ARR - Annual Report

General project outline and background

The structure of granules or agglomerates can be defined as the spatial arrangement of its basic components [1]. The basic components are primary particles, binder or liquid components and intra particle porosity. The quantification of granule structure is crucial for setting up processing maps and input data for simulations such as DEM and computational modelling [2]. Spatial statistics, also called stereology, provide well-defined measures to quantify the different aspects of powder structure. For infinite systems the covariance function (CVF) defines the distance relations of the particles and pores. In agglomerates a radial distribution function (RDF) quantifies shell or boundary structures. These statistical measures are well suited as a basis for stochastical property modelling. Several image analysis procedures provide the above mentioned data, e.g. morphological sieves, point sampling techniques or chord length measurements. The characteristic curves can also be correlated with stochastical processes e.g. Poisson processes. While structure measures have been determined in a number of applications, the fundamental combination of physical properties and structure is still immature. The parameter of the above mentioned stochastic models need to be linked to the key parameter of the structure generation process e.g. primary particle size, binder content, stress and growth history. Results of other simulation techniques like VOF (Volume of fluid) or Population Balance models can serve as input to generate the correlation between statistical parameter and process. The added value of a structure model would be its statistical reliability and ease of use for parameter variations. Some key powder properties are well understood physically [3-6] but lack systematic incorporation of structure measures above phase volume and particle size. Mathematical techniques to calculate structure dependent properties include cellular automata and convolution algorithms. The additional challenge is to convert local behavioural probabilities into bulk properties.

Section I. Project results: University of Delaware

Our primary goal is to trace whether there is a connection between gelation and the attractive driven glass. If gelation is the result of an arrested phase separation, then the gel line may be an extension of the attractive driven glass line down into the two-phase region of the colloidal phase diagram. Likewise, if the local microstructure of a gel is similar to a glass, then the high density regions in a gel may have the same microrheology as a glass. Observations of the potential similarities between the microstructure of the high density regions of a gel and the attractive driven glass could potentially be missed if gels were only studied using bulk rheology techniques where measurements would be an average over the entire structure. Thus, the development of microrheology is critical for understanding the origin and properties of colloidal gels.

Our work this year focused on characterizing interaction potentials in the model colloidal suspensions used for microrheology experiments. Model suspensions are finely tuned to enable simultaneous optical micromanipulation using laser tweezers and direct confocal imaging of the suspension microstructure. At the same time, gravitational sedimentation is minimized through density matching. One of the key problems has been understanding charging and the electrostatic repulsion that arises between particles in the brominated solvents used in these suspensions. The first half of our work focused on characterizing these suspensions. This has led us to begin developing replacement model systems in order to better control the colloidal interactions in these studies.

Section II: Project results: University of Michigan

Microstructural recovery of yielded colloidal gels

Introduction and Background

Colloidal gels are dynamically arrested, space-spanning networks of particles formed when the pair potential between colloids is strongly attractive at small separations. The structure, dynamics, and rheology of gels are strongly dependent upon the colloidal volume fraction. At low volume fractions, fractal clusters have been observed. At higher volume fractions, glassy states with slow dynamics are formed when short-range attractions modify the cage structure. At intermediate volume fractions, gels form with different morphologies depending on the interparticle potential: cluster-like networks form with strong attractions and contain large voids and corresponding aggregates of particles, while string-like networks form with under stronger attractions and consist of long, conjoined branches of particles. Gelation is thought to involve the competing processes between kinetic arrest, percolation, and equilibrium phase separation.

Gels and glasses undergo yielding when a sufficiently large strain is applied, resulting in fluidization and bond rupture. This process is thought to be characterized by the formation of large voids and aggregates. The mechanism and causation of yielding has been examined extensively using light scattering and neutron scattering. Alternatively, investigation of microstructural changes using optical microscopy techniques potentially allows identification of the exact spatial location of the particles in the gel network as they undergo deformation. Unfortunately, typical deformation rates for yielding, particularly those most relevant to industrial processes, do not allow tracking of individual particle trajectories. As a result, the analysis of orientations and trajectories of colloidal particles during flow has been limited to low shear rates.

Executive Summary

The aim of this study is to understand the behavior of mineral particles in concentrated electrolyte solutions using surface force techniques. To this end there are two significant challenges.

1. The first challenge relates to the type of surface forces that dominate at high electrolyte concentration. They are very short in range and poorly understood theoretically, but it is known that they are related to the solvation of the surface layer of a material or ions adsorbed to that layer, hence they are called solvation forces, or in aqueous solutions, hydration forces.
2. The second challenge is to prepare surfaces that are suitable for investigation by surface force measurement techniques and is intimately related to the first challenge as the very short range over which hydration forces operate requires that surface roughness is controlled at a level comparable to or less than the range of the hydration forces.

EXECUTIVE SUMMARY

Milling is a common unit operation deployed in many industrial sectors for particle size reduction. In this project, we aim to develop a robust methodology to link material grindability with particle dynamics in a mill in order to provide an innovative step change in mill fingerprinting and optimisation. This involves characterising the stressing events that prevail in a milling operation and establishing material grindability in the context of the stressing events. The material grindability will require a detailed study of the fundamental fracture and breakage mechanisms of individual particles under different loading regimes, and how they relate to the mechanical properties and the final size distribution. This will provide the fundamental scientific basis for developing appropriate grindability tests capable of analysing particle breakage subjected to particle impact, compression, shear and abrasion etc. pertaining to a milling process, which in turn will provide the basis for an improved particle breakage model calibrated against defined grindability.

Executive Summary

During the first year of this project, a postdoctoral research was hired with background in DEM and started in January of 2013. One student was working on subjects that are close to this project. A second student was added in summer. A parallel project with Abbvie focuses on the modeling of compaction and strength of single type particles and leverages the effort of this project. In summary the following activities were undertaken:

• A literature survey was performed to identify prior efforts on DEM for powder compaction.
• A careful study was conducted to identify potential obstacles for the application of DEM on powder compaction.
• LIGGGHTS, an open source, highly parallelized code for granular phenomena was installed and used extensively.
• A preliminary model that takes into account contact interactions was implemented in LIGGGHTS and appears to perform better than prior efforts (Storakers model). Results from this work are being analyzed.
• Preliminary results for the compaction of two phase mixture were obtained by using the Storakers model. Despite its lack of accuracy, this work provides interesting insights in the problem in terms of relative magnitude of interparticle forces on different types of contacts.
• Ongoing work focuses on finalizing the selection of force-displacement model for high densities, introduction of different size and different properties effect in it and their cross interaction. Our work has also shown, there may be a need to introduce an elastic component in the force-displacement response, in order to understand some of the aspects of mechanical behavior of compacted powder mixtures.

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.

The aim of this study is to understand the behavior of mineral particles in concentrated electrolyte solutions using surface force techniques. To this end there are two significant challenges.

1. The first challenge relates to the type of surface forces that dominate at high electrolyte concentration. They are very short in range and poorly understood theoretically, but it is known that they are related to the solvation of the surface layer of a material or ions adsorbed to that layer, hence they are called solvation forces, or in aqueous solutions, hydration forces.
2. The second challenge is to prepare surfaces that are suitable for investigation by surface force measurement techniques and is intimately related to the first challenge as the very short range over which hydration forces operate requires that surface roughness is controlled at a level comparable to or less than the range of the hydration forces.

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.

PROJECT POWDER STRUCTURE CONTROL

The project powder structure control is concerned with the definition and calculation of mathematical descriptors of granule and powder structure. The additional goal is to give the structure descriptors a physical meaning by linking them to product properties e.g. dissolution behaviour and mechanical strength.

This report covers the last year (Dec. 2011 - Nov. 2012) of work on the powder structure control project. In this period the focus has been on the development of a software package for structure evaluation. The other main part of work was concerned with a literature review on stereological methods in practical application and on the relationship between process, structure and properties.

The software package includes first and second-order stereological methods. The volume fractions of the three phases and the interfaces between those have been calculated for a test image of spheres and for exemplary images of granules. Results are in good agreement with the known test image and with visual examination of the granule images. For the evaluation of the spatial arrangement of granules second-order methods are necessary. The chord length distribution, the volume weighted star volume and the covariance function deliver results that are plausible regarding the exemplary images. In the literature review publications of all disciplines have been screened and sorted into 3 different groups: description or derivation of stereological methods, practical application of stereological methods and relationship between process, structure and properties of granules. As the stereological investigation of structure is known for a long time a lot of review publications are available, especially for first-order stereology [9, 10, 12, 15, 21, 50]. Second-order stereology has been in the focus of recent publications, especially the normalized covariance function and the pair correlation function have been of interest.

Applications of these methods could be found in different fields of research and for different spatial materials like biological tissue, concretes and porous materials. Granular materials play an important role in industry and the control of their behaviour and structure is of interest. Different approaches can be made to correlate structure, process properties and product properties. The relationship between process and product properties is very common in literature. Process properties like impeller speed of a granulator or the recipe of the raw materials are varied and product properties like strength, porosity or dissolution behaviour are compared to each other [23, 37, 39]. Further publications are concerned with the relation between structure and granule properties [2, 5, 11]. Thereby porosity and primary particle size distribution has been a frequently used parameter.

Based on these findings the next step is a structure analysis that includes spatial arrangement of structure elements because first-order measures like porosity are not suitable for every issue. When the structure can be fully described by one or more of the mathematical descriptors it should become possible to predict product properties. Process parameters as well as the raw materials will be altered systematically to generate a variety of structures.

The investigation of the functional relationship between process, structure and properties shall be examined in the following year of this project. The implemented structure measures shall be tested and optimised by using experimental input for further interpretation and understanding. Different structure generation and different recipes are planned to achieve a good variability of internal structures of the granules.

Executive Summary – University of Delaware

The goal of this work is to determine whether there is a connection between gelation and the attractive glass state of colloidal suspensions. If gelation is the result of an arrested phase separation, then the gel line may exist as an extension of the attractive glass line down into the two-phase region of the colloidal phase diagram. Likewise, if the local microstructure of a gel is similar to a glass, then the high density regions in a gel will have the same microrheology as a glass. The potential similarities between the microstructure of the high density regions of a gel and the attractive driven glass are potentially missed if gels were only studied using bulk rheology techniques, where measurements would be an average over the entire structure. Thus, the development of microrheology and simultaneous direct confocal imaging is critical for understanding the origin and properties of colloidal gels.

Executive Summary - University of Michigan

The goal of our work is to determine a simple correlation between microstructure and strain-dependent elasticity in colloidal gels by visualizing the evolution of cluster structure in high strain-rate flows. We control the initial gel microstructure by inducing different levels of isotropic depletion attraction between particles suspended in refractive index matched solvents. Contrary to previous ideas from mode coupling and micromechanical treatments, our studies show that bond breakage occurs mainly due to the erosion of rigid clusters that persist far beyond the yield strain. This rigidity contributes to gel elasticity even when the sample is fully fluidized; the origin of the elasticity is the slow Brownian relaxation of rigid, hydrodynamically interacting clusters. We find a power-law scaling of the elastic modulus with the stress-bearing volume fraction that is valid over a range of volume fractions and gelation conditions. These results provide a conceptual framework to quantitatively connect the flow-induced microstructure of soft materials to their nonlinear rheology, and imply that the modification of particle shape and surface roughness may allow us to design gels that have improved mechanical properties at even lower volume fractions.