Mixing the grant cocktail:towards an understanding of the outcomes of financial support to small firms

One of the key policy objectives of government at national and regional level, is to overcome the constraints preventing local industry achieving greater competitiveness in the international market-place. This paper examines the impact of grant assistance to Northern Ireland small firms delivered over the period 1994 ^ 97 by the former Local Enterprise Development Unit through its Growth Business Support Programme (GBSP). Previous work by the authors showed that there was some tentative evidence to suggest a link between employment growth and grant aid provided to very small firms (fewer than 10 employees) assisted under the GBSP. The central objective of the empirical work reported in this paper is to extend the previous analysis by understanding the extent to which the value of financial assistance influences growth (employment, turnover, and productivity measures) and if differential impacts arise depending on the nature and timing (lag structures) of the grant assistance.

Flow field analysis of some mixing and conveying screw element regions, within a closely intermeshing, co-rotating twin-screw extruder.

Grafting of antioxidants and other modifiers onto polymers by reactive extrusion, has been performed successfully by the Polymer Processing and Performance Group at Aston University. Traditionally the optimum conditions for the grafting process have been established within a Brabender internal mixer. Transfer of this batch process to a continuous processor, such as an extruder, has, typically, been empirical. To have more confidence in the success of direct transfer of the process requires knowledge of, and comparison between, residence times, mixing intensities, shear rates and flow regimes in the internal mixer and in the continuous processor.The continuous processor chosen for the current work in the closely intermeshing, co-rotating twin-screw extruder (CICo-TSE). CICo-TSEs contain screw elements that convey material with a self-wiping action and are widely used for polymer compounding and blending. Of the different mixing modules contained within the CICo-TSE, the trilobal elements, which impose intensive mixing, and the mixing discs, which impose extensive mixing, are of importance when establishing the intensity of mixing. In this thesis, the flow patterns within the various regions of the single-flighted conveying screw elements and within both the trilobal element and mixing disc zones of a Betol BTS40 CICo-TSE, have been modelled using the computational fluid dynamics package Polyflow. A major obstacle encountered when solving the flow problem within all of these sets of elements, arises from both the complex geometry and the time-dependent flow boundaries as the elements rotate about their fixed axes. Simulation of the time dependent boundaries was overcome by selecting a number of sequential 2D and 3D geometries, used to represent partial mixing cycles. The flow fields were simulated using the ideal rheological properties of polypropylene and characterised in terms of velocity vectors, shear stresses generated and a parameter known as the mixing efficiency. The majority of the large 3D simulations were performed on the Cray J90 supercomputer situated at the Rutherford-Appleton laboratories, with pre- and postprocessing operations achieved via a Silicon Graphics Indy workstation. A mechanical model was constructed consisting of various CICo-TSE elements rotating within a transparent outer barrel. A technique has been developed using coloured viscous clays whereby the flow patterns and mixing characteristics within the CICo-TSE may be visualised. In order to test and verify the simulated predictions, the patterns observed within the mechanical model were compared with the flow patterns predicted by the computational model. The flow patterns within the single-flighted conveying screw elements in particular, showed good agreement between the experimental and simulated results.

Investigation of chaotic mixing in laminar fluid systems by the use of computational fluid dynamics

This work presents significant development into chaotic mixing induced through periodic boundaries and twisting flows. Three-dimensional closed and throughput domains are shown to exhibit chaotic motion under both time periodic and time independent boundary motions, A property is developed originating from a signature of chaos, sensitive dependence to initial conditions, which successfully quantifies the degree of disorder withjn the mixing systems presented and enables comparisons of the disorder throughout ranges of operating parameters, This work omits physical experimental results but presents significant computational investigation into chaotic systems using commercial computational fluid dynamics techniques. Physical experiments with chaotic mixing systems are, by their very nature, difficult to extract information beyond the recognition that disorder does, does not of partially occurs. The initial aim of this work is to observe whether it is possible to accurately simulate previously published physical experimental results through using commercial CFD techniques. This is shown to be possible for simple two-dimensional systems with time periodic wall movements. From this, and subsequent macro and microscopic observations of flow regimes, a simple explanation is developed for how boundary operating parameters affect the system disorder. Consider the classic two-dimensional rectangular cavity with time periodic velocity of the upper and lower walls, causing two opposing streamline motions. The degree of disorder within the system is related to the magnitude of displacement of individual particles within these opposing streamlines. The rationale is then employed in this work to develop and investigate more complex three-dimensional mixing systems that exhibit throughputs and time independence and are therefore more realistic and a significant advance towards designing chaotic mixers for process industries. Domains inducing chaotic motion through twisting flows are also briefly considered. This work concludes by offering possible advancements to the property developed to quantify disorder and suggestions of domains and associated boundary conditions that are expected to produce chaotic mixing.

Solids mixing and segregation in a gas spout-fluid bed-effect of the distributor design

This work is concerned with the assessment of a newer version of the spout-fluid bed where the gas is supplied from a common plenum and the distributor controls the operational phenomenon. Thus the main body of the work deals with the effect of the distributor design on the mixing and segregation of solids in a spout-filled bed. The effect of distributor design in the conventional fluidised bed and of variation of the gas inlet diameter in a spouted bed were also briefly investigated for purpose of comparison. Large particles were selected for study because they are becoming increasingly important in industrial fluidised beds but have not been thoroughly investigated. The mean particle diameters of the fraction ranged from 550 to 2400 mm, and their specific gravity from 0.97 to 2.45. Only work carried out with binary systems is reported here. The effect of air velocity, particle properties, bed height, the relative amount of jetsam and flotsam and initial conditions on the steady-state concentration profiles were assessed with selected distributors. The work is divided into three sections. Sections I and II deal with the fluidised bed and spouted bed systems. Section III covers the development of the spout-filled bed and its behaviour with reference to distributor design and it is shown how benefits of both spouting and fluidising phenomena can be exploited. In the fluidisation zone, better mixing is achieved by distributors which produce a large initial bubble diameter. Some common features exist between the behaviour of unidensity jetsam-rich systems and different density flotsam-rich systems. The shape factor does not seem to have an affect as long as it is only restricted to the minor component. However, in the case of the major component, particle shape significantly affects the final results. Studies of aspect ratio showed that there is a maximum (1.5) above which slugging occurs and the effect of the distributor design is nullified. A mixing number was developed for unidensity spherical rich systems, which proved to be extremely useful in quantifying the variation in mixing and segregation with changes in distributor design.

Ordered mixing of drugs with particulate excipients

A novel direct compression tableting excipient has been made by recrystallisation of lactose. The particles produced had high porosity, high specific surface area and high surface roughness. The resistance to segregation of ordered mixes formed between a model drug; potassium chloride and the excipients recrystallised lactose, spray crystallised maltose-dextrose (Emdexl and a direct compacting sugar (Dipac) was studied using a vibrational segregation model. The highly porous excipients, Emdex and recrystallised lactose formed ordered mixes which did not segregate even at high accelerations and low frequencies whereas the relatively smooth excipient, Dipac, displayed marked segregation in most vibration conditions. The vibrations were related to practical conditions measured in pharmaceutical process machinery. The time required to form an ordered mix was inversely related to the stability of the mix when subjected to vibration. An ultracentrifuge technique was developed to determine the interparticle adhesion forces holding drug and excipient particles together as ordered units. Excipient powders such as Emdex and recrystallised lactose, which formed non-segregating ordered mixes, had high interparticle adhesion forces. Other ordered mixes that segregated when subjected to different vibration conditions were found to have large quantities of weekly-bound drug particles; such mixes included those with Dipac as the carrier excipient as well as those containing a high concentration of drug. The electrostatic properties of different drug and excipient powders were studied using a Faraday well and an electrometer. Excipient powders such as Emdex and recrystallised lactose which formed stable ordered mixes also had a widely different surface charge in comparison with drug particles, whereas Dipac had a similar surface charge to the drug particles and formed unstable ordered mixes. A specially constructed triboelectric charging apparatus based on an air cyclone was developed to increase the affinity of drug particles for different excipient particles. Using triboelectrification to increase the interparticle adhesion forces, the segregation tendencies of unstable ordered mixes were greatly reduced. The stability of ordered mixes is shown to be related to both the surface physical characteristics and the surface electrical properties of the constituent carrier (excipientl particles.

Investigation of two-wave mixing in arbitrary oriented sillenite crystals

A generalized systematic description of the Two-Wave Mixing (TWM) process in sillenite crystals allowing for arbitrary orientation of the grating vector is presented. An analytical expression for the TWM gain is obtained for the special case of plane waves in a thin crystal (|g|d«1) with large optical activity (|g|/?«1, g is the coupling constant, ? the rotatory power, d the crystal thickness). Using a two-dimensional formulation the scope of the nonlinear equations describing TWM can be extended to finite beams in arbitrary geometries and to any crystal parameters. Two promising applications of this formulation are proposed. The polarization dependence of the TWM gain is used for the flattening of Gaussian beam profiles without expanding them. The dependence of the TWM gain on the interaction length is used for the determination of the crystal orientation. Experiments carried out on Bi12GeO20 crystals of a non-standard cut are in good agreement with the results of modelling.

Resonant two-wave mixing in photorefractive materials with the aid of dc and ac fields

A recently predicted resonant effect for the enhancement of two-wave mixing in photorefractive materials is investigated. The resonance occurs when the frequency of the applied ac field agrees with the eigenfrequency of the excited space-charge wave. Experimentally a clear resonance is found, as predicted by the theory, for high dc electric fields, but the resonance is smeared out for lower fields. A modified theory, taking into account the second temporal harmonic of the space-charge wave, shows good agreement with the experimental results.

Observations of diffraction and self diffraction effects during two wave mixing in a nematic liquid crystal

We report observations of the diffraction pattern resulting when a nematic liquid crystal is illuminated with two equal power, high intensity beams of light from an Ar+ laser. The time evolution of the pattern is followed from the initial production of higher diffraction orders to a final striking display arising as a result of the self-diffraction of the two incident beams. The experimental results are described with good approximation by a model assuming a phase distribution at the output plane of the liquid crystal in the form of the sum of a gaussian and a sinusoid.

The effects of optical activity and absorption on two wave mixing in Bi12SiO20

We consider non-degenerate two-wave mixing in photorefractive Bi12SiO20. It is shown theoretically that the presence of absorption and optical activity in the photorefractive media may result in a number of maxima for the gain as the frequency detuning between the two beams is varied. Further, when the beam interaction is used for optical amplification, there may also exist an optimum crystal length beyond which there is a reduction in the useful gain obtainable. Experimental results are presented in confirmation of the theory.

Two-wave mixing in BTO in the presence of detuning

The gain of a weak signal beam is measured in the usual two-wave mixing configuration in a photorefractive BTO crystal by varying a set of parameters, namely the applied electric field, the detuning, the beam ratio and the input intensity of the pump beam. All the experimental results are shown to be in good agreement with a theory based on that of Kukhtarev et al.

Amplification of temporally modulated signal beams via two-wave mixing in Bi12SiO20

A theoretical analysis of two-wave mixing in a BSO crystal is developed in the undepleted-pump approximation for a modulated signal beam. It is shown that, for a modulation of high enough frequency, significant ac amplification is possible at three distinct values of pump-beam detuning. A signal beam that is amplitude modulated by a square wave is analyzed by means of the theory, and experimental results are presented in confirmation of the analysis. Finally, it is shown that in the presence of absorption the optimum detunings for dc and ac amplification are different.