Diffusion and permeation in binary solutions: Application to\ud protein ultrafiltration

During the ultrafiltration of colloidal solutions the particles can form a porous medium (filter cake) or a diffuse boundary layer (concentration polarization) above the semipermeable membrane depending on the magnitude of the filtration pressure. In order to provide a unified description of these phenomena the present work develops some connections between irreversible thermodynamics and poroelasticity. In particular, Fick’s and Darcy’s laws are shown to provide an equivalent description except in two limiting cases – infinite dilution and infinite rigidity of the solute. A new expression for the generalized Stokes-Einstein equation is also obtained, which incorporates the poroelastic Biot-Willis coefficient accounting for the compressibility of the solvent. The theory is utilized to predict the pressure and concentration profiles during the ultrafiltration of a protein solution. The model captures the formation of a diffuse polarization layer at low pressures and a nearly rigid filter cake at higher pressures, as well as intermediate stages. The predicted Darcy pressure profile across the polarization layer is in good quantitative agreement with experimental measurements

Particle trapping and banding in rapid solidification

Solidification of suspensions of small particles, from nanometer to colloidal (sub-micrometer) sizes, produces biomimetic materials with novel microstructure and expanding applications in microfluidics, nanotechnology and tissue engineering. To facilitate understanding and control of the solidification process, a thermodynamically consistent theory is here developed. We use the Boltzmann particle velocity distribution to determine the probability a particle is engulfed by an advancing solid-liquid interface and obtain the resulting kinetic phase diagram. We demonstrate use of the theory by predicting the formation of bands in rapidly solidified alumina suspensions, in quantitative agreement with experiment

The kinetics of ice-lens growth in porous media

We analyse the growth rate of segregated ice (ice lenses) in freezing porous media. For typical colloidal materials such as soils we show that the commonly-employed Clapeyron equation is not valid macroscopically at the interface between the ice lens and the surrounding porous medium owing to the viscous dynamics of flow in premelted films. This gives rise to an ‘interfacial resistance’ to flow towards the growing ice which causes a significant drop in predicted ice-growth (heave) rates and explains why many previous models predict ice-growth rates that are much larger than those seen in experiments. We derive an explicit formula for the ice-growth rate in a given porous medium, and show that this only depends on temperature and on the external pressures imposed on the freezing system. This growth-rate formula contains a material-specific function which can be calculated (with a knowledge of the of the geometry and material of the porous medium), but which is also readily experimentally-measurable. We apply the formula to plate-like particles, and obtain good agreement with previous experimental data. Finally we show how the interfacial resistance explains the observation that the maximum heave rate in soils occurs in medium-grained particles such as silts, while heave rates are smaller for fine- and coarse- grained particles

Crust formation in drying colloidal suspensions

During the drying of colloidal suspensions, the desiccation process causes the suspension near the air interface to consolidate into a connected porous matrix or crust. Fluid transport in the porous medium is governed by Darcy’s law and the equations of poroelasticity, while the equations of colloid physics govern processes in the suspension. We derive new equations describing this process, including unique boundary conditions coupling the two regions, yielding a moving-boundary model of the concentration and stress profiles during drying. A solution is found for the steady-state growth of a one-dimensional crust during constant evaporation rate from the surface. The solution is used to demonstrate the importance of the system boundary conditions on stress profiles and diffusivity in a drying crust

Frost heave in compressible soils

We develop a mathematical model of frost heave in compressible soils based on a morphological instability of the ice–soil interface. The theory accounts for heave and soil consolidation,while avoiding the frozen fringe assumption. Using a Lie-B¨acklund transformation an analytical solution to the governing equations is found. Two solidification regimes occur: a compaction regime in which the soil consolidates to accommodate the ice lenses, and a heave regime during which the soil is fully consolidated and heaves. The rate of heave is found to be independent of the rate of freezing, consistent with field and laboratory observations

Morphological instability of a nonequilibrium icecolloid interface

We assess the morphological stability of a nonequilibrium icecolloidal suspension interface, and apply the theory to bentonite clay. An experimentally convenient scaling is employed which takes advantage of the vanishing segregation coefficient at low freezing velocities, and when anisotropic kinetic effects are included the interface is shown to be unstable to travelling waves. The potential for traveling wave modes reveals a possible mechanism for the polygonal and spiral ice lenses observed in frozen clays. A weakly nonlinear analysis yields a long-wave evolution equation for the interface shape containing a new parameter related to the highly nonlinear liquidus curve in colloidal systems. We discuss the implications of these results for the frost susceptibility of soils and the fabrication of microtailored porous materials

Gender equality and education in the Sustainable Development Goals

This paper was commissioned by the Global Education Monitoring Report as background information to assist in drafting the 2016 report. It has not been edited by the team. The views and opinions expressed in this paper are those of the author(s) and should not be attributed to the Global Education Monitoring Report or to UNESCO. The papers can be cited with the following reference: “Paper commissioned for the Global Education Monitoring Report 2016, Education for people and planet: Creating sustainable futures for all”. For further information, please contact [email protected]

Onsager reciprocity in premelting solids

The diffusive motion of foreign particles dispersed in a premelting solid is analyzed within the framework of irreversible thermodynamics. We determine the mass diffusion coefficient, thermal diffusion coefficient and Soret coefficient of the particles in the dilute limit, and find good agreement with experimental data. In contrast to liquid suspensions, the unique nature of premelting solids allows us to derive an expression for the Dufour coefficient and independently verify the Onsager reciprocal relation coupling diffusion to the flow of heat

Restructuring of the demand for labour: a study of labour market adjustment mechanisms in Stockton-on-tees

This thesis investigates the inter-relationships between industrial restructuring, labour demand and unemployment through detailed case studies in the Travel to Work Area (TTWA) of Stockton-on-Tees in the North-East of England. After examining the legacy of previous rounds of investment in the TTWA the changing labour demands of six local employers are monitored and analysed over a one year period to July 1987. Focus of attention is on how employers adjust their labour inputs to meet changes in labour demand, as derived from the requirements of the production process. By selecting employers known (or thought) to be establishing new working patterns and practices it was possible to study the 'dynamics of employment' in a variety of settings. These include a 'branch plant' employing mainly female labour, investing in new technology and changing from full-time to part-time workers; a joinery company which has suffered from the decline in public sector housebuilding and has been the subject of a series of takeovers; the District General Hospital attempting to cope with cash constraints in the public sector; a small engineering firm 'sandwiched' between large suppliers and customers; a recently arrived Japanese company producing electronic components and an historic engineering company that attempted (unsuccessfully) to diversify into the offshore supply industry. In each case, an attempt is made to assess the net impact of 'flows' of labour to and from employment on the (official) unemployment count, drawing on data held on the National Online Manpower Information System (NOMIS)