When bubbles are continuously released from a localised source at the bottom of a liquid layer, a bubble plume is produced. As the bubble plume rises due to its buoyancy, it entrains surrounding liquid, which is carried upward with the stream of bubbles. This dissertation investigates the effects of bubble size and density variation in the liquid on bubble plume behaviour and mixing pattern produced in the surrounding environment. The research was divided primarily into two areas. Firstly, the motion of a plume of low-Reynolds number bubbles in a stratified system consisting of two homogeneous layers of different densities was investigated. The liquid environment was of finite lateral extent. A theoretical model for the flow of the bubble plume and the surrounding liquid was developed. The theoretical predictions obtained were compared with new experimental results using plumes of small bubbles generated via electrolysis of an aqueous solution of sodium chloride and with previous experimental results (McDougall, 1978; Baines and Leitch, 1992). Secondly, a comparative study on the behaviour of a plume of large-Reynolds number bubbles in a stratified environment was carried out. The effect of the bubble size on plume structure and flow pattern was investigated. It was found that the wake transport led to an increase in the density at higher levels in the tank. This was at variance with the mixing induced by a plume of low-Reynolds number bubbles, which did not possess wakes but were more efficient at destratifying the lower regions of the tank (Chen and Cardoso, 2000). Coupling the radial density gradients and the continuous exchange of liquid between the plume and the surrounding environment, a dispersive effect on the density profile in the environment was observed. The experimental results showed that the extents of advection and dispersion in the environment depend on the size of individual bubbles and the degree of stratification in the environment. The theoretical model developed in this work was used to investigate the viability of using bubble plumes to induce mixing in reservoirs of liquefied petroleum gas.

In the strongly nematic state main chain liquid crystalline polymers have hairpin defects along their length. When these chains are cross-linked together they show unusual elastic properties experimentally. The elastic properties of a main chain elastomer are modelled here by calculating the stiffness of chains with hairpin defects and of those without. The dramatically different spring constants motivate a non-affine model for deformation of the resulting elastomer. The chains with hairpin defects are less stiff than those without and so take up more of the macroscopic strain. As the elastomer is stretched the macroscopic strain becomes more concentrated in the elastically weaker hairpinned chains, and so the rubber shows a plateau in its stress-strain curve. A mechanisms of developing a polarisation in chiral main chain LCE is analysed. In this mechanism the dipoles of the chiral monomers can be aligned by a shear deformation. It is shown that the polarisation of a pure LCE is zero in equilibrium due to rotation of the detector. The response of the director must be altered in a specific way in order to realise a non-zero result. Three methods of circumventing this result are explored: oscillating shear, pinning the detector with smectic layers, and using a mixture of chiral and non-chiral chains. Each of these methods is shown to produce a polarisation which is much larger per unit stress than that of quartz crystal. A fully non-linear model of elasticity in smectic A elastomers is developed from a phantom network model. The rigid constraints required by the layered smectic system are analysed from a geometric perspective. This model is then used to look for soft modes in biaxial smectic. A elastomers and smectic C elastomers. A general procedure for the calibration of soft modes is developed and specific examples of soft modes given.

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This thesis is concerned with the behaviour under flow of concentrated spherical colloids with a central hard core. Chapters two to four deal with hard spheres in a Newtonian fluid, without conservative forces (such as buoyancy effects or polymer coats) or Brownian forces. The central observation from previous computer simulations is that when a simple shear startup flow is imposed on such a system at sufficiently high concentration, a steady state is not achieved: the dispersion locks up after a finite amount of strain, at which point the shear stress is divergent. These chapters develop and analyse a theoretical model for this 'jamming' behaviour, in terms of the percolation of clusters of particles forming near the compression direction of the simple shear flow. The previously observed sensitivity of rheology to short range particle interactions is discussed in the context of this clustering theory at the close of chapter four. As a concrete example, chapter five contains a related theory of clustering in weakly aggregating colloids, which leads to power law shear thinning, and which is compared to both computer simulations and experimental results from the literature. To illustrate the calculation of particle interactions, chapter six contains an analysis of the lubrication modes of a pair of sponge coated colloidal particles. Chapter seven considers the problem of the behaviour of disordered regions in a shearing crystal of colloidal particles, which is loosely related to the idea of clustering earlier in the thesis. In the last two chapters, we return to the behaviour of the final jammed states of the colloid, considered at the start of the thesis, when the system becomes a type of granular material. A review of some recent ideas in the field of stress propagation in static granular matter is presented in chapter eight, together with a discussion of a model material introduced here to illustrate some of the points at issue. Chapter nine then discusses a more sophisticated model of stress fluctuations in granular matter due to R.C. Ball, and the behaviour of the model under coarse graining is analysed.

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Designing porous materials capable of hosting molecular species in cavities of molecular dimensions is an important goal in materials science and engineering. Contrary to the small, transient cavities that exist in the interstitial voids between the molecules of any conventional liquid, a "porous liquid" possesses well-defined, permanent voids inherent to the molecular architecture of the liquid molecules. The efficacy of such a microporous liquid lies in the ability of these intramolecular cavities to selectively house molecular guests. In this thesis we use computer simulations to embark on the first investigation into the microporous nature of potential "porous liquids", and establish whether this novel concept is viable. Simulations studies, using models as an approximation to the geometry of cage-like molecules, suggest that it is possible to design a system that exhibits permanent microporosity in the liquid phase. By calculating the distribution of cavity sizes in the liquid samples and simulating gas absorption experiments, we also establish that an existing system (synthesised by our experimental collaborators) is a potential candidate as the first microporous liquid.