Dissertations / Theses on the topic 'Crystallisation;Hard Sphere Systems'

The primary focus of this work is to develop an understanding of crystallisation in hard sphere systems. The thesis is presented in two parts. The first section is an investigation of the liquid/crystal interface at equilibrium using molecular dynamical simulations. The objective is to understand how the interface might bridge between the disordered and ordered states in liquid/crystal environments. Topological measures of structure are used to investigate whether any precursor structures are present in the liquid phase, close to the interface, that would allow transition from disorder to order. This differs from other work where simpler measures of structure, classifying phases into either liquid or crystal, are used. The results indicate that the liquid/crystal interface of a hard sphere system is very narrow and no readily observable structures were found that extended past the width of the equilibrium interface. The second section of the thesis is a theoretical study of growth kinetics in hard sphere systems using density functional theory. The kinetics in a fixed volume are examined with a single conserved order parameter. The work is extended incorporating both conserved particle and non-conserved structure dynamics. The kinetics of growth are examined and it is shown that the small initial crystals are quickly isolated from the higher pressure of the surrounding system through the development of a depletion zone.

The primary focus of this work is to develop an understanding of crystallisation in hard sphere systems. The thesis is presented in two parts. The first section is an investigation of the liquid/crystal interface at equilibrium using molecular dynamical simulations. The objective is to understand how the interface might bridge between the disordered and ordered states in liquid/crystal environments. Topological measures of structure are used to investigate whether any precursor structures are present in the liquid phase, close to the interface, that would allow transition from disorder to order. This differs from other work where simpler measures of structure, classifying phases into either liquid or crystal, are used. The results indicate that the liquid/crystal interface of a hard sphere system is very narrow and no readily observable structures were found that extended past the width of the equilibrium interface. The second section of the thesis is a theoretical study of growth kinetics in hard sphere systems using density functional theory. The kinetics in a fixed volume are examined with a single conserved order parameter. The work is extended incorporating both conserved particle and non-conserved structure dynamics. The kinetics of growth are examined and it is shown that the small initial crystals are quickly isolated from the higher pressure of the surrounding system through the development of a depletion zone.

An improved crystallisation spectrometer has been designed, built and tested. It is to be used by others to gain new knowledge about the solidification of matter by study of the crystallisation of hard sphere colloid samples that are an established model for the behaviour of some aspects of atoms. In this crystallisation spectrometer, expanded and collimated green laser light is Bragg scattered from the colloidal crystals as they form, and the diffracted light is focused by a liquid filled hollow glass hemispherical lens onto low cost CCD array detectors that are rotated about the optical axis to average the intensities around the whole Debye-Scherrer cone of scattered light. The temperature of the sample is controlled to +/-0.1„a, and because of the ability to change the refractive index of the sample particles with temperature, this is utilised to control the amount of scattering from the sample Also, this spectrometer uniquely exploits the refractive index match of the colloidal particles, the solvent, the bath liquid, and the glass used for both the sample bottle and the hollow glass hemisphere. A unique facility has been incorporated to permit tumbling of the sample prior to the measurement commencing to shear-melt any pre-existing crystals. This ensures that the sample is completely fluid and is at the correct temperature at the start of the measurement. The instrument is assembled on an optical table and is computer controlled. Results presented show that this new spectrometer with its use of the whole Debye-Scherrer cone of Bragg scattered light and other enhancements gives insight into the crystallisation process more than one order of magnitude of time earlier than previous light scattering experiments, providing new knowledge about the crystallisation process.

I have studied the effects of polydispersity on the phase behaviour of suspensions of PMMA colloidal spheres on their own and in the presence of non-adsorbed polymer. Fractionation studies on coexisting phases enabled verification of a recent universal law of fractionation in slightly polydisperse systems.

Particulate systems in practical applications such as biomass combustion, blood cellular systems and granular particles in fluidized beds, have often been computationally represented using spherical surfaces, even though the majority of particles in archetypal fluid-solid systems are non-spherical. While spherical particles are more cost-effective to simulate, notable deficiencies of these implementations are their substantial inaccuracies in predicting the dynamics of particle mixtures. Alternatively, modeling dense fluid-particulate systems using non-spherical particles involves increased complexity, with computational cost manifesting as the biggest bottleneck. However, with recent advancements in computer hardware, simulations of three-dimensional particulate systems using irregular shaped particles have garnered significant interest. In this research, a novel Discrete Element Method (DEM) model that incorporates geometry definition, collision detection, and post-collision kinematics has been developed to accurately simulate non-spherical particulate systems. Superellipsoids, which account for 80% of particles commonly found in nature, are used to represent non-spherical shapes. Collisions between these particles are processed using a distance function computation carried out with respect to their surfaces. An event - driven model and a time-driven model have been employed in the current framework to resolve collisions. The collision model's influence on non–spherical particle dynamics is verified by observing the conservation of momentum and total kinetic energy. Furthermore, the non-spherical DEM model is coupled with an in-house fluid flow solver (GenIDLEST). The combined CFD-DEM model's results are validated by comparing to experimental measurements in a fluidized bed. The parallel scalability of the non-spherical DEM model is evaluated in terms of its efficiency and speedup. Major factors affecting wall clock time of simulations are analyzed and an estimate of the model's dependency on these factors is documented. The developed framework allows for a wide range of particle geometries to be simulated in GenIDLEST.
Master of Science
CFD – DEM (Discrete Element Method) is a technique of coupling fluid flow solvers with granular solid particles. CFD – DEM simulations are beneficial in recreating pragmatic applications such as blood cellular flows, fluidized beds and pharmaceutics. Up until recently, particles in these flows have been modeled as spheres as the generation of particle geometry and collision detection algorithms are straightforward. However, in real – life occurrences, most particles are irregular in shape, and approximating them as spheres in computational works leads to a substantial loss of accuracy. On the other hand, non – spherical particles are more complex to generate. When these particles are in motion, they collide and exhibit complex trajectories. Majority of the wall clock time is spent in resolving collisions between these non – spherical particles. Hence, generic algorithms to detect and resolve collisions have to be incorporated. This primary focus of this research work is to develop collision detection and resolution algorithms for non – spherical particles. Collisions are detected using inherent geometrical properties of the class of particles used. Two popular models (event-driven and time-driven) are implemented and utilized to update the trajectories of particles. These models are coupled with an in – house fluid solver (GenIDLEST) and the functioning of the DEM model is validated with experimental results from previous research works. Also, since the computational effort required is higher in the case of non – spherical particulate simulations, an estimate of the scalability of the problem and factors influencing time to simulations are presented.

The search for the closest lattice point arises in many communication problems, and is known to be NP-hard. The Maximum Likelihood (ML) Detector is the optimal detector which yields an optimal solution to this problem, but at the expense of high computational complexity. Existing near-optimal methods used to solve the problem are based on the Sphere Decoder (SD), which searches for lattice points confined in a hyper-sphere around the received point. The SD has emerged as a powerful means of finding the solution to the ML detection problem for MIMO systems. However the bottleneck lies in the determination of the initial radius. This thesis is concerned with the detection of transmitted wireless signals in Multiple-Input Multiple-Output (MIMO) digital communication systems as efficiently and effectively as possible. The main objective of this thesis is to design efficient ML detection algorithms for MIMO systems based on the depth-first search (DFS) algorithms whilst taking into account complexity and bit error rate performance requirements for advanced digital communication systems. The increased capacity and improved link reliability of MIMO systems without sacrificing bandwidth efficiency and transmit power will serve as the key motivation behind the study of MIMO detection schemes. The fundamental principles behind MIMO systems are explored in Chapter 2. A generic framework for linear and non-linear tree search based detection schemes is then presented Chapter 3. This paves way for different methods of improving the achievable performance-complexity trade-off for all SD-based detection algorithms. The suboptimal detection schemes, in particular the Minimum Mean Squared Error-Successive Interference Cancellation (MMSE-SIC), will also serve as pre-processing as well as comparison techniques whilst channel capacity approaching Low Density Parity Check (LDPC) codes will be employed to evaluate the performance of the proposed SD. Numerical and simulation results show that non-linear detection schemes yield better performance compared to linear detection schemes, however, at the expense of a slight increase in complexity. The first contribution in this thesis is the design of a near ML-achieving SD algorithm for MIMO digital communication systems that reduces the number of search operations within the sphere-constrained search space at reduced detection complexity in Chapter 4. In this design, the distance between the ML estimate and the received signal is used to control the lower and upper bound radii of the proposed SD to prevent NP-complete problems. The detection method is based on the DFS algorithm and the Successive Interference Cancellation (SIC). The SIC ensures that the effects of dominant signals are effectively removed. Simulation results presented in this thesis show that by employing pre-processing detection schemes, the complexity of the proposed SD can be significantly reduced, though at marginal performance penalty. The second contribution is the determination of the initial sphere radius in Chapter 5. The new initial radius proposed in this thesis is based on the variable parameter α which is commonly based on experience and is chosen to ensure that at least a lattice point exists inside the sphere with high probability. Using the variable parameter α, a new noise covariance matrix which incorporates the number of transmit antennas, the energy of the transmitted symbols and the channel matrix is defined. The new covariance matrix is then incorporated into the EMMSE model to generate an improved EMMSE estimate. The EMMSE radius is finally found by computing the distance between the sphere centre and the improved EMMSE estimate. This distance can be fine-tuned by varying the variable parameter α. The beauty of the proposed method is that it reduces the complexity of the preprocessing step of the EMMSE to that of the Zero-Forcing (ZF) detector without significant performance degradation of the SD, particularly at low Signal-to-Noise Ratios (SNR). More specifically, it will be shown through simulation results that using the EMMSE preprocessing step will substantially improve performance whenever the complexity of the tree search is fixed or upper bounded. The final contribution is the design of the LRAD-MMSE-SIC based SD detection scheme which introduces a trade-off between performance and increased computational complexity in Chapter 6. The Lenstra-Lenstra-Lovasz (LLL) algorithm will be utilised to orthogonalise the channel matrix H to a new near orthogonal channel matrix H ̅.The increased computational complexity introduced by the LLL algorithm will be significantly decreased by employing sorted QR decomposition of the transformed channel H ̅ into a unitary matrix and an upper triangular matrix which retains the property of the channel matrix. The SIC algorithm will ensure that the interference due to dominant signals will be minimised while the LDPC will effectively stop the propagation of errors within the entire system. Through simulations, it will be demonstrated that the proposed detector still approaches the ML performance while requiring much lower complexity compared to the conventional SD.

Computational Fluid Dynamics Coupled to Discrete Element Method (CFD-DEM) is widely used in simulating a large variety of particulate flow system. This Eulerian-Lagrangian technique tracks all the particles included in the system by the application of point mass models in their equation of motion. CFD-DEM is a more accurate (and more expensive) technique compared to an Eulerian-Eulerian representation. Compared to Particle Resolved Simulations (PRS), CFD-DEM is less expensive since it does not require resolving the flow around each particles and thus can be applied to larger scale systems. Nevertheless, simulating industrial and natural scale systems is a challenge for this numerical technique. This is because the cost of CFD-DEM is proportional to the number of particles in the system under consideration. Thus, massively parallel codes are used to tackle these problems with the help of supercomputers. In this thesis, the CFD-DEM capability in the in-house code Generalized Incompressible Direct and Large Eddy Simulation of Turbulence (GenIDLEST) is used to investigate large scale dense particulate flow systems. Central to the contributions made by this work are developments to reduce the computational cost of CFD-DEM. This includes the development and validation of reduced order history force model for use in large scale systems and validation of the representative particle model, which lumps multiple particles into one, thus reducing the number of particles that need to be tracked in the system. Numerical difficulties in the form of long integration times and instabilities encountered in fully coupling the fluid and particle phases in highly energetic systems are alleviated by proposing a partial coupling scheme which maintains the accuracy of full-coupling to a large extent but at a reduced computational cost. The proposed partial-coupling is found to have a better convergence behavior compared to the full coupling in large systems and can be used in cases where full coupling is not feasible or impractical to use. Alternative modeling approaches for the tangential treatment of the soft-sphere impact model to avoid storing individual impact deformation are proposed and tested. A time advancement technique is developed and proposed for use in dense particulate systems with a hard-sphere impact model. The new advancement technique allows for the use of larger time steps which can speed-up the time to solution by as much as an order of magnitude.
PHD

The phase behavior of CO2 + polymer systems is of interest in polymer synthesis, flue and natural gas processing, polymer foam and nanoparticle processing, and drug delivery. Theoretical and experimental evidence suggests that CO2 is able to interact with electron donating functional groups in polymers to form weak Lewis acid – base or EDA (Electron Donor Acceptor) complexes. These complexes can have a significant effect on the phase behavior of associated CO2 + polymer systems. In spite of this, however, the phase equilibria of only a few associated CO2 + polymer systems have been measured. Some success in modeling the phase behavior of polymer solutions has been achieved by various versions of the Statistical Association Fluid Theory (SAFT), as well as by several Lattice Models. However, many of these models incorporate two to four adjustable parameters that often depend on temperature (T), pressure (P), and/or molecular weight (MW). As a result, a large amount of experimental data is required to apply these models. The goal of the present work was therefore to develop a new thermodynamic model for associating systems that would include no more than two temperature-independent adjustable parameters. The new model presented in this work is based on the Guggenheim-Huggins-Miller lattice and includes complex formation in the development of the partition function. The EOS obtained from the resulting partition function includes two mixture parameters – the enthalpy of association or complex formation and a reference value of the equilibrium constant for complex formation . Most importantly, can be obtained from in situ Attenuated Total Reflection Fourier Transform Infrared (ATR – FTIR) measurements. This work therefore demonstrates the use of ATR – FTIR spectra to obtain molecular level information regarding the interaction of CO2 and electron donating functional groups in polymers. Unlike other studies, this work uses the bending vibration of CO2 to estimate the enthalpies of association ( ) of CO2 + polymer systems. Values of were directly incorporated in the new model and were found to lie between -7 and -12 kJ/mol for the systems investigated in this work. They increased (i.e. became more negative) in the order: CO2 + PS-co-PMMA < CO2 + PMMA