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The rejection of single electrolytes at six different nanofiltration membranes has been experimentally studied. The membranes were chosen to cover the range of pore sizes from ultrafiltration to reverse osmosis and to represent the different types of polymer used for membrane fabrication. The experimental data has been interpreted using a model based on the extended Nernst-Planck equation, with the capability of predicting the rejection at a charged membrane in single and mixed electrolytes. The model accounts for the hindered nature of transport in the membranes. When used in conjunction with experimental data for single salt solutions, the model allows the determination of two important parameters: an effective membrane thickness and an effective membrane charge density. A knowledge of the effective membrane thickness and effective membrane charge density allows the model to predict the separation of mixtures of electrolytes at the membranes. Excellent agreement between these predictions and experimental data for mixtures is obtained.

A numerical model was developed to compute the unsteady flow of a compressible fluid using time-marching. The turbulence viscosity was defined in terms of the turbulence kinetic energy and the rate at which this kinetic energy was dissipated. The model was applied to a two-dimensional passage containing a flat plate. Because of the coarse grid spacings (as compared to the vortex dimensions) used in the present work, the model did not simulate vortex shedding and therefore resonance excitations were not produced. But the resonances of interest were either identified from the dying away transients or from artificial excitations. Comparison of the results from numerical computations and experimental investigations is good. The model has demonstrated that dynamically correct time marching methods are practical for unsteady flow problems.

Finite element numerical simulations are presented for two-dimensional creeping, planar and axisymmetric incompressible isothermal complex flows of both Newtonian and viscoelastic fluids. A number of constitutive equations are used to define fluid properties, including Newtonian, Oldroyd-B and Phan-Thien/Tanner (PTT) models. For viscoelastic flow, a modified semi-implicit Taylor-Galerkin method is presented with a consistent streamline upwind Petrov-Galerkin technique for the stress terms. Velocity gradient recovery is also employed. This multi-stage numerical solution algorithm implements a time marching, pressure-correction procedure. The significant influence of die-swell on the free surface flow development for wire-coating flows is reported and discussed in the results. The simulation of Poiseuille and annular flow of Newtonian and Oldroyd-B fluid for stick-slip and die-swell problems is presented. A planar- Newtonian stick-slip flow is compared with the analytical solution, whilst an axisymmetric die-swell case is compared against the theory and other numerical methods. Analysis for two free surface formulations is performed and results are shown for varying structure and mesh refinement. Investigation into the influence of elasticity and drag flow components on free surface location is performed for an Oldroyd-B fluid. The results indicate that, as elasticity increases, pressure and stresses do likewise. The swelling ratio, expressed in terms of extrudate swell, depends especially on this elastic influence. Newtonian fluid with slip effects and a viscoelastic analysis of PTT models are described for a low density, high speed wire-coating process on pressure-tooling and tube-tooling dies. Fluid coating flows such as these are especially useful in industrial wire coating processes for covering surface areas with one or more thin uniform layers of polymer melt. Pressure-tooling dies are used for coating narrow-gauge wires, whilst tube-tooling dies deal with wide-bore cables. The impact of variation in slip models at the die walls, and the effects of drag pressure driven flow are explored. Slip influence reduces swelling-ratio, but increases oscillations in the pre-die exit region. Comparison of pressure-tooling between PTT models are shown with variation in shear-thinning and stain-softening properties. The effects of deviation in polymeric viscosity and Weissenberg number are presented. The results have been confirmed through mesh refinement.

An experimental and theoretical study of the hydraulic transport of coarse solids in both water and shear-thinning fluids has been carried out with a view to developing an improved procedure for the prediction of pressure drop for flow in horizontal pipes. An examination of the experimental results and correlations used by previous workers has shown that none of the presently available methods of calculating the pressure drop is capable of forming a reliable basis for a design procedure. Results obtained by different workers under seemingly similar experimental conditions can yield pressure drops differing by as much as 11-fold. It is suggested that two important factors have not been adequately taken into account in the past. The first is that cognisance has not been taken of the fact that the in-line concentration of solids (which determines the flow conditions within the pipe) may be considerably different from the concentration in the mixture discharged from the pipe because of the existence of a 'slip' between the liquid and the particles. Secondly, very few workers have measured the coefficient of friction between the solid particles and the pipe wall, a variable which has a very strong influence on the pressure drop when bed formation occurs. In the experimental programme during which suspensions were transported in a recirculating loop consisting of 38 mm diameter piping, measurements were made of in-line concentrations and of mean liquid velocities within the pipe. In addition, off-line measurements of solids-wall coefficients of friction were made. The experimental results were interpreted using a simplified form of the 'two-layer' model, in which it was assumed that all particles were conveyed in the bed-layer. By use of the conclusion from the experimental work that the slip velocity is close to the terminal settling velocity of the particles, it has not been necessary to make any assumption concerning the interfacial shear between the surface of the bed and the liquid in the upper part of the pipe. The model has been found to predict results of this present study to within ±15%. Comparison with the results of other investigators has been limited because rarely have they measured the coefficient of solids friction. An empirical correlation has been developed for transport in shear-thinning liquids which predicts results for a wide range of data to within ±22%. In addition, a proportion of these results have been interpreted in terms of the proposed model.

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The simulation of groundwater contamination by nonaqueous phase liquids (NAPLs), such as organic solvents and petroleum hydrocarbons, requires a solution of the multiphase flow, heat flow and pollutant transport through soil. Also, the contaminant can exist within the gas and water phases. A multi-phase flow model, based on the two-phase flow model of Brooks and Corey, that expresses the dependence of saturation and relative permeability on capillary pressure is presented. The nonlinear behaviour of the saturation versus relative permeability functions is incorporated into a Galerkin finite element model that is used to simulate the vertical infiltration of immiscible/miscible fluid in unsaturated and saturated porous media. The governing partial differential equations, in terms of soil displacements, fluid pressures, energy balance and concentrations are coupled and behave non-linearly but can be solved by the finite element method. In order to apply the finite element model to a specific problem a number of parameters must be evaluated. These include relative permeabilities, saturation-pressure relations, mass transfer coefficients and densities. Numerical implementation of the formulation is discussed, and example problems are presented for verification. As a demonstration of the model's applicability, the migration of a contaminant is simulated in 1D and 2D problems. Also, an approximate numerical solution to the theoretical model is presented. The weighted residual finite element approach is employed to achieve spatial discretisation of the problem while temporal discretisation is achieved by a fully implicit scheme. A verification and validation programme has been implemented to assess the integrity of the theory, discretisation approach and the code itself. Several exercises verifying the consolidation model are presented. Validation exercises for the cases of isothermal, non-isothermal, saturated and unsaturated conditions of the coupled flow of heat, water and gas in a deforming porous medium, are performed. Finally, the fully coupled model is verified by comparison with results from an alternative model.

An investigation has been made of a technique in which bubbles of nitrogen gas were formed simultaneously at adjacent orifices in aqueous solutions of potassium chloride, ethanol and n-octanol. The bubble coalescence time, defined as the time between the first touching of the bubbles until they coalesce, was measured by high speed cinephotography or video tape recording. The film formed between the bubbles increases in radius steadily with time. It was found that coalescence was markedly affected by solute concentration, gas flow rate and temperature. Excellent reproducibility in coalescence times was observed. With potassium chloride solutions, it was found that the coalescence time increased with increasing concentration until a fairly sharply defined concentration (500 mol/m ) was reached, above which the bubbles detached from the orifices without coalescing. With ethanol solutions, coalescence time increased with increasing concentration. Coalescence was not completely inhibited at the lower gas flow rates at any concentration. With n-octanol solutions, coalescence time increased sharply with increasing concentration above 7x10-3 mol/m3, and coalescence was completely inhibited above a concentration of 11x10-3 mol/m. The experimental observations have been discussed in terms of a two-stage mechanism of coalescence. In the first stage rapid stretching of the film formed between the bubbles, produces a surface tension gradient, at the periphery; stretching is arrested when this surface tension gradient is just balanced by the pressure in the film. For non-volatile solutes, in the second stage the film continues to grow in area, but the fresh film -formed at the periphery becomes progressively thinner because the proportion of liquid which escapes by viscous flow increases with increasing film radius. However, for volatile solutes after the stretching process has halted, the coalescence time of the film is determined by the supply of solute to the surface by gas phase diffusion. Decrease in coalescence times at elevated temperatures is due to decreases in surface tension, viscosity and an increase in vapour pressure.

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