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A mathematical study has been undertaken to model various kinds of granular flows including the perfect plasticity flow and the viscous elasto-plasticity flow. The work is mainly based on the double-shearing theory originated by Spencer and developed by many others. The focus of the project is on the formulation of the theory, the construction of mathematical models and the development of robust simulation techniques.Based on a general formulation of the double-shearing theory, the perfect plasticity flow is shown to be governed by a set of highly nonlinear first order hyperbolic partial differential equations with two distinct characteristics. A sophisticated numerical algorithm is then developed based on the method of characteristics to determine the stress discontinuity and the velocity and stress fields. With the method developed, a numerical study is then undertaken to model the flow of granular materials in a hopper in the presence of stress discontinuity and to investigate the influence of various parameters on the distribution of hopper wall pressures.Utilising the double shearing theory, a set of stress-strain constitutive equations in explicit form has been derived, which makes it possible to formulate the double-shearing theory within the framework of the finite element method. Thus, consequently, a sophisticated finite element technique has been developed to solve the general boundary value problem governing the viscous elasto-plasticity flows obeying the double-shearing theory. Numerical implementation of the frictional boundary condition is also presented. The model is then illustrated with a numerical example demonstrating the influence of wall friction on the distribution of pressures on silo walls throughout the dynamic process of material discharge from silos.

This thesis develops and tests a two-dimensional discrete dynamic model for the simulation of granular flows in silos and hoppers. The granular material considered is assumed to be an assembly of viscoelastic discs and the motion of such a particle system is shown to be governed by a set of nonlinear first order ordinary differential equations. This system of equations is then solved numerically using the centered finite difference scheme. Based on the model presented, a computer program has been developed and used to analyse the flow behaviour of granular materials during filling and emptying of a silo. The results show that the discrete dynamic model developed is capable of modelling granular flows in silos, particularly predicting wall pressures and analysing flow blockage.

Purpose: The aim of this thesis was to investigate a novel method of preparing crosslinked alginate matrices. Current methods use large quantities of water and hence are not suitable for large scale manufacturing of drug alginate particulate systems. Moreover, the current processes offer little scope for control of the crosslinking process. The aim was to overcome these problems through studies of paracetamol alginate granular matrices prepared by the novel method and to explore if these granules could be used to improve the taste of paracetamol. Methods: The novel method involves preparation of dried drug alginate granules (moisture content: <5-6 %) using conventional granulation followed by crosslinking treatment of the dried granules with calcium chloride or a combination of calcium and magnesium ion solution in a crosslinking bath. The effect of the process (shear rate, binder quantity) to prepare untreated granules, composition of the raw materials (drug particle size and type of alginate) and subsequently the crosslinking treatment process variables (Ca�⁺ ion concentration, agitation rate, time and temperature of Ca�⁺ solution) on the physicochemical properties of granule systems were studied using factorial designs together with supporting studies. The granules were characterized using sodium and calcium content analysis, drug release studies (mainly sub-60s release) matrix swelling rate and equilibrium swelling studies, tensile strength studies, ion permeation studies, SEM and X Ray analysis and gravimetric studies. Sensory studies correlating sub-60 s drug release (determined using a specially designed apparatus) and human taste scores (measured using an analogue scale) were then undertaken. Selected formulations were evaluated for taste improvement and to determine if mucoadhesion led to an increased unpalatability of paracetamol. Results: Of the crosslinking treatment factors, the calcium concentration had the greatest effect on crosslinked granules. Although other treatment factors also affected the granule properties, alteration of the salt concentration allowed considerable control over the crosslinking process (not possible in the conventional method) in addition to providing a mechanistic understanding of the crosslinking process in the dried state. The use of low calcium concentrations (< 20 mg/ml, CaCl₂. 2H₂O) during treatment led to granule erosion (hence drug loss) due to overall incomplete crosslinking but led to a reduction in the short-term drug release compared to the granules treated with intermediate (100- 250 mg/ml) or high calcium concentrations (>400 mg/ml) due to reduction in the granule porosity after crosslinking. Although intermediate calcium concentrations led to complete crosslinking and longer release times (T 85 %: 25 min) high calcium crosslinking restricted the crosslinking to the surface of the granules leading to faster drug release (T 85 %: 8 min) with low calcium granules showing intermediate crosslinking and drug release rates (T 85 %: 18 min). High calcium treatment limited drug loss during crosslinking (95 % recovered compared to 83 % recovery at intermediate calcium concentration) without affecting the short-term drug release much. Low calcium granules showed the lowest drug recovery (< 70 %) and slowest sub-60s drug release followed closely by intermediate and high calcium treated granules. The granule preparation factors (shear rate, binder quantity) and type of alginate used, considerably affected the sub-60s drug release by affecting surface porosity especially when a low shear rate was used. However, these factors only slightly reduced the drug loss during crosslinking treatment phase (about 4 % increase in drug recovery). Smaller drug particle size had a slightly larger incremental effect on drug recovery (about 8 % increase in the drug recovery) during crosslinking treatment due to better embedding of the drug particles inside the untreated granule matrix. This was true as long as the particle size of the drug was > 98 [mu]m. Below this size drug recovery remained unaffected by changes in drug particle size. Although granule surface porosity considerably affected the sub-60s drug release, its effect on drug release (long-term) was much less. A linear correlation was observed between the sub-60s drug release and sensory scores despite high individual variability. Both granule formulations evaluated showed taste improvement and mucoadhesion did not lead to an increase in the bitter taste of the uncrosslinked paracetamol alginate granules. Conclusions: Unlike the traditional method, the new technique of preparation of crosslinked drug alginate particulate systems uses very little water and allows greater control over the the crosslinking process compared to the swollen state crosslinking. The novel process of preparation is versatile, and should be scalable. It offers the formulator a platform to prepare a matrix, reservoir or a combination of these two systems using alginates and other drugs and polymers as well. Adequate short-term control over paracetamol release, very little loss of paracetamol during treatment (< 5 % loss), reduction in mucoadhesion of the granules and lastly improvement of the taste of paracetamol is possible using alginate based systems especially if high calcium is used during the crosslinking treatment. Hence, it is likely that these taste-improved granules could be used to prepare tablets without the need for a protective film coating to improve taste. Finally, this research established the utility of short-term drug release in taste improvement research and characterization of solid controlled release dosage forms.

The influence of periodic vibrations on the granular flow of materials is of great interests to scientists and engineers due to both theoretical and practical reasons. In this paper, the stability of a vertically vibrated granular layer is examined by linear stability analysis. This includes two major steps, firstly, the base state at various values of mass holdup (Mt) and energy input (Qt) is calculated and secondly, small perturbations are introduced to verify the stability of the base state by solving the resultant eigenvalue problem derived from the linearized governing equations and corresponding boundary conditions. Results from the base state solution show that, for a given pair of Mt and Qt, solid fraction tends to increase at first along the layer height and then decrease after a certain vertical position while granular temperature decreases rapidly from the bottom plate to the top surface. This may be due to the existence of inelastic collisions between particles that dissipate the energy input from the bottom. It is also found that more energy input results in a lower solid fraction and a higher granular temperature. The stability diagram is constructed by checking the stability property at different points in the Mt-Qt plane. For a fixed Mt, the base state is stable at low energy inputs, and becomes unstable if Qt is larger than a critical value Qtc1. A higher value of Mt corresponds to a larger Qtc1. There also exists a critical mass holdup (Mtc), for Mt larger than Mtc, the patterns corresponding to the instabilities are standing waves (stationary mode); otherwise the flat layer appears (layer mode). Moreover, the stationary mode turns into the layer mode when Qt is increased beyond a critical value Qtc2. These findings agree with the experimental observations of other researchers (Hsiau and Pan, 1998). The effects of restitution coefficients (ep, ew) and material properties (dp, ρp) on the stability diagram are also investigated. Together with Mt and Qt these variables can be classified into two groups, i.e. the stabilizing factors (Mt, dp, ρp) and the destabilizing factors (Qt, ep, ew). The stability of the system is enhanced with increasing stabilizing factors and decreasing destabilizing factors. / Singapore-MIT Alliance (SMA)

The rotary valve is a widely used mechanical device in many solids-handling industrial processes. However, it may also be responsible for most of the attrition effects occurring in a typical process. In this study, the attrition effects occurring in a rotary valve operating as a stand-alone device and as part of a pneumatic conveying system were investigated. In the former case granular attrition was carried out at three different rotary valve speeds and the experimental results obtained were found to be in good agreement with the Gwyn correlation. In the latter case three typical air flow rates were used in the pneumatic conveying system. The size distribution of the attrition product obtained at the lowest air flow rate used was not adequately described by the Gwyn correlation. The attrition process and mechanisms involved were analysed and the minimum size of the attrition product obtained from both modes of operations was found to be similar. / Singapore-MIT Alliance (SMA)

Chloramines are used for disinfection in many water treatment facilities because of their ability to provide residual protection of water supplies while minimizing the formation of disinfection-by-products. However, chloramines can impart taste and odor to the water, which can lead to customer complaints. Furthermore, the removal of monochloramine from water is essential for certain industries. Previous research at the University of Texas at Austin has demonstrated the potential of several granular activated carbons (GAC) for removal of monochloramine under conditions typical of water treatment plants. The goal of this research project is to further quantify steady-state monochloramine reduction in fixed bed reactors (FBR) with three commercially available GACs, and improve the understanding of the physical and chemical properties that influence removal. The research was divided into 3 phases: 1. A laboratory scale fixed bed reactor experiment was used to quantify steady state monochloramine removal over time. City of Austin tap water viii was used for three GAC types (Jacobi CAT, Norit CAT, Nority CNS) at pH 8 and 9. 2. Physical characterization of each GAC was performed using analysis of nitrogen adsorption isotherms. Specific surface area, pore volume, and pore distribution were determined. Chemical characterization was performed quantitatively using Boehm titrations. Qualitative analysis was performed by analyzing FTIR spectra of untreated activated carbon samples. 3. The Monochloramine Catalysis (MCAT) model was calibrated using results from the Phase 1 and 2 experiments. Simulations of full scale point of use drinking water filters were run for various empty bed contact times and influent monochloramine concentrations. These results were compared against National Sanitation Foundation monochloramine reduction certification criteria. Results show that steady state removal was achieved for all of the activated carbons tested and this removal efficiency can reach nearly 90% using a 0.75-minute empty bed contact time. This steady state performance indicated that catalysis of the monochloramine was occurring, and removal could theoretically occur for very long periods of time. The second stage of the research shows correlation between chemical characteristics (acidity and basicity) and removal efficiency. Furthermore, physical characteristics, mainly micro-porosity, were shown to largely impact performance. Finally, the MCAT model provides a reasonable estimate of steady state removal, and is used to predict full scale point of use performance. / text

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