ARR - Annual Report
This report introduces a quasicontinuum formulation for heterogeneous granular systems. The description assumes that the relative displacements between particles are described by a constrained field while the interparticle forces are resolved locally. Equilibrium is enforced weakly by virtue of the principle of virtual displacement. The methodology accounts for particles of variable size and different species. Interaction forces between particles in different cells are computed using a rule which allows for local operations and renders symmetric tangent operators. Energy relaxation from static condensation of an internal node is proposed as an indicator for adaptive meshing. Simulations of uniaxial densification show the robustness and versatility of the formulation for heterogeneous granular beds. The numerical tests also recover the general trends observed in compaction experiments.
Executive Summary
The major objective of our IFPRI project, which started in 1998, is to develop a comprehensive mathematical model of the extrusion process for “concentrated” dense suspensions using the Finite Element Method. The results of the numerical analysis need to be verified through experimental studies carried-out on industrial-scale and well-instrumented extruders. Other objectives include the development of various methods and apparati to probe the rheological behavior and microstructural characteristics of concentrated suspensions (“dense suspensions”) especially in the confines of the extrusion process. Single and twin screw extrusion processes (including co-rotating and counter-rotating twin screw extruders) and flow through dies are included in the scope of the project. The ability to determine the distributions of the pressure, stress, velocity and temperature which develop during the course of the extrusion process is the minimum information wherewithal necessary to understand the development of the structure and the ultimate properties of the processed suspensions. The project is carried out with massive support from other sources also including te US Army, Naval Surface Warfare Center and various corporations.
The major tasks of Year #2 were the modification of our FEM based source codes to accommodate the wall slip behavior of dense suspensions in 3-D, the initiation of the experimental studies of dense suspensions using a well-instrumented and industrial-size co-rotating twin screw extruder and the comparisons of the experimental and simulation results on various isolated sections of the twin screw extruder. The coupled flow occurring at a slit die and the exit section of the twin screw extruder was focused upon using a model suspension, which was well characterized. The experimental results (pressure and temperature distributions) agreed well with the results of our numerical simulation using 3-D FEM. During the next year we intend to expand our mathematical analysis to multiple sections of the extruder simultaneously on the single screw extruder, carry-out detailed experimental studies with realistic suspensions using again a well-instrumented single screw extruder with a complex shaping die and compare the experimental results with the numerical results.
EXECUTIVE SUMMARY
Our basic or beginning concept in the project was as follows: for a fundamental discussion on the phenomena of electrostatic charging of powder, it is essential to study the charge generation due to a single impact or contact on a single particle. To realize the concept we proposed and performed, in our previous works, so called “impact charging experiments” in which, however, samples were spherical particles mainly with 3 mm in diameter. The size was too much bigger comparing with normal powder size. The major subject of this project of IFPRI was, therefore, to perform the single particle study in the region of the normal particle size from tens to hundreds micro-meter. We proposed two approaches to realize the project:
Approach 1:
Improvement of the Original Method: To apply the former version “impact charging experiments” to the smaller particle size, there were two major subjects: improvement of the sensitivity of the charge measurement, and trajectory control of the accelerated particles.
- In the first year: the trajectory problem was solved with adopting “aerosol beam generator,” also the sensitivity of the charge measurement was improved successfully. These resulted in that the particles with hundreds micro-meter became available.
- In the second year: Actual “impact charging experiments” were performed successfully with using PMMA particles mainly of 200 pm in diameter. The experimental results showed good agreements with “charge relaxation model” which we have proposed as a scheme determining impact charges.
Approach 2:
Development of the Method of Electrostatic Adhesive Force Measurement: This is the completely new approach to determine the amount of charge transferred onto a particle due to a contact from a measurement of adhesive force curve at approaching and separating particle against a metal target.
- In the first year: A concept of the mechanism was studied and clarified, and a strict theory was developed to calculate the force curve of a particle charged partially only on a supposed contact area.
- In the second year: As a preparation to realize an actual equipment, performances of some essential parts were tested. After the results of the first and second year activities, the project work objects in the third year are:
In approach 1:
- Actual and further data accumulation will be continued.
- The model called “charge relaxation model” may be verified its applicability for an actual powder region of the particle size, the hundreds micro-meter particle size.
- A further improvement of the sensitivity of the charge measurement to make possible to apply a smaller particle size, from tens under to some micrometer particle. Especially, to realize the measurement of particle size around ten micro-meter may be important because the size is of toner particles in electrophotograpy process.
In approach 2:
In the first and second year, the concept of the new experimental apparatus was established, and some performances of essential parts of it were tested. In the third year, a prototype will be established and its performance will be tested.
The increasing particle-particle-interactions with increasing fineness are an essential problem during wet comminution in stirred media mills. These interactions have an influence on the stability of the product suspension towards agglomeration and on the rheology. Experimental results show that during comminution the measured particle size increases again after reaching a product fineness of approx. 500 nm, although a further increase of the specific surface can be determined (BET-method). The reasons for this phenomenon are the increasing particle-particle-interactions and spontaneous agglomeration.
Possibilities of the stabilization of the product suspension in the stirred media mill are therefore mainly discussed in this report. With respect to this, first results of sample preparation are mentioned. It is shown that during the comminution changes of the pH value, the conductivity and thus the ionic strength as well as the zeta potential occur in dcpendencc of the materials of the grinding chamber lining and the stirrer discs as well as the grinding media material and the product material.
In further investigations the product suspension shall be stabilized electrostatically during the grinding process. The comminution progress as well as the electrochemical properties of the product suspension shall be characterized by online measurements. For this measurements a possible experimental set-up is introduced and discussed. Only after this steps the systematic investigations concerning the influence of the grinding media size are reasonable.
This year research on the rheological behavior of concentrated suspensions has proceeded along three parallel efforts as described below. The goal is to provide a quantitative microstructurally-based description of suspension rheology for a range of concentrations and particle-level interactions. The problem is addressed by both analytical and computational (simulation) approaches. Not all of the work described here has been supported by IFPRI; for example, the work on an accelerated version of Stokesian Dynamics has not. The report is intended to give an integrated view of our current efforts.
The process of disintegration of liquid/solid suspension sheets and jets is analysed in a fundamental manner and visualized by suitable measurement method which allow qualitative and quantitative evaluation of the process. Supporting numerical analysis and theoretical derivations will contribute to basic understanding and control of the suspension atomization process. Model suspensions based on water and water/glycerol mixture with various suspended particles will be atomized by means of conventional and specifically designed atomizers.
The second year activities which are reported here include:
- Experimental investigations of suspension rheology
- Stability analysis of twin fluid suspension atomization
- Experimental investigations of suspension atomization in twin-fluid atomizer
Model suspensions based on distilled water with neutrally buoyant polymer particles have been studied.
Summary
In the particle technology, it is fundamentally important to know the interaction and adhesive forces between particles and to find the correlation of those forces with the microscopic characteristics of particle surface, because these forces are the origin of many phenomena which particles exhibit in industrial processes. The aim of this project is to clarify in-sihc at the molecular level the microstructure of surfaces in solutions of industrial importance and the correlation with interaction and adhesive forces between surfaces, using not only an atomic force microscope (AFM) but also computer simulations.
It was planned to clarify the phenomena and mechanism on the subjects shown in the map of’ the following figure, which were considered to be fundamental in understanding the phenomena in industrial particle processes.
The objective of this work is systematic understanding of particle-particle nanorheology based on the single particle-particle contact of two atomically-smooth solid surfaces in molecularly-thin proximity. The main relevance is to understanding the origins of suspension rheology, especially the origins of rheological anomalies that arise when interfacial films between two solid bodies are so thin that the intuition of what to expect based on bulk rheology no longer applies. Based on this understanding, we are seeking to develop new methods to control and manipulate the properties of their interfacial films.
Dynamic Mechanical Properties
Specifically, the dynamic mechanical properties of the resulting inter-facial film are being studied directly with special emphasis on how they depend on both vibration frequency and strain rate. A homebuilt apparatus is employed to this purpose with the following unique properties:
- Surface-surface spacing are variable from thousands of Angstroms to molecular contact. The surface force needed to produce this separation is measured while at the same time measuring shear nanorheology. The tip is imaged in situ directly during each experiment, therefore force can be normalized by area to produce stress.
- Oscillatory deformations with variable frequency in the range 0.01 to 103 rad-sec-1 can be applied, with deformations either in the shear direction or in the normal (pumping) direction.
- The amplitude of deformation can be varied from sub-Angstrom to thousands of Angstroms. The reason to use very small deformations is to produce a linear viscoelastic response (representative of the rest state, this can be studied by methods of equilibrium statistical thermodynamics). The reason to use very large deformations is to produce strongly nonlinear deformations characteristic of very high shear rates.
To the best of our knowledge, no other instrument with these properties exists in any other laboratory in the world. We would like to take this opportunity to encourage IPPRI members to suggest new systems that would be interesting to study with these unique methods. The main finding during Year I was to develop criteria with predictive power to understand whether opposed particles will move past one another with intermittent stick-slip motion or with smooth sliding. We found that stick-slip motion occurred only when thin films were deformed faster than their intrinsic relaxation time. The observation offered a new strategy to look for methods to avoid stick-slip motion by engineering the relaxation time of a confined film.
The increasing particle-particle-interactions with increasing fineness are an essential problem during wet comminution in stirred media mills. These interactions have an influence on the stability of the product suspension towards agglomeration and on the rheology. Experimental results show that during comminution the measured particle size increases again after reaching a product fineness of approx. 500 nm, although a further increase of the specific surface can be determined (BET-method). The reasons for this phenomenon are the increasing particle-particle-interactions and spontaneous agglomeration.
Possibilities of the stabilization of the product suspension in the stirred media mill are therefore mainly discussed in this report. With respect to this, first results of sample preparation are mentioned. It is shown that during the comminution changes of the pH value, the conductivity and thus the ionic strength as well as the zeta potential occur in dependence of the materials of the grinding chamber lining and the stirrer discs as well as the grinding media material and the product material. In further investigations the product suspension shall be stabilized electrostatically during the grinding process.
The comminution progress as well as the electrochemical properties of the product suspension shall be characterized by online measurements. For this measurements a possible experimental set-up is introduced and discussed. Only after this steps the systematic investigations concerning the influence of the grinding media size are reasonable.
The fluidised dense-phase (FDP) conveying of powders and low-velocity slug-flow (LVSF) of granular bulk solids are the most common and popular modes of dense-phase used in industry. However, the accur’ate prediction of conveying performance still is not possible from first principles and relies heavily on empiricism.
The main aim of this project is to develop the necessary understanding, databases, guidelines and models for the purpose of predicting accurate optimal operating conditions for the two modes of dense-phase. However, as mentioned in the original research grant application, it is unlikely that both the FDP and LVSF sections can be completed thoroughly in a single 3-year period (ie due to the amount of work involved). Hence, top priority has been given initially to the LVSF section of the project, although some progress also has been made with the FDP section of work.
Several difficulties were encountered during the course of the project (eg unexpected results and phenomena) and have delayed progress in various areas. In some cases, it was not possible to complete certain scheduled tasks (eg testing aluminium and mild steel pipe and wide range of granular solids). In other cases, it was necessary to pursue new work (eg rotary valve air leakage, new pipe friction and stress transmission testers). However, in terms of achieving the main goals, there is no doubt that the project will be successful in terms of improved understanding and the development of new databases and models for the prediction of LVSF performance. Unfortunately, due to the various problems and delays to date, the full range of pipe wall materials and bulk solids will not be able to be tested - such work is necessary to confirm the accuracy and validity of the new models (eg majority of work to date has concentrated on poly pellets). Also, a significant amount of additional time will be needed for the relatively more complex FDP section of work (eg only one product and a few different pipelines will be able to be tested by the end of the initial 3-year period).
This Annual Report summarises the research progress and major achievements to date, as well the forward plan for the next 12 months.