Powder Flow
This report provides a summary of the results to date.
Research Plan & Summary
- Test the applicability of two non-local theoretical models.
- Obtaining a quantitative connection between the two geometries by measuring the non-local measurements of velocity, shear and stress at higher inertial numbers.
- Using the avalanche geometry as an alternative to the annular shear cell, to obtain yield ratio µs for both sets of particles.
Cambridge in January 2018 for two weeks. The goals of this 1-year collaborative project were:
NCSU in November 2017 for two weeks, while Zhu Tang travelled to the University of NC State. The collaboration grant involved two reciprocal visits; Amalia Thomas visited (intermediate flow, higher inertial number I) than was available in the annular Couette cell at nonlocal rheologies [Kamrin and Koval 2012, Bouzid et al. 2013] using a faster flow.
EPILOGUE TO THE PROJECT
density.
components and the individual components when compacted to the same pressure or the same
compacts. This work has clearly demonstrated the differences between a mixture of two
develop during compaction of powder mixtures as well as the residual stresses in the resulting
(2) We employed the Discete Element Method (DEM) to explore the distribution of forces that
pharmaceutical formulations) because it may replicate their interaction with moisture.
be considered as a model material for soluble crystalline components in mixtures (e.g., APIs in
of X with the appropriate properties (in this case matching of the elasticity modulus). NaCl can
controls strength in NaCl-X mixtures allows us to optimize their properties deliberate selection
material interactions. The most important result is that understanding the mechanism that
(1) The work in the NaCl system, in terms of in depth understanding of the mechanisms and the
In this report we present the results of the last year in particular:
paramount importance to the understanding of interacting mixtures.
In general, a mechanistic understanding of the ingredients and their interactions is of
the non-interacting mixtures.
received attention in the literature and was misinterpreted by studying it in the context of
this kind of behavior within the framework of the NaCl-Starch system, which had
during post compaction property evolution. We have attempted to demonstrate some of
stages of the processing of the mixtures, for example during milling of the mixture or
properties or the behavior of the others. This interaction can take place in any of the
- Indirect interactions, where the presence of one of the ingredients in the mixture alters the
such as those involving moisture transport, or local interdiffusion
- Direct interactions, such as chemical reactions between the powders, physical interactions
possible type of interactions. To begin with we attempt to classify them into:
- Directly interacting mixtures. This is a very broad category of problems because of the
mixtures is can be tricky.
high density regime. Therefore utilizing it to more complex problems such as the one of the
substantial effort (which was part of our project) is still relatively new and untested, in the
The problem here is that the DEM approach, even for single components, despite our
approach. We have presented this first order approach and have highlighted its weakness.
no trivial. This is the problem that we have attempted to address using the discrete element
Even in this case the direct comparison between the individual constituents and the mixture is
not the process of mixing affect the physical and chemical characteristics of the powders.
- Non interacting mixtures. This is the simplest case in which neither the powder themselves
mixtures according the possibility and the type of interaction between their constituents:
important concept that became obvious in the early days of the project is the classification of
some ideas that will provide the scientific basis for the exploration of this problem. The most
the years by the academic and scientific community. We attempted in the project to explore
The problem of compaction of powder mixtures and their properties has received attention over
Executive Summary
2019.
Compacting GmbH. It is expected that the system will be ready for some preliminary test in Q2 of
Furthermore, a forced filling system is currently under construction in collaboration with Fette
obtained but further data analysis is required. These results will be reported at IFPRI 2019 AGM.
constructed and a systematical experimental work was perfomed. Some interesting results were
In addition, significant progress was also made in exploring suction filling, an experimental rig was
air sensitivity index increase, while it decreases with the increase of specific energy and cohesion.
filling velocity increases proportionally as the mean particle size, flow function, air permeability and
as cohesion, flowability, average particle size and air sensitivity index. In particular, the critical
filling velocity. It was found that the critical filling velocity is strongly dependent on such properties
properties were examined. The efficiency of die filling is evaluated using the concept of critical
material characteristics (e.g. particle size distribution, sphericity and morphology) and flow
this system, die filling behaviours of 7 commonly used pharmaceutical excipients with various
filling occurs when the die passes through a stationary shoe positioned above the die table. Using
rectangular die. The die table can rotate at an equivalent translational velocity of up to 1.5 m/s. The
tablet press. The system consists of a round die table of 500 mm diameter, equipped with a
A model rotary die filling system was developed to mimic the die filling process in a typical rotary
Ms. Zakhvatayeva. It primarily covers a comprehensive study of rotary die filling.
This report summarizes the work performed during the last 12 month primarily by the project student,
Executive Summary
constraint factor increases with an increase in rolling friction coefficient or interface energy.
suggest that the constraint factor remains constant across all stress levels, and that
the addition of coarse material and decrease with the addition of fines. DEM simulations
The constraint factor of bi-disperse, cohesive glass beads has been shown to decrease with
long as they cover a sufficiently wide range.
applied in a shear test are shown to have limited influence on the generated yield locus, so
insufficient to overcome the influence of prior handling. The precise normal stresses
driven by variability in the pre-shear shear stress, thus implying the conditioning is
at lower stresses the variability in measured yield data increases; this appears to be largely
normal stress data being unavailable. Repeated testing in the Schulze shear cell shows that
titania powders. A direct comparison could not be made with the Schulze shear cell due to
been shown to apply normal stresses noticeably greater than the target stresses for these
shear cell and the Schulze RST.XS.s shear cell. At lower pre-shear stresses the FT4 has
The flow behaviour of various titania grades is found to be largely similar between the FT4
universal for all powders.
measurements to be made at lower stresses, though the optimal lid design is unlikely to be
in the shear plane. Reducing the vane height of the shear cell lid allows indentation
to critically consolidated beds since an insufficient fraction of the exposed bed is located
consolidated beds. It is shown that at lower stresses it is challenging to apply indentation
condition, with critically consolidated beds providing a greater hardness than vertically
Indentation hardness measurements have been shown to be dependent on the loading
investigated using the Discrete Element Method (DEM).
experimentally, and the influence of a broader range of particle properties has been
size distribution and interface energy on constraint factor have been assessed
for several grades of titania with two different shear cells. Furthermore, the influence of
has been assessed in ball indentation, and shear cell measurements have been carried out
used to measure flowability of titania under a range of stresses. The bed preparation method
inconsistent. The ball indentation, uniaxial compression and shear cell methods have been
Measurement of powder flowability under low stress conditions is often unreliable or
Executive Summary
relations based directly upon PEPT-derived stress computations.
in greater detail in the next phase of the project wherein we formulate mixing scaling
timescale to the macroscopic shearing timescale more naturally. This idea will be explored
like the Inertial number, also appears to describe the ratio of the microscopic rearrangement
extend beyond simply quantifying the relative importance of advection and di.usion, and
number that is computed directly from the PEPT data. Interestingly, it’s validity seems to
an alternate definition. In this regard we propose a granular temperature-dependent Péclet
The limitations in the standard definition of the Péclet number precipitated the need for
mills) that operate in the high Froude regimes.
the data. These findings have significant implications for industrial systems (like tumbling
cascading and cataracting) the Reverse Brazil Nut E.ect (RBNE) is clearly evident from
the Brazil Nut E.ect (BNE) at low Froude numbers; however, at higher Froude numbers
The initial analyses of PEPT data clearly show radial segregation by size consistent with
developed flow conditions.
assumption, we extract the bed shape, solids fraction and kinematics for steady, fully
of representative radio-labelled beads (the tracer) into Eulerian fields under the ergodic
and cataracting Froude regime. After converting the measured Lagrangian trajectories
matrix spanned four fill fractions and seven drum rotation rates across the cascading
plastic beads) within a laboratory rotating drum fitted with lifter bars. The experimental
was used to measure the 3D trajectory of a binary mixture (3mm and 5mm diameter
In our first phase of the project (year one) Positron Emission Particle Tracking (PEPT)
many investigators that ultimately lead to a restricted mechanistic interpretation.
is not well understood. A further limitation relates to the low Froude regimes explored by
known to exhibit axial and radial mixing; however, their interplay for optimal performance
system encountered in the mineral processing, food and pharmaceutical industry is well
the high shear zones where most of the energy is dissipated. The canonical rotating drum
processes is the inability to control the relative mix of grinding balls and small rocks in
ingredient and excipient. Central to the low efficiency (< 5%) reported in mineral grinding
industry, the e.ectiveness of the drug is directly related to the mixture of active
Mixing (and segregation) play a vital role in several industrial processes. In the pharmaceutical
Executive Summary
Segregation model development holds promise for translation of academic research into industrial practice. Two significant issues that hamper the applicability of models in industry, however, are (1) the inherent difficulty in measuring segregation rates (especially in an experimental setting) for validation purposes and (2) the significant dearth of validated scale-up studies for these models. In this project, we seek to alleviate these two shortcomings of segregation research through a combined theoretical, computational, and experimental program. One unique aspect of our work is that we use flow perturbations to establish an “equilibrium” between segregation and mixing in free surface granular flows in order to alter the steady-state distribution of particles. By achieving this balance between the rate of segregation and the perturbation rate, we can combine the model expressions that we are interested in testing with dramatically simplified experiments to ultimately deduce the segregation rate (and validate the expressions). Moreover, by exploring a novel view of the interplay between granular rheology and segregation, we aim to introduce a new way of structuring segregation rate models that will make them inherently more scalable than any models previously reported. Thus far we have demonstrated which models from the literature may be considered state-of-the-art, but, more importantly, we have begun theoretical development of novel inherently-scalable models based on rheologically-relevant dimensionless groups. As this project continues to mature our ultimate aim is (experimentally) validated segregation models that can be incorporated into device-level transport equations in order to supply quantitative prediction of segregation at process scale.
Executive Summary
At moderate to high stresses shear cells are the preferred method of powder flow measurement, however at low stresses the determination of unconfined yield strength by this technique is often marred with inconsistencies in the measurement, or in comparison to observed behaviour. An alternative approach for measuring powder flow is ball indentation, which directly measures hardness; related to unconfined yield strength by the constraint factor. The ball indentation and shear cell methods are applied for a wide range of powders, and the constraint factor is found to increase if particle size is reduced or the particle size distribution is reduced. Constraint factor is found to be independent of stress for almost all tested powders, though varies from 1.8 – 5.5 for the different powders tested, and hence its determination is required in order to provide meaningful unconfined yield strength values from ball indentation. For many powders the variation in unconfined yield strength with major principal stress is shown to be much more pronounced at low stresses (< 1 kPa) when analysed by ball indentation. Shear cell measurements at this low stress range generally agree with this trend, though for some powders discrepancies exist between the values reported by each technique. The hardness measurement at low stress is highly reproducible, though relies on a constant constraint factor in order to determine unconfined yield strength. In contrast, the reproducibility of the yield locus generated in the shear cell weakens at lower stresses, with the minimum stress that provides reliable measurements being material dependent. For maize starch the shear cell measurement appears to be reliable even at a pre-shear normal stress of 60 Pa, and the determined unconfined yield strength agrees very well with that determined by ball inden
Executive Summary
During this reporting year, we focused on the following activities:
- Parametric studies were conducted that elucidate the effect of the differences in material properties of two components in a mixture on the strength of the mixture and some reasons that there is a deviation from the rule of mixtures.
- Appropriate definitions of damage were derived in order to understand the evolution of the strength of a compacted mixture during the compaction/unloading/ejection sequence.
- The issue of damage directionality become obvious in a parallel leveraged project. We present here only a single yet important relevant simulation. Detailed presentation of this topic will be done in the final report.
Executive Summary
This report summarizes the work performed during the last 12 month primarily by the project student, Mr. El Hebieshy. It primarily covers a comprehensive study of size and density induced segregation.
Segregation mechanisms of powder mixtures during die filling were experimentally investigated. Binary mixtures of powders with either similar particle density but different mean particle sizes or similar particle size but different particle densities were considered to investigate segregation due to size or density differences. A segmented shoe and die were constructed to quantitatively explore, the size induced segregation and density induced segregation during die filling. The results indicated that, during die filling, depending on the shoe speed, different segregation mechanisms came into effect; the sieving segregation mechanism often occurring in hoppers was observed during all condition, where air could freely escape. The fluidization segregation mechanism was observed when the air inside the die, while being displaced by the powder, was only able to escape by permeating through the powder bulk in the shoe. It was also found that the composition ratio of the mixtures only had a minor effect on the segregation tendency for the materials considered in this study.
In addition, progress was also made in exploring rotary die filling, for which a rotatory die filling system was constructed and an extensive experimental work was conducted to compare die filling behaviours using the linear and rotatory die filling systems. A large quantity of data was collected and is currently being analysed and will be reported at IFPRI 2018 AGM. Furthermore, a suction filling system was designed and is currently under construction, it is expected that the system will be ready for research work in early 2018 and preliminary work will be reported at IFPRI 2018 AGM.
EXECUTIVE SUMMARY
Currently, there is no first-principles, general theory of intermediate dry granular flow that predicts its rheological response as a function of particle size, shape, and friction (even leaving aside adhesion, which is more challenging still). It is an open question what constitutive equations best describe such flows. Therefore, there is a need for experimental data which tests these theories, and thereby provides an improved understanding of how particle properties control the rheology of granular materials, independent of the flow geometry. Rather than using empirical relations fit to bulk data for a particular flow geometry and particles, we aim to connect grain-scale parameters to macroscale behaviors.
In this second year of effort, we have have continued our laboratory testing of one nonlocal theory cooperative model, Kamrin and Koval 2012, and added a comparison to a second model gradient model, Bouzid et al. 2013. To test the efficacy of these two models across different packing fractions and shear rates, we performed experiments in a quasi-2D annular shear cell with a fixed outer wall and a rotating inner wall, using photoelastic particles. The apparatus is designed to measure both the stress ratio µ (the ratio of shear to normal stress) and the inertial number I through the use of a torque sensor, laser-cut leaf springs, and particle-tracking. We obtain
µ(I) curves for several different packing fractions and rotation rates, and successfully find that a single set of model parameters is able to capture the full range of data collected once we account for frictional drag with the bottom plate. Our measurements confirm the prediction that there is growing lengthscale at a finite value µs, associated with a frictional yield criterion. Finally, we newly identify the physical mechanism behind this transition at µs by observing that it corresponds to a drop in the susceptibility to force chain fluctuations.
We have begun experiments testing the influence of other particle-properties, starting with particle material and shape. Our preliminary investigations have revealed that the shape of the interparticle contacts (rounded vs. angular) is an important control on µs, separate from material properties such as the coefficient of friction or elastic modulus. In addition, we observe that the model parameters will require adjustment in order to fit µ(I) and velocity profile data collected for different particle types, as expected.