Powder Flow
Key updates
I was not able to recruit a dedicated PhD student, hence we are now on gap year. This issue was addressed in January 2020 and a PhD student Vishal Shinde was recruited. He graduated from Leicester in 2018 with an MSC with Distinction. He is expected to start in 2-3 months time after getting his visa.
Complementary to the project, I will be hosting a visiting PhD student from China (Ruochen Sun) from September 2020 for a period of 1 year, subject to approval of his China Scholarship Council application for funding. He will perform molecular dynamics simulations to analyse the interaction of mannitol and ibuprofen with iron. This is not related to the IFPRI project, but it could provide relevant insight.
A detailed planning for the following year will be prepared 1 month after the start of the PhD project. Also, I am planning an open workshop with participation of all academics and industrialists who are actively researching the problem of sticking at the present time of who have recently completed projects. This workshop will be planned 2-3 months after the start of the PhD project.
industry.
experimental results, and used to inform a `best practice' for the application of DEM in
number of benchmark systems are assessed and compared both to one another and to
(DEM) modelling to participate in a `round robin' in which their attempts to model a
This project brings together a cohort of companies who utilise discrete element method
1. Brief Summary of Project
Introduction to the Project
Summary
This report documents the work performed during the last 36 months funded by IFPRI. It covers the following four aspects: 1) suction filling; 2) Rotary die filling; 3) Forced die filling with a paddle wheel; and 4) Segregation during die filling.
For suction filling, a model suction filling system was developed. Die filling efficiency was evaluated in terms of fill ratio, and four different types of pharmaceutical powders were used and. Effects of filling and suction velocities, as well as powder properties, on the efficiency of die filling were systematically investigated. It was observed that for a given die filling system an optimal ratio of filling to suction velocity (i.e. the optimal velocity ratio, v*) could be defined. Therefore, three distinctive phases in suction filling could be identified: i) a filling to suction velocity ratio (vr) below v* would result in piston reaching the specified terminal position before the shoe completes its transit over the die; this is referred to as slow filling ii) when vr = v*, the suction and filling synchronise so that the piston reaches the terminal position precisely when the trailing edge of the shoe starts transiting over the die, which is referred to as the synchronised filling; iii) when vr > v*, the piston reaches the terminal position after the shoe has completed the transit over the die, and this is referred to as fast filling. In slow filling, cohesive and free flowing materials showed two distinctive die filling behaviours: cohesive materials produced a gradual increase of fill ratio, reaching its maximum value at v*, whereas for free flowing materials the fill ratio decreases slightly as the vr increases and at v*, 5-10% reduction in fill ratio was observed. In fast filling, the die filling behaviour is similar to that of gravity filling at high filling velocities, where the fill ratio decreases as vr increases.
For rotary die filling, a model rotary die filling system was developed to mimic the die filling process in a typical rotary tablet press. The system consists of a round die table of 500 mm diameter, equipped with a rectangular die. The die table can rotate at an equivalent translational velocity of up to 1.5 m/s. The filling occurs when the die passes through a stationary shoe positioned above the die table. Using this system, die filling behaviours of 7 commonly used pharmaceutical excipients with various material characteristics (e.g. particle size distribution, sphericity and morphology) and flow properties were examined. The efficiency of die filling is evaluated using the concept of critical filling velocity. It was found that the critical filling velocity is strongly dependent on such properties as cohesion, flowability, average particle size and air sensitivity index. In particular, the critical filling velocity increases proportionally as the mean particle size, flow function, air permeability and air sensitivity index increase, while it decreases with the increase of specific energy and cohesion.
For forced die filling with a paddle wheel, the flow behavior of powders was studied systematically using a model die filling system. The fill effects of different turret speed and paddle speed were carried out using a simulated system with four cylindrical dies. Three grades of microcrystalline cellulose powders were examined to explore the effect of particle size and shape on die fill. Flow properties were quantified using the concept of critical fill speed. It was found that critical filling speed and parameter n depend on not only the properties of powders but also the size and shape of die. The ratio of powders entering the die was primarily influenced by turret speed, while paddle speed has a slight impact. High speed video was used to discuss the trait of flow pattern. Mass uniformity was positively correlated with critical fill speed. The powder bed is loosened when the last die through the fill area and consequently it was filled more than others. The researched critical process parameters help optimize powder formulation and process design.
For segregation during die filling, particle size-induced segregation during die filling of binary pharmaceutical blends, consisting of fine and coarse particles in various fractions, was investigated. Coarse fraction was made of milled and sieved acetylsalicylic acid, whereas the fine fraction was mannitol. The die filling process was carried out in gravity filling and suction. The segregation was assessed through determination of the coarse component concentration using UV-Visible spectrophotometry. The obtained values of concentration, determined for ten units of identical volume inside the die, were used to calculate the Segregation Index (SI), which was an indicator of uniformity of the powder blend deposited into the die. It was found that high segregation tendency was generally observed during suction filling at low velocity, due to the effect of air drag, and during gravity filling at low velocity, as it was carried out through three consecutive filling steps. The lowest segregation tendency was observed during suction filling, irrespective of the filling velocity and concentration. The horizontal segregation was mostly observed in the top layers of the die, due to mainly two mechanisms: coarse particles cascading down the heap formed by the powder in the final steps of die filling, which produces higher coarse concentration in the near side of the die, observed at low coarse concentration; or coarse particle cascading down the top surface of the flowing powder stream into the die, which increases the coarse concentration in the far end of the die.
Research Plan & Executive Summary
In this project, we modified the boundary conditions of our existing photoelastic avalanche experiment to quantify their control on the flowability of granular materials and the extent of non-local effects in this flow. This 1-year project involved the following three work packages:
- Spatial evolution: explore the evolution of key parameters in the flume.
- Oscillating basal boundary condition: add a spatially oscillating basal boundary condition.
- Wall shear-stress: install an external wall shear stress sensor on the basal boundary condition.
Annual Report
This separate collaboration grant was funded (CRR-02-15) in 2018 - 2019 to leverage the highly-successful and cost-effective IFPRI-funded collaboration CRR-02-14, between the Daniels and Vriend lab, during 2017 - 2018. This new extension identified three different goals to modify the boundary conditions of our existing photoelastic avalanche experiment to quantify their control on the flowability of granular materials and the extent of non-local effects in this flow. The project involves the following three work packages:
- Spatial evolution: explore the evolution of key parameters—the fluidity field, the force and velocity fluctuations—as a function of downstream position in the flume (M1 – M2).
- Realization: at this moment we only characterized one location, at 0.25 m from the inflow, but we have the ability to scan and measure the entire length (2m) of the experiment.
- Aim: investigate whether the pilot-observations of non-locality at one location are consistent across the entire experiment.
- Oscillating basal boundary condition: quantify the effect on the non-local/local flow transition by adding a spatially oscillating basal boundary condition (M2 – M5).
- Realization: periodically displacing the boundary insert (global rearrangement) or installing an actuator, for example an electromagnetic driver (e.g. MB Dynamics PM50A), for intermittent pulses (local rearrangement).
- Aim: determine the mechanisms by which oscillations with different length- and time-scales influence the flowability and fluidity of the flow.
- Wall shear-stress: install an external wall shear stress sensor on the basal boundary condition (M4 – M7).
- Realization: Create a custom-made transducer (beam & floating plate) or an off-the-shelf external wall shear sensor (e.g. L108 Lenterra).
- Aim: investigate whether the flow exhibits slip, stick or sliding on the boundary, and whether stress fluctuations are measurable at the boundary.
Executive Summary
In our second phase of the project (year two) we build upon the serendipitous finding made in phase one (year one): The significance of the new Pèclet number Pe = γ˙ d/√T extends beyond simply quantifying the relative importance of advection to diffusion, Akin to the definition of the Inertial number (I) and viscous number (Iv), Pe also represents the ratio of microscopic kinetic rearrangement timescale d/√T to the macroscopic shearing timescale (1/γ˙ ). Consequently, kinetic rearrangement—the fundamental driver of mixing—to the definition of the Inertial number (I) and viscous number (Iv), Pe also represents the ratio of microscopic kinetic rearrangement timescale d/√T to the macroscopic shearing is now controlled by the actual relative motion between particles, as opposed to assuming that the microscopic motion (so-called particle fall) is driven by pressure.
So building the new Pèclet-based rheology into a macroscopic-level process model of the rotating drum flow, could yield after suitable scaling, a dimensionless number that fully characterises the local mixing state of the granular assembly. And in terms of the IF- PRI project, the dimensionless number should facilitate robust scaling of the mixing state between different operating conditions.
However, before building the process model and dimensionless number upon a possible “house of cards” we embarked on an extensive testing process of the Pèclet-based rheology via simulation. Within the context of the DEM simulation framework, we treat the DEM outputs as “data” and apply coarse graining to yield the continuum-level stress and strain fields. Using > 200 simulation configurations spanning dry, wet, dense and dilute granular flows, we show that the Mohr-Coulomb friction coefficient µ = τ /σ, where τ is the shear stress and σ the pressure, varies linearly with √Pe for a variable yield stress ratio µs consistent with the different geometric configurations and flow regimes investigated.
µ = cµ√Pe, (1)
where the scaling parameter cµ is dependent on driving conditions, and hence the material contact friction coefficient µc.
The linear collapse of the data according to equation (1) spanned a wider range of the phase space than the µ (I)-rheology, viscoinertial rheology, non-local rheology and extended kinetic theory. We argue that cµ partly encodes the anisotropy of the tangential contact force network, and equation (1) relates this structure anisotropy to the stress ratio. Noting that these anisotropies are also signatures of the granular mixture state, we hypothesise that the most robust mixing rules will emerge from encoding the new Pèclet-based rheology into the formulation of the mixing rules.
The reproducibility of flow measurement at low stresses is similar for the RST-XS.s shear cell and for the ball indentation method by sieve filling using an indentation attachment to the FT4 Powder Rheometer, however the measured values of unconfined yield stress do not agree. A small hopper will be designed based on the flow measurements of both instruments at low stresses. The critical outlet diameter for flow initiation will be experimentally determined and compared to the dimensions predicted by the flow measurements of these two instruments. To minimise the powder quantity, gypsum powder is proposed for this investigation due to its high bulk density and cohesive flow behaviour.
Shear cell measurements using the FT4 shear cell and Schulze RST-XS.s low stress shear cell agree at moderate stresses, however below 2 kPa the FT4 shear cell does not achieve the intended applied stresses for titania DT51, and therefore does not provide a reliable measurement in this range. The Schulze RST-XS.s provides unconfined yield stress measurements < 5% for the very cohesive titania at pre-shear stresses as low as 100 Pa, however the variability increaseses for more free-flowing powders.
Powder flow measurement at low stresses is more challenging due to (i) the required resolution of the force measurement and (ii) the reproducibity of the loose packing state. Shear cells pre-shear the sample in an effort to ensure a reproducible packing state, however the vertical consolidation applied in indentation and uniaxial compression approaches does not achieve this alone. Ball indentation measurements are assessed by pre-shearing and by blade conditioning, wire conditioning and sieve filling prior to vertical consolidation. At low stresses, pre-shearing is found to provide a large coefficient of variation in the bed hardness measurement by indentation, whereas sieve-filling is able to produce a coefficient of variation < 5% at low consolidation stresses. Uniaxial compression measurements correlate with ball indentation measurements at moderate stresses, allowing constraint factor to be determined and ultimately for unconfined yield stress to be inferred from indentation measurements. However, at lower stresses the uniaxial compression test underestimates the unconfined yield stress.
Measurement of powder flow behaviour is important for many powder handling operations. The most widely established method for measuring powder flow is by shear cell analysis, with procedures developed for designing hoppers based on mass or funnel flow behaviour using shear cell measurements. As the consolidation stress applied to the powder is reduced, the reliability and reproducibility of the measurement decreases. Powder flow measurement at low stresses is assessed here by ball indentation, uniaxial compression and shear cell methods.
Executive Summary
EXECUTIVE SUMMARY
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. In Years 4-6 of this project, we aim to address current shortcomings in how to calibrate and apply NLR to real granular systems. We aim to establish that, for a given set of particles, can we (1) make flow measurements in one geometry which determine the constitutive parameters and (2) use these parameters to predict flows in other geometries. Thus, our current work focuses on separating which flow properties are set by the particle properties, versus those set by the wall properties.
During this first year of the renewal grant, we have observed that boundary roughness strongly controls both the flow profile v(r) and shear rate profile γ˙ (r), particularly as measured at the outer wall. This is also the region of the flow most sensitive to nonlocal effects. We also observed that the pressure P , and therefore the stress ratio µ(r), are affected by the roughness of the wall. All of this is expected, and we can now begin a quantitative understanding of these effects during Year 5. We have done significant development work on photoelastic methods to prepare for these studies. In addition, we continued working on the IFPRI-funded collaboration with Nathalie Vriend.
This resulted in measurements taken at faster flow rates than are accessible in this apparatus (I 1), and resulted in a published paper [21] that included NCSU authors. Along with our other work during Years 1-3, this paper emphasizes the importance of understanding the timescales over which the force chains fluctuate. In performing the next year’s work, will utilize photoelastic methods (both statics and dynamics) as well as our older particle-tracking methods to meet the three aims.
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 continue to develop a new way of structuring segregation rate models that 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 developed several novel inherently scalable, theoretical models based on rheologically-relevant dimensionless groups that are applicable to density, size, shape, and cohesive segregation. We have experimentally validated some of these segregation models and plan to expand others, while incorporating the validated models into device-level transport equations in order to supply quantitative prediction of segregation at process scale.
Executive Summary
scale.
device-level transport equations in order to supply quantitative prediction of segregation at process
our ultimate aim is (experimentally) validated segregation models that can be incorporated into
applicable to density, size, shape, and cohesive segregation. As this project continues to mature
novel inherently-scalable models based on rheologically-relevant dimensionless groups that are
be considered state-of-the-art, but, more importantly, we have begun theoretical development of
previously reported. Thus far we have demonstrated which models from the literature may
way of structuring segregation rate models that make them inherently more scalable than any models
of the interplay between granular rheology and segregation, we aim to continue to develop a new
deduce the segregation rate (and validate the expressions). Moreover, by exploring a novel view
expressions that we are interested in testing with dramatically simplified experiments to ultimately
this balance between the rate of segregation and the perturbation rate, we can combine the model
free surface granular flows in order to alter the steady-state distribution of particles. By achieving
is that we use flow perturbations to establish an “equilibrium” between segregation and mixing in
combined theoretical, computational, and experimental program. One unique aspect of our work
In this project, we seek to alleviate these two shortcomings of segregation research through a
- for validation purposes
- the significant dearth of validated scale-up studies for these models.
are (1) the inherent difficulty in measuring segregation rates (especially in an experimental setting)
practice. Two significant issues that hamper the applicability of models in industry, however,
Segregation model development holds promise for translation of academic research into industrial
EXECUTIVE SUMMARY
depends on both the particle shape and material.
while the local rheological parameter is largely independent of particle-shape, the nonlocal parameter
from material properties such as the coefficient of friction or elastic modulus. We observe that
shape of the interparticle contacts (rounded vs. angular) is an important control on s, separate
with three different elastic moduli, and small range of particle sizes. We have observed that the
parameters, using particles of three different shapes (circles, ellipses, and pentagons), materials
We have successfully performed experiments to test how the particle properties affect the model
observing that it corresponds to a drop in the susceptibility to force chain fluctuations.
yield criterion. Finally, we newly identify the physical mechanism behind this transition at s by
the prediction that there is growing lengthscale at a finite value s, associated with a frictional
collected once we account for frictional drag with the bottom plate. Our measurements confirm
successfully find that a single set of model parameters is able to capture the full range of data
We obtain (I) curves for several different packing fractions and rotation rates, and
and the inertial number I through the use of a torque sensor, laser-cut leaf springs, and particle tracking.
The apparatus is designed to measure both the stress ratio (the ratio of shear to normal stress)
photoelastic particles.
quasi-2D annular shear cell with a fixed outer wall and a rotating inner wall, including using
different packing fractions, shear rates, and particle properties, we performed experiments in a
model [gradient model, Bouzid et al. 2013]. To validate the efficacy of these two models across
nonlocal theory [cooperative model, Kamrin and Koval 2012], and added a comparison to a second
Through the three years of this project, we have have conducted laboratory testing of one
to macroscale behaviors.
to bulk data for a particular flow geometry and particles, we aim to connect grain-scale parameters
of granular materials, independent of the flow geometry. Rather than using empirical relations fit
and thereby provides an improved understanding of how particle properties control the rheology
best describe such flows. Therefore, there is a need for experimental data which tests these theories,
aside adhesion, which is more challenging still). It is an open question what constitutive equations
predicts its rheological response as a function of particle size, shape, and friction (even leaving
Currently, there is no first-principles, general theory of intermediate dry granular flow that