CRR - Collaboration Report

This report concerns the ongoing collaboration on the numerical modeling of the shear rheology for capillary suspensions via the Fast Stokesian Dynamics algorithm. Up to and including December 2024, we have completed major work on the base simulation software: Python-JAX Fast Stokesian Dynamics (JSFD). This includes enabling shear, both oscillatory and steady, and the implementation of several validation checks for the physics under consideration – a publication on the software is under preparation and this will be submitted in the coming month. JSFD is already publicly available and being tested by collaborators external to the project (Prof. G. Petekidis, FORTH, Greece). It is presently capable of simulating the effect of low-Reynolds-number hydrodynamic interactions between monodisperse spheres that are subjected to external forces and various interparticle potentials. The latter can be readily modified to purpose.

In order to compare experimental rheology with our numerical modeling, we have to map experimentally obtained – using confocal microscopy – particle coordinates into our simulation. We have devised such a mapping and have had success in creating simulation appropriate initial conditions based on experimental input. We remove any overlaps that come from replacing polydisperse particle (10%, experiment) by monodisperse spheres using gradient descent. The quality of this mapping has been characterized and we are investigating whether we can improve upon it, for example, by adding information on the position of the capillary bridges in the sample as obtained using confocal.

Our first rheological measurements were shown during the IFPRI 2024 Annual General Meeting (AGM), although these were based on very preliminary analysis. We have since realized that there are some fundamental issues that need to be overcome. We are presently studying the literature to find out the most accurate way to compute the loss and storage modulus within the Stokesian Dynamics framework. There appears to be a lack of consensus on the topic, which needs to be resolved, as we will detail in our report. Our present approach is to reproduce the rheology of a dilute dumbbell fluid, where the connection between the beads made using a Hookean spring. Lastly, we are in the process of implementing changes to the interaction potential that models the capillary bridges, as per the suggestions received during the AGM. We aim to complete these activities by May 2025, which closes the collaboration project, also including publication of our findings.

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.

Solid oral dosage forms represent the predominant method of delivering active pharmaceutical ingredients (APIs), constituting up to 80% of all administered medications (Eggenreich et al., 2016). Among these, immediate release tablets stand out as the preferred choice for various reasons, including their ease of administration, precise dosing, high patient adherence, and extended shelf life (Bredenberg et al., 2003). In many cases, the industry utilises a granulation process – with wet granulation as a common choice – to improve manufacturability of the drug substance. Wet granulation involves enlarging particle size through liquid binding agents, offering control over granule and final product attributes.

There has been significant progress in developing process models for granulation, but there is a demand for more accurate models depicting granule functionality. Mechanistic models are sought after to predict key rate processes of granules that describe its disintegration for predicting product performance. The limited understanding of granule performance is also linked to a lack of suitable measurement techniques that probe the fundamental disintegration mechanisms.

In-vivo disintegration initiates when a patient ingests an oral dosage form and it encounters physiological fluids, starting with saliva as the initial fluid. While saliva may not be the primary fluid facilitating most disintegration processes for many dosage forms, it serves as a crucial initial phase. Subsequently, the oral dosage form navigates through the gastrointestinal tract, where the bulk of tablet disintegration and dissolution takes place (Markl and Zeitler, 2017).

In both in-vivo and in-vitro disintegration, the tablet undergoes the same physicochemical changes as part of the disintegration and dissolution processes. There are a number of bonds within a tablet that must be broken for disintegration to take place; this includes cohesive forces (hydrogen bonding, van der Waals and electrostatic interactions) and mechanical interactions (solid/binder/crystalline bridges and mechanical interlocking) (Ellison et al., 2008). Disintegration is the breakdown of tablets into smaller pieces; this generates a larger surface area which enables dissolution to take place more rapidly. Incomplete disintegration limits the surface area available for dissolution and therefore hinders drug release. To negate this potential issue pharmaceutical formulations will often have a disintegrant added.

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:

1. Spatial evolution: explore the evolution of key parameters in the flume.
2. Oscillating basal boundary condition: add a spatially oscillating basal boundary condition.
3. 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:

1. 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.
2. 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.
3. 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.

This report provides a summary of the results to date.

Research Plan & Summary

1. Test the applicability of two non-local theoretical models.
2. Obtaining a quantitative connection between the two geometries by measuring the non-local measurements of velocity, shear and stress at higher inertial numbers.
3. 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.

The mechanical properties of spherical alumina and zeolite particles were measured to provide an insight to their susceptibility to milling in a pin-mill. Nanoindentation was applied to determine Young’s modulus and hardness, whilst microindentation and SEM observation were carried out to measure fracture toughness. Preliminary indents determined the suitable load to apply for each material. The Young’s modulus, hardness and fracture toughness were found to be greatest for alumina, and increased with size of zeolite particles. Large scatter was present in the measurements, as is typically the case. The scatter was greater for the zeolite particles than the alumina. The mechanical and physical properties of these particles lead to the prediction that the larger zeolite is more prone to impact breakage caused by a pin mill, with the alumina particles being least susceptible.

The impact breakage of the smaller zeolite particles was assessed in a single particle impact rig at a range of impact velocities and angles. The extent of breakage was shown to correlate with normal impact velocity, regardless of impact angle. This is expected to be the case for larger zeolite particles, however alumina particles should be subjected to similar tests to assess if impact angle is influential on the extent of breakage.

The mechanical properties of spherical alumina and zeolite particles were measured to provide an insight to their susceptibility to milling in a pin - mill. Nanoindentation was applied to determine Young’s modulus and hardness, whilst microindentation and SEM observation were carried out to measure fracture toughness. Preliminary indents determined the suitable load to apply for each material. The Young’s modulus, hardness and fracture toughness were found to be greatest for alumina, and increased with size of zeolite particles. Large scatter was present in the measurements, as is typically the case. The scatter was greater for the zeolite particles than the alumina. The mechanical and physical properties of these particles lead to the prediction that the larger zeolite is more prone to impact breakage caused by a pin mill, with the alumina particles being least susceptible.

The impact breakage of the smaller zeolite particles was assessed in a single particle impact rig at a range of impact velocities and angles. The extent of breakage was shown to correlate with normal impact velocity, regardless of impact angle. This is expected to be the case for larger zeolite particles, however alumina particles should be subjected to similar tests to assess if impact angle is influential on the extent of breakage.

Introduction

This interim report summarises work carried out between April and December, 1989. The project is scheduled for completion in mid-1990. The investigation consists largely of a case study of granulation using three commercial binders; here we describe the context of the work, summarise the relevant studies which have recently been carried out at the University of Surrey and give preliminary results of the case study.