A number of fluid dynamical calculations are presented as models for various aspects of two-phase flow in porous media. In order to ensure mathematical tractability, only simple, idealized problems are studied. Useful information can however be deduced about the governing physical processes in the more complicated configurations which occur in a real porous medium. The stability to small disturbances of the interface of an infinitely long thread of viscous fluid surrounded by another and confined in a uniform pipe is first considered. Sufficiently long wavelength perturbations are found to be unstable when surface tension acts. A nonlinear analysis in which the outer fluid annulus is assumed thin shows that all disturbances evolve to a steady state in which the outer film has broken up into disconnected lobes. This analysis is extended to model a thread in a constricted tube, and a possible mechanism for its breakup is found. Next, end effects on these processes are discussed, and the adjustment of a stationary droplet in a pipe considered. The theory agrees with published observations. A preliminary analysis of a droplet moving under an applied pressure gradient is then given. Finally, a two-dimensional model problem, in which an interface adjusts inside a circular boundary is presented, and the peeling of the interface from the wall studied. Applications of the model to other problems involving strongly deformed surface tension interfaces are briefly discussed.

No description available.

No description available.

No description available.

The major focus of the work is on the measurement and simulation of the particle residence time distribution in the square cross section riser of a laboratory scale, cold model, circulating fluidised bed. To this end, a novel measurement technique was developed using phosphorescent tracer particles and a light based tracer injection and detection system. Experimental results confirm that the RTD is sensitive to changes in superficial gas velocity, external solids flux and the geometry of the riser exit. Simulations made using a novel stochastic particle RTD model are in good agreement with the experimental results. The measurements of the particle RTD, separately confirm the findings of a study of the riser exit using local pressure measurements, that demonstrate the influence of the riser exit on the solids flow pattern can be significant. A series of dimensionless correlations were developed to predict this influence. The effect of the exit has been shown to be dependent upon only one dimensionless group, the riser exit Froude number, <i>Fr_R.</i> A dimensionless correlation was also developed for predicting the thickness of the annular film present at the wall of CFB risers operating in the fast fluidisation regime. This correlation is superior to those published in the literature. A further series of correlations were developed to predict the size, shape, decent velocity, solids concentration and wall coverage of the particle clusters that are a characteristic feature of the gas-solid suspension in a CFB riser.

The properties of colloidal dispersions, particularly under flow, are important in many areas of life, and yet present many fascinating and profound scientific problems. This dissertation presents an investigation of the positional and orientational order found in stable dispersions of anisotropic colloidal particles under shear. In order to understand the reasons behind the order present, it is necessary to study simple systems. To keep the dispersions simple, an emphasis is placed upon knowing and controlling the shape, size distribution and interactions of the particles investigated. A number of dispersions of anisotropic particles were prepared and stabilised to give an approximation to 'hard' particles. A technique was developed to measure the orientation distribution using the diffraction from mono-crystalline colloidal particles. The positional order was measured using small angle scattering. New shear geometries were designed and tested for shearing samples in a neutron beam. Two dispersions of plate shaped particles were studied. Plates with an aspect ratio of 5 and a polydispersity of 13 % (nickel (II) hydroxide) displayed an equilibrium phase transition to a columnar phase. Under low shear an aligned columnar phase was observed with columns oriented near the flow direction, and plate normals in the compressional quadrant at 20 degrees to the flow direction. As the shear rate was increased a 'phase transition' was observed to a smectic structure, with layers and particles normal to the gradient direction. Upon ceasing shear the structure returned to the columnar phase without the particles reorienting. Plates with a higher aspect ratio and a broader size distribution (kaolinite) were observed to align with normals in the compressional quadrant, moving towards the gradient direction at higher shear rates. At volume fractions below 0.13 the orientational order increased with concentration, while at higher concentrations the orientational order decreased with increasing concentration.

The framework of normal modes of a stable flow in a channel is reviewed: two kinds of modes, regular and singular, are found. This framework is then used to study an initial-value problem, with initial conditions consisting of super-­positions of singular modes. Theoretical predictions are made concerning the excitation of regular modes in certain special cases. Chapter 3 describes numerical simulations of the relevant equations, which are shown to be in agreement with our predictions. In chapter 4 we review previous studies of non linear critical layers, in particular the asymptotic Stewartson-Warn & Warn (SWW) solution, and the instability analysis by Killworth & McIntyre. We investigate the pos­sibility that small non linearities, inherent in the full asymptotic solution, but suppressed in the SWW solution, could grow and trigger the instability. These non linearities have exponentially small amplitudes, but we present a heuristic scaling argument to show that they could indeed grow fast enough to significantly affect the evolution of the flow. Chapter 5 describes the nu­merical methods that were used in high-precision simulations that resolve the unstable modes. Finally in chapter 6 we describe the results of these simulations. We use these to extrapolate the asymptotic limit considered by SWW, and show that indeed after a certain time, that we measure, the un­stable modes grow to large amplitudes, and that the SWW flow is no longer the correct leading-order solution after this time.

No description available.

No description available.

No description available.