A CFD study of biomass pyrolysis in a downer reactor equipped with a novel gas-solid separator - I:hydrodynamic performance

This study presents the first part of a CFD study on the performance of a downer reactor for biomass pyrolysis. The reactor was equipped with a novel gas-solid separation method, developed by the co-authors from the ICFAR (Canada). The separator, which was designed to allow for fast separation of clean pyrolysis gas, consisted of a cone deflector and a gas exit pipe installed inside the downer reactor. A multi-fluid model (Eulerian-Eulerian) with constitutive relations adopted from the kinetic theory of granular flow was used to simulate the multiphase flow. The effects of the various parameters including operation conditions, separator geometry and particle properties on the overall hydrodynamics and separation efficiency were investigated. The model prediction of the separator efficiency was compared with experimental measurements. The results revealed distinct hydrodynamic features around the cone separator, allowing for up to 100% separation efficiency. The developed model provided a platform for the second part of the study, where the biomass pyrolysis is simulated and the product quality as a function of operating conditions is analyzed. Crown Copyright © 2014 Published by Elsevier B.V. All rights reserved.

A CFD study of biomass pyrolysis in a downer reactor equipped with a novel gas-solid separator-II thermochemical performance and products

A Eulerian-Eulerian CFD model was used to investigate the fast pyrolysis of biomass in a downer reactor equipped with a novel gas-solid separation mechanism. The highly endothermic pyrolysis reaction was assumed to be entirely driven by an inert solid heat carrier (sand). A one-step global pyrolysis reaction, along with the equations describing the biomass drying and heat transfer, was implemented in the hydrodynamic model presented in part I of this study (Fuel Processing Technology, V126, 366-382). The predictions of the gas-solid separation efficiency, temperature distribution, residence time and the pyrolysis product yield are presented and discussed. For the operating conditions considered, the devolatilisation efficiency was found to be above 60% and the yield composition in mass fraction was 56.85% bio-oil, 37.87% bio-char and 5.28% non-condensable gas (NCG). This has been found to agree reasonably well with recent relevant published experimental data. The novel gas-solid separation mechanism allowed achieving greater than 99.9% separation efficiency and < 2 s pyrolysis gas residence time. The model has been found to be robust and fast in terms of computational time, thus has the great potential to aid in future design and optimisation of the biomass fast pyrolysis process.

Fast pyrolysis of biomass in a circulating fluidised bed reactor

The objective of this work was to design, construct, test and operate a novel circulating fluid bed fast pyrolysis reactor system for production of liquids from biomass. The novelty lies in incorporating an integral char combustor to provide autothermal operation. A reactor design methodology was devised which correlated input parameters to process variables, namely temperature, heat transfer and gas/vapour residence time, for both the char combustor and biomass pyrolyser. From this methodology a CFB reactor was designed with integral char combustion for 10 kg/h biomass throughput. A full-scale cold model of the CFB unit was constructed and tested to derive suitable hydrodynamic relationships and performance constraints. Early difficulties encountered with poor solids circulation and inefficient product recovery were overcome by a series of modifications. A total of 11 runs in a pyrolysis mode were carried out with a maximum total liquids yield of 61.50% wt on a maf biomass basis, obtained at 500°C and with 0.46 s gas/vapour residence time. This could be improved by improved vapour recovery by direct quenching up to an anticipated 75 % wt on a moisture-and-ash-free biomass basis. The reactor provides a very high specific throughput of 1.12 - 1.48 kg/hm2 and the lowest gas-to-feed ratio of 1.3 - 1.9 kg gas/kg feed compared to other fast pyrolysis processes based on pneumatic reactors and has a good scale-up potential. These features should provide significant capital cost reduction. Results to date suggest that the process is limited by the extent of char combustion. Future work will address resizing of the char combustor to increase overall system capacity, improvement in solid separation and substantially better liquid recovery. Extended testing will provide better evaluation of steady state operation and provide data for process simulation and reactor modeling.

Ablative pyrolysis of biomass

The primary objectives of this work were to design, construct, test and operate a novel ablative pyrolysis reactor and product recovery system. Other key objectives included the development of an ablative pyrolysis reactor design methodology, mathematical modelling of the ablation process and measurement of empirical ablation rate data at 500°C. The constructed reactor utilised a rotating blade approach to achieve particle ablation in a 258mm internal diameter reactor. By fulfilling the key requirements of high relative motion and high contact pressure, pine wood particles of maximum size 6.35 mm were successfully ablated.Sixteen experiments were carried out: five initial commissioning experiments were used to test the rotating blade concept and to solve char separation problems. Mass balances were obtained for the other eleven experiments with good closures. Based on ablatively pyrolysed dry wood, a maximum organic liquid yield of 65.9 wt% was achieved with corresponding yields of 12.4 wt% char, 11.5 wt% water and 9.2 wt% non-condensable gas. Reactor throughputs of 2 kg/h dry ablated wood were achieved at 600°C. The theoretical ablative pyrolysis reactor design methodology was simplified and improved based upon empirical data derived from wood rod ablation experiments. Yields of chemicals were qualitatively similar to those of other fast pyrolysis processes.The product recovery system, comprising hot char removal, liquids collection in two ice-cooled condensers followed by gas filtration and drying, gave good mass balance closures. The most significant problem was char separation and removal from the reactor. This was solved by using a nitrogen blow line. In general, the reactor and product collection systems performed well.Future development of the reactor would involve modification of the reactor feed tube to allow the reactor residence time to be reduced and testing of the rotating blade approach with different blade angles, configurations and numbers of blades.

Improvement of bio-oil stability in wood pyrolysis process

Pyrolysis is one of several thermochemical technologies that convert solid biomass into more useful and valuable bio-fuels. Pyrolysis is thermal degradation in the complete or partial absence of oxygen. Under carefully controlled conditions, solid biomass can be converted to a liquid known as bie-oil in 75% yield on dry feed. Bio-oil can be used as a fuel but has the drawback of having a high level of oxygen due to the presence of a complex mixture of molecular fragments of cellulose, hemicellulose and lignin polymers. Also, bio-oil has a number of problems in use including high initial viscosity, instability resulting in increased viscosity or phase separation and high solids content. Much effort has been spent on upgrading bio-oil into a more usable liquid fuel, either by modifying the liquid or by major chemical and catalytic conversion to hydrocarbons. The overall primary objective was to improve oil stability by exploring different ways. The first was to detennine the effect of feed moisture content on bio-oil stability. The second method was to try to improve bio-oil stability by partially oxygenated pyrolysis. The third one was to improve stability by co-pyrolysis with methanol. The project was carried out on an existing laboratory pyrolysis reactor system, which works well with this project without redesign or modification too much. During the finishing stages of this project, it was found that the temperature of the condenser in the product collection system had a marked impact on pyrolysis liquid stability. This was discussed in this work and further recommendation given. The quantity of water coming from the feedstock and the pyrolysis reaction is important to liquid stability. In the present work the feedstock moisture content was varied and pyrolysis experiments were carried out over a range of temperatures. The quality of the bio-oil produced was measured as water content, initial viscosity and stability. The result showed that moderate (7.3-12.8 % moisture) feedstock moisture led to more stable bio-oil. One of drawbacks of bio-oil was its instability due to containing unstable oxygenated chemicals. Catalytic hydrotreatment of the oil and zeolite cracking of pyrolysis vapour were discllssed by many researchers, the processes were intended to eliminate oxygen in the bio-oil. In this work an alternative way oxygenated pyrolysis was introduced in order to reduce oil instability, which was intended to oxidise unstable oxygenated chemicals in the bio-oil. The results showed that liquid stability was improved by oxygen addition during the pyrolysis of beech wood at an optimum air factor of about 0.09-0.15. Methanol as a postproduction additive to bio-oil has been studied by many researchers and the most effective result came from adding methanol to oil just after production. Co-pyrolysis of spruce wood with methanol was undertaken in the present work and it was found that methanol improved liquid stability as a co-pyrolysis solvent but was no more effective than when used as a postproduction additive.

Bioreaction and separation in preparative batch chromatographic columns : the hydrology of lactose to yield glucose,galactose and oligosaccharides

The initial aim of this project was to improve the performance of a chromatographic bioreactor-separator (CBRS). In such a system, a dilute enzyme solution is pumped continuously through a preparative chromatographic column, while pulses of substrate are periodically injected on to the column. Enzymic reaction and separation are therefore performed in a single unit operation. The chromatographic columns used were jacketed glass columns ranging from 1 to 2 metres long with an internal diameter of 1.5 cm. Linking these columns allowed 1, 2, 3 and 4 metre long CBRS systems to be constructed. The hydrolysis of lactose in the presence of β~galactosidase was the reaction of study. From previous work at Aston University, there appeared to be no difficulties in achieving complete lactose hydrolysis in a CBRS. There did, however, appear to be scope for improving the separative performance, so this was adopted as an initial goal. Reducing the particle size of the stationary phase was identified as a way of achieving this improvement. A cation exchange resin was selected which had an average particle size of around half that previously used when studying this reaction. A CBRS system was developed which overcame the operational problems (such as high pressure drop development) associated with use of such a particle size. A significant improvement in separative power was achieved. This was shown by an increase in the number of theoretical plates (N) from about 500 to about 3000 for a 2 metre long CBRS, coupled with higher resolution. A simple experiment with the 1 metre column showed that combined bioreaction and separation was achievable in this system. Having improved the separative performance of the system, the factors affecting enzymic reaction in a CBRS were investigated; including pulse volume and the degree of mixing between enzyme and substrate. The progress of reaction in a CBRS was then studied. This information was related to the interaction of reaction and separation over the reaction zone. The effect of injecting a pulse over a length of time as in CBRS operation was simulated by fed batch experiments. These experiments were performed in parallel with normal batch experiments where the substrate is mixed almost instantly with the enzyme. The batch experiments enabled samples to be taken every minute and revealed that reaction is very rapid. The hydrodynamic characteristics of the two injector configurations used in CBRS construction were studied using Magnetic Resonance Imaging, combined with hydrodynamic calculations. During the optimisation studies, galactooligosaccharides (GOS) were detected as intermediates in the hydrolysis process. GOS are valuable products with potential and existing applications in food manufacture (as nutraceuticals), medicine and drug targeting. The focus of the research was therefore turned to GOS production. A means of controlling reaction to arrest break down of GOS was required. Raising temperature was identified as a possible means of achieving this within a CBRS. Studies were undertaken to optimise the yield of oligosaccharides, culminating in the design, construction and evaluation of a Dithermal Chromatographic Bioreactor-separator.

Studies in three phase gas-liquid-solid fluidised systems

The work is a logical continuation of research started at Aston some years ago when studies were conducted on fermentations in bubble columns. The present work highlights typical design and operating problems that could arise in such systems as waste water, chemical, biochemical and petroleum operations involving three-phase, gas-liquid-solid fluidisation; such systems are in increasing use. It is believed that this is one of few studies concerned with `true' three-phase, gas-liquid-solid fluidised systems, and that this work will contribute significantly to closing some of the gaps in knowledge in this area. The research work was mainly experimentally based and involved studies of the hydrodynamic parameters, phase holdups (gas and solid), particle mixing and segregation, and phase flow dynamics (flow regime and circulation patterns). The studies have focused particularly on the solid behaviour and the influence of properties of solids present on the above parameters in three-phase, gas-liquid-solid fluidised systems containing single particle components and those containing binary and ternary mixtures of particles. All particles were near spherical in shape and two particle sizes and total concentration levels were used. Experiments were carried out in two- and three-dimensional bubble columns. Quantitative results are presented in graphical form and are supported by qualitative results from visual studies which are also shown as schematic diagrams and in photographic form. Gas and solid holdup results are compared for air-water containing single, binary and ternary component particle mixtures. It should be noted that the criteria for selection of the materials used are very important if true three-phase fluidisation is to be achieved: this is very evident when comparing the results with those in the literature. The fluid flow and circulation patterns observed were assessed for validation of the generally accepted patterns, and the author believes that the present work provides more accurate insight into the modelling of liquid circulation in bubble columns. The characteristic bubbly flow at low gas velocity in a two-phase system is suppressed in the three-phase system. The degree of mixing within the system is found to be dependent on flow regime, liquid circulation and the ratio of solid phase physical properties. Evidence of strong `trade-off' of properties is shown; the overall solid holdup is believed to be a major parameter influencing the gas holdup structure.

The chromatographic separation of carbohydrate mixtures

The separation performance of a semicontinuous counter-current chromatographic refiner (SCCR7), consisting of twelve 5.4 cm id x 75cm long columns packed with calcium charged cross-linked polysytrene resin (KORELA VO7C), was optimised. An industrial barley syrup was used containing 42% fructose, 52% glucose and 6% maltose and oligosaccharides. The effects of temperature, flow rates and concentration on the distribution coefficients were evaluated and quantified by deriving general relationships. The effects of flow rates, feed composition and concentration on the separation performance of the SCCR7 were identified and general relationships between them and the switch time, which was found to be the controlling parameter, were developed. Fructose rich (FRP) and glucose rich (GRP) product purities of 99.9% were obtained at 18.6% w/v feed concentrations. When a 66% w/v feed concentration was used and product splitting technique was employed, the throughput was 32.1 kg sugar solids/m3 resin/hr. The GRP contained less than 4.5% fructose, the FRP was over 95% pure, and the respective concentrations were 22.56 and 11.29% w/v. Over 94% of the glucose and 95.78% of the fructose in the feed were recovered in the GRP and FRP respectively. By recycling the dilute product split fractions, the GRP and FRP concentrations were increased to 25.4 and 12.96% w/v; the FRP was 90.2% pure and the GRP contained 6.69% w/v fructose. A theoretical link between batch and semicontinuous chromatographic equipments has been determined. A computer simulation was developed predicting successfully the purging concentration profiles at `pseudo-equilibrium', and also certain system design parameters. An important further aspect of the work has been to study the behaviour of chromatographic bioreactor-separators. Such batch systems of 5.4cm id and lengths varying between 30 and 230cm, were used to investigate the effect of scaling up on the conversion of sucrose into dextran and fructose in the presence of the dextransucrase enzyme. Conversions of over 80% were achieved at 4 hr sucrose residence times. The crude dextransucrase was purified using centrifugation, ultrafiltration and cross-flow microfiltration techniques. Better enzyme stability was obtained by first separating the non-solid impurities using cross-flow microfiltration, and then removing the cells from the enzyme immediately before use by continuous centrifugation.

Developments and extensions of Roth's method of double Fourier series with applications to the solution of electromagnetic field problems

The first part of the thesis compares Roth's method with other methods, in particular the method of separation of variables and the finite cosine transform method, for solving certain elliptic partial differential equations arising in practice. In particular we consider the solution of steady state problems associated with insulated conductors in rectangular slots. Roth's method has two main disadvantages namely the slow rate of con­vergence of the double Fourier series and the restrictive form of the allowable boundary conditions. A combined Roth-separation of variables method is derived to remove the restrictions on the form of the boundary conditions and various Chebyshev approximations are used to try to improve the rate of convergence of the series. All the techniques are then applied to the Neumann problem arising from balanced rectangular windings in a transformer window. Roth's method is then extended to deal with problems other than those resulting from static fields. First we consider a rectangular insulated conductor in a rectangular slot when the current is varying sinusoidally with time. An approximate method is also developed and compared with the exact method.The approximation is then used to consider the problem of an insulated conductor in a slot facing an air gap. We also consider the exact method applied to the determination of the eddy-current loss produced in an isolated rectangular conductor by a transverse magnetic field varying sinusoidally with time. The results obtained using Roth's method are critically compared with those obtained by other authors using different methods. The final part of the thesis investigates further the application of Chebyshdev methods to the solution of elliptic partial differential equations; an area where Chebyshev approximations have rarely been used. A poisson equation with a polynomial term is treated first followed by a slot problem in cylindrical geometry.

A legal perspective of integrated surface mining, solid waste landfill reclamation and land conservation

In the area of international environmental law this thesis proposes the formulation of one-step planning and permitting regulation for the integrated utilisation of new surface mines as depositories for municipal solid waste. Additionally, the utilisation of abandoned and currently operated surface mines is proposed as solid waste landfills as an integral step in their reclamation. Existing laws, litigation and issues in the United Kingdom, the U.S. and Canada are discussed because of their common legal system, language and heritage. The critical shortage of approved space for disposal of solid waste has caused an urgent and growing problem for both the waste disposal industry and society. Surface mining can serve three important environmental and societal functions inuring to the health and welfare of the public: (1) providing basic minerals for goods and construction; (20 sequentially, to provide critically needed, safe burial sites for society's wastes, and (3) to conserve land by dual purpose use and to restore derelict land to beneficial surface use. Currently, the first two functions are treated environmentally, and in regulation, as two different siting problems, yet they both are earth-disturbing and excavating industries requiring surface restoration. The processes are largely duplicative and should be combined for better efficiency, less earth disturbance, conservation of land, and for fuller and better reclamation of completed surface mines returning the surfaces to greater utility than present mined land reclamation procedures. While both industries are viewed by a developed society and its communities as "bad neighbours", they remain essential and critical for mankind's existence and welfare. The study offers successful examples of the integrated process in each country. The study argues that most non-fuel surface mine openings, if not already safe, can economically, through present containment technology, be made environmentally safe for use as solid waste landfills. Simultaneously, the procedure safeguards and monitors protection of ground and surface waters from landfill contamination.

The effects of solid contamination in hydraulic fluids on axial piston pumps

The fluids used in hydraulic systems inevitably contain large numbers of small, solid particles, a phenomenon known as 'fluid contamination'. Particles enter a hydraulic system from the environment, and are generated within it by processes of wear. At the same time, particles are removed from the system fluid by sedimentation and in hydraulic filters. This thesis considers the problems caused by fluid contamination, as they affect a manufacturer of axial piston pumps. The specific project aim was to investigate methods of predicting or determining the effects of fluid contamination on this type of pump. The thesis starts with a theoretical analysis of the contaminated lubrication of a slipper-pad bearing. Statistical methods are used to develop a model of the blocking, by particles, of the control capillaries used in such bearings. The results obtained are compared to published, experimental data. Poor correlation between theory and practice suggests that more research is required in this area before such theoretical analysis can be used in industry. Accelerated wear tests have been developed in the U.S.A. in an attempt to predict pump life when operating on contaminated fluids. An analysis of such tests shows that reliability data can only be obtained from extensive test programmes. The value of contamination testing is suggested to be in determining failure modes, and in identifying those pump components which are susceptible to the effects of contamination. A suitable test is described, and the results of a series of tests on axial piston pumps are presented and discussed. The thesis concludes that pump reliability data can only be obtained from field experience. The level of confidence which can be placed in results from normal laboratory testing is shown to be too low for the data to be of real value. Recommendations are therefore given for the ways in which service data should be collected and analysed.

Computationsl modelling of dimethyl ether separation and steam reforming in fluidized bed reactors

This study presents a computational fluid dynamic (CFD) study of Dimethyl Ether (DME) gas adsorptive separation and steam reforming (DME-SR) in a large scale Circulating Fluidized Bed (CFB) reactor. The CFD model is based on Eulerian-Eulerian dispersed flow and solved using commercial software (ANSYS FLUENT). Hydrogen is currently receiving increasing interest as an alternative source of clean energy and has high potential applications, including the transportation sector and power generation. Computational fluid dynamic (CFD) modelling has attracted considerable recognition in the engineering sector consequently leading to using it as a tool for process design and optimisation in many industrial processes. In most cases, these processes are difficult or expensive to conduct in lab scale experiments. The CFD provides a cost effective methodology to gain detailed information up to the microscopic level. The main objectives in this project are to: (i) develop a predictive model using ANSYS FLUENT (CFD) commercial code to simulate the flow hydrodynamics, mass transfer, reactions and heat transfer in a large scale dual fluidized bed system for combined gas separation and steam reforming processes (ii) implement a suitable adsorption models in the CFD code, through a user defined function, to predict selective separation of a gas from a mixture (iii) develop a model for dimethyl ether steam reforming (DME-SR) to predict hydrogen production (iv) carry out detailed parametric analysis in order to establish ideal operating conditions for future industrial application. The project has originated from a real industrial case problem in collaboration with the industrial partner Dow Corning (UK) and jointly funded by the Engineering and Physical Research Council (UK) and Dow Corning. The research examined gas separation by adsorption in a bubbling bed, as part of a dual fluidized bed system. The adsorption process was simulated based on the kinetics derived from the experimental data produced as part of a separate PhD project completed under the same fund. The kinetic model was incorporated in FLUENT CFD tool as a pseudo-first order rate equation; some of the parameters for the pseudo-first order kinetics were obtained using MATLAB. The modelling of the DME adsorption in the designed bubbling bed was performed for the first time in this project and highlights the novelty in the investigations. The simulation results were analysed to provide understanding of the flow hydrodynamic, reactor design and optimum operating condition for efficient separation. Bubbling bed validation by estimation of bed expansion and the solid and gas distribution from simulation agreed well with trends seen in the literatures. Parametric analysis on the adsorption process demonstrated that increasing fluidizing velocity reduced adsorption of DME. This is as a result of reduction in the gas residence time which appears to have much effect compared to the solid residence time. The removal efficiency of DME from the bed was found to be more than 88%. Simulation of the DME-SR in FLUENT CFD was conducted using selected kinetics from literature and implemented in the model using an in-house developed user defined function. The validation of the kinetics was achieved by simulating a case to replicate an experimental study of a laboratory scale bubbling bed by Vicente et al [1]. Good agreement was achieved for the validation of the models, which was then applied in the DME-SR in the large scale riser section of the dual fluidized bed system. This is the first study to use the selected DME-SR kinetics in a circulating fluidized bed (CFB) system and for the geometry size proposed for the project. As a result, the simulation produced the first detailed data on the spatial variation and final gas product in such an industrial scale fluidized bed system. The simulation results provided insight in the flow hydrodynamic, reactor design and optimum operating condition. The solid and gas distribution in the CFB was observed to show good agreement with literatures. The parametric analysis showed that the increase in temperature and steam to DME molar ratio increased the production of hydrogen due to the increased DME conversions, whereas the increase in the space velocity has been found to have an adverse effect. Increasing temperature between 200 oC to 350 oC increased DME conversion from 47% to 99% while hydrogen yield increased substantially from 11% to 100%. The CO2 selectivity decreased from 100% to 91% due to the water gas shift reaction favouring CO at higher temperatures. The higher conversions observed as the temperature increased was reflected on the quantity of unreacted DME and methanol concentrations in the product gas, where both decreased to very low values of 0.27 mol% and 0.46 mol% respectively at 350 °C. Increasing the steam to DME molar ratio from 4 to 7.68 increased the DME conversion from 69% to 87%, while the hydrogen yield increased from 40% to 59%. The CO2 selectivity decreased from 100% to 97%. The decrease in the space velocity from 37104 ml/g/h to 15394 ml/g/h increased the DME conversion from 87% to 100% while increasing the hydrogen yield from 59% to 87%. The parametric analysis suggests an operating condition for maximum hydrogen yield is in the region of 300 oC temperatures and Steam/DME molar ratio of 5. The analysis of the industrial sponsor’s case for the given flow and composition of the gas to be treated suggests that 88% of DME can be adsorbed from the bubbling and consequently producing 224.4t/y of hydrogen in the riser section of the dual fluidized bed system. The process also produces 1458.4t/y of CO2 and 127.9t/y of CO as part of the product gas. The developed models and parametric analysis carried out in this study provided essential guideline for future design of DME-SR at industrial level and in particular this work has been of tremendous importance for the industrial collaborator in order to draw conclusions and plan for future potential implementation of the process at an industrial scale.

Eye movement problems and differential diagnosis of the parkinsonian syndromes

Differential clinical diagnosis of the parkinsonian syndromes, viz., Parkinson’s disease (PD), progressive supranuclear palsy (PSP), dementia with Lewy bodies (DLB), and multiple system atrophy (MSA) can be difficult. Eye movement problems, however, are a chronic complication of many of these disorders and may be a useful aid to diagnosis. Hence, the presence in PSP of vertical supranuclear gaze palsy, fixation instability, lid retraction, blepharospasm, and apraxia of eyelid opening and closing is useful in separating PD from PSP. Moreover, atypical features of PSP include slowing of upward saccades, moderate slowing of downward saccades, the presence of a full range of voluntary vertical eye movements, a curved trajectory of oblique saccades, and absence of square-wave jerks. Downgaze palsy is probably the most useful diagnostic clinical symptom of PSP. By contrast, DLB patients are specifically impaired in both reflexive and saccadic execution and in the performance of more complex saccadic eye movement tasks. Problems in convergence in DLB are also followed by akinesia and rigidity. Abnormal ocular fixation may occur in a significant proportion of MSA patients along with excessive square-wave jerks, a mild supranuclear gaze palsy, a gaze-evoked nystagmus, a positioning down-beat nystagmus, mild-moderate saccadic hypometria, impaired smooth pursuit movements, and reduced vestibulo-ocular reflex (VOR) suppression. There may be considerable overlap between the eye movement problems characteristic of the various parkinsonian disorders, but taken together with other signs and symptoms, can be a useful aid in differential diagnosis, especially in the separation of PD and PSP.

Quasi-separation of the biharmonic partial differential equation

In this paper, we consider analytical and numerical solutions to the Dirichlet boundary-value problem for the biharmonic partial differential equation on a disc of finite radius in the plane. The physical interpretation of these solutions is that of the harmonic oscillations of a thin, clamped plate. For the linear, fourth-order, biharmonic partial differential equation in the plane, it is well known that the solution method of separation in polar coordinates is not possible, in general. However, in this paper, for circular domains in the plane, it is shown that a method, here called quasi-separation of variables, does lead to solutions of the partial differential equation. These solutions are products of solutions of two ordinary linear differential equations: a fourth-order radial equation and a second-order angular differential equation. To be expected, without complete separation of the polar variables, there is some restriction on the range of these solutions in comparison with the corresponding separated solutions of the second-order harmonic differential equation in the plane. Notwithstanding these restrictions, the quasi-separation method leads to solutions of the Dirichlet boundary-value problem on a disc with centre at the origin, with boundary conditions determined by the solution and its inward drawn normal taking the value 0 on the edge of the disc. One significant feature for these biharmonic boundary-value problems, in general, follows from the form of the biharmonic differential expression when represented in polar coordinates. In this form, the differential expression has a singularity at the origin, in the radial variable. This singularity translates to a singularity at the origin of the fourth-order radial separated equation; this singularity necessitates the application of a third boundary condition in order to determine a self-adjoint solution to the Dirichlet boundary-value problem. The penultimate section of the paper reports on numerical solutions to the Dirichlet boundary-value problem; these results are also presented graphically. Two specific cases are studied in detail and numerical values of the eigenvalues are compared with the results obtained in earlier studies.

Hierarchical nanoporous solid base catalysts for biofuels

Novel macroporous solid bases have been developed as alternative clean technologies to existing commercial homogeneous catalysts for the production of biodiesel from triglycerides; the latter suffer process disadvantages including complex separation and associated saponification and engine corrosion, and are unsuitable for continuous operation. To this end, tuneable macroporous MgAl hydrotalcites have been prepared by an alkali-free route and characterised by TGA, XRD, SEM and XPS. The macropore architecture improves diffusion of bulky triglyceride molecules to the active base sites, increasing activity. Lamellar and macroporous hydrotalcites will be compared for the transesterification of both model and plant oil feedstocks, and structure-reactivity relations identified.