For cohesionless materials, DEM (Discrete Element Method) codes are now being used to describe flow patterns on the scale of 10,000 to 250,000 particles. A strategy that embraces the effects of particle size, equipment size and internal geometry, is advocated for the future. The aim would be to elucidate engineering principles of general utility. As part of the overall approach, the findings must be backed by experiment. For cohesive materials, there is scope to develop methods coming from population balance modeling. There is also scope to develop an understanding by subjecting well defined cohesive materials to clear patterns of strain.

It may now be possible to use the methods of digital photography to obtain data which can be fed into a method of mixture characterisation that is free of the problems of sample size. Together with an understanding of the relationship between observation at a surface and the average of a flow as a whole, such a method would, if successful, be of immense utility. At the least, performance charts for industrial equipment would finally become available.

The next stage of development is to build on the emerging knowledge and methods so that the basics for design are laid down. Design then becomes predictable and operation subject to effective control of performance.

Executive Summary

This is the final report on work performed on the IFPRI project during the period September 2005 through October, 2010. The research is focused on the study of Powder Mechanics and the ultimate goal is to develop a quantitative description of active flows for a wide variety of powders. The study is centered on the slow, frictional and the dense, “intermediate” regimes of flow where both frictional and inertial effects are important. The novelty of the project is the study of a large range of materials and several flow geometries to gain meaningful insight. We report on a series of materials from simple (round beds) to complex (fine, odd-shaped, elastic and/or compressible), used in a shear cell of the Jenike type, an axial-flow Couette, a centripetal geometry characteristic of a “spheronizer” and a hopper flow with a moving discharge (characteristic of a tabletting device) to measure stresses and porosity (void fraction), and their fluctuations as a function of geometry and shear rate.

The development of constitutive model for the intermediate regime of flow was also undertaken. The axial-flow Couette device was used as a “rheometer” to characterize the flowability of powders, develop a constitutive equation and use it in a continuum theoretical model to predict flow patterns, velocity and porosity distributions and forces on boundaries such as stationary walls. The PI is collaborating with several groups of simulators (DEM and MDS) and mathematicians to implement these models and compare theoretical results to computations as well as develop a continuous model “in house” based on commercially available software (FLUENT) and applied to the “Speronizer” geometry. Good results are reporter for the “fast” Jenike cell (collaboration with the group of Professor Sundar Sundarasen of Princeton University, see section 3.3.3.), the Couette device, using a continuous-type theory emplying FeatFlow, a Finite Element (FE) model developed by a group of mathematicians at the University of Dortmund in Germany (Professor Stefan Turek, see Appendix A).

Abstract

This review describes the packing of powders, and ways to modify it according to practical needs. Packing is affected by the assembling procedure, the container form, the shape, rugosity, and size distribution of grains, the nature of forces at each contact, the ambient fluid and the external loads acting on the packing. The variety of powders properties required by concrete applications precludes the use of universal recipes for packing optimization valid for all of them. Therefore, in this report we discuss ideas and methods that can help engineers to solve their specific technical problems related to packing.

Over the past several years, work at Duke has focused on understanding jamming and flow properties in a quasi-2D hopper. During that time, we have carried out extensive measurements to characterize the basic physics of hopper flow, including measurements of jamming probabilities, flow rates, velocity fields, and force fields. We have developed a model that describes the observed jamming statistics and that allows additional insight into the physical processes associated with jamming and flow. This work has been described in previous IFPRI reports, and is not repeated here.

New work has four goals which are extending the previous work in directions that address both underlying fundamental science and also help to better inform jamming in flows that occur in practical situations. These goals include:

1. Implementing the IFPRI-NSF collaboratory project;
2. Obtaining quantitative measures of fluctuations, diffusion, and correlations (these play key role in setting the flow properties);
3. Extending photoelastic studies of jamming flow to:
   • flows of non-spherical, particles,
   • quasi-3D, flows, and
   • flows of particles with cohesion;
4. Extending hopper flows to fully 3D using laser-scanning and x-ray fluoroscopy for imaging.

In three of these areas, we have substantive results. In the fourth, we developing new experiments, and new results should be available soon. I also organized the IFPRI AGM in June of 2011, which took place at Chapel Hill, NC. This meeting was followed by a meeting of participants in the IFPRI-NSF collaborator project.

Summary:

Over the past several years, IFPR-supported work at Duke has focused on understanding jamming and flow properties in a quasi-2D hopper. During that time, we first carried out extensive measurements to characterize the basic physics of hopper flow, including measurements of jamming probabilities, flow rates, velocity fields, and force fields for circular polydisperse particles. We showed that the flow rates are well described by the Beverloo equation. Using the idea of a free-fall region near the outlet that implies uncorrelated motion near the outlet, we developed a probabalistic model that describes the observed jamming statistics as a Poisson process. In the past year, we have implemented a two-camera approach that allows us to simultaneously image the particles with and with and without polarizers. Data with polarizers yields the particle-scale force. Data without polarizers allows us to track the kinematic properties of the particles. We have also carried out extensive studies of the flow and jamming properties of elliptical particles in our 2D hoppers. These studies show surprising scaling that also gives a broader insight into the jamming of hoppers. In particular, the semi-major axis of the ellipse appears to set the length scale associated with flow and jamming. Yet, the particle orientation near the outlet is contrary to this expectation. An ongoing aspect of the present work is to provide an understanding of jamming in hopper flow in light of the shear jamming process. The discovery of shear jamming was made during the course of work that is not supported by IFPRI. This work involves an understanding of jamming in a different sense, namely as a shear-induced transition between states that are fluid-like and states that are solid-like. This work has appeared in Bi et al., Nature (2011) and Zhang et al., Granular Matter (2010). As it turns out, the Bi et al./Zhang et al. work now seems of particular relevance to jamming in hoppers, and hence, to the IFPRI project. The important connection comes through the dominance of shear in hopper flows. I discuss this further below. The Ph.D. student supported by this project, Junyao Tang, successfully defended his Ph.D. dissertation on November 17, 2012. An additional project involves the IFPRI-NSF Collaboratory, which at this stage mostly involves the writing of papers. I will also briefly discuss experiments in 3D where we can correlate the grain scale response and the macroscopic response to strain. This latter work is primarily supported by other means, but it is of interest to the present studies.