Kerry A. Landman

Solid/liquid separation of flocculated suspensions

Solid-liquid separation operations leading to the concentration and isolation of fine particles dispersed in liquids are important in the chemical and mineral processing industries. In spite of this, the procedures available for the prediction of equipment performance remain crude. Almost all major mineral and chemical processing companies now have a clear priority in RD a major part of the problem faced by these industries relates to the effect of management of waste slurries. The processes that manage final waste slurries are often classical “end-of-pipe” solutions. One of the key aims of the present broad program is to understand how to manipulate the structure of slurries within the process so that finally it is possible to engineer clear liquor and simultaneously manageable or tractable waste solids. The best way to process such wastes relies on understanding how to control the compressibility and viscosity of these materials. A generalized approach to understanding and prediction of solid-liquid separation methods based on the measurement of fundamental material properties is reviewed here. This is of value in designing more efficient methods and ultimately to optimizing the performance of solid-liquid separation methods and the selection of flocculants for any given slurry. The model identifies two key parameters, the compressional yield stress Py(φ) and the hindered settling factor r(φ) and laboratory test procedures for the direct measurement of both have been developed. The application of this model to a variety of thickening and filtration processes is demonstrated and a direct relationship between the model parameters and the conventional cake resistance as utilised by current filtration engineers is provided.

DEWATERING OF FLOCCULATED SUSPENSIONS BY PRESSURE FILTRATION

Pressure filtration is an important method for removing liquids from a suspension. Previous work used linear models or applied to stable suspensions. Nonlinear models for flocculated suspensions are studied here. The equations governing the consolidation of flocculated suspensions under the influence of an applied pressure are based on the assumption that when the volume fraction is high enough, the network formed from the aggregation of flocs possesses a compressive yield stress Py(φ) that is a function of local volume fraction φ only. There are two modes of operation of the pressure filter—the fluid flux or the applied pressure is specified—and both of these are studied. The resulting nonlinear partial differential equations involve the time‐dependent piston position, and in the case of the suspension being initially unnetworked, another internal moving boundary below which the suspension is networked. The small time behavior of these systems is obtained with an asymptotic method. In general, at later t...

Mathematical and experimental insights into the development of the enteric nervous system and Hirschsprung's Disease

The vertebrate enteric nervous system is formed by a rostro‐caudally directed invasion of the embryonic gastrointestinal mesenchyme by neural crest cells. Failure to complete this invasion results in the distal intestine lacking intrinsic neurons. This potentially fatal condition is called Hirschsprungs Disease. A mathematical model of cell invasion incorporating cell motility and proliferation of neural crest cells to a carrying capacity predicted invasion outcomes to imagined manipulations, and these manipulations were tested experimentally. Mathematical and experimental results agreed. The results show that the directional invasion is chiefly driven by neural crest cell proliferation. Moreover, this proliferation occurs in a small region at the wavefront of the invading population. These results provide an understanding of why many genes implicated in Hirschsprungs Disease influence neural crest population size. In addition, during in vivo development the underlying gut tissues are growing simultaneously as the neural crest cell invasion proceeds. The interactions between proliferation, motility and gut growth dictate whether or not complete colonization is successful. Mathematical modeling provides insights into the conditions required for complete colonization or a Hirschsprungs‐like deficiency. Experimental evidence supports the hypotheses suggested by the modeling.

Neural crest regionalisation for enteric nervous system formation: Implications for Hirschsprung's disease and stem cell therapy

Midbrain, hindbrain and vagal neural crest (NC) produced abundant enteric nervous system (ENS) in co-grafted aneural hindgut and midgut, using chick-quail chorio-allantoic membrane grafts, forming complete myenteric and submucosal plexuses. This ability dropped suddenly in cervical and thoracic NC levels, furnishing an incomplete ENS in one or both plexuses. Typically, one plexus was favoured over the other. This deficiency was not caused by lower initial trunk NC number, yet overloading the initial number decreased the deficiency. No qualitative difference in neuronal and glial differentiation between cranial and trunk levels was observed. All levels formed HuC/D+ve, NOS+ve, ChAT+ve, and TH-ve enteric neurons with SoxE+ve, GFAP+ve, and BFABP+ve glial cells. We mathematically modelled a proliferative difference between NC populations, with a plexus preference hierarchy, in the context of intestinal growth. High proliferation achieved an outcome similar to cranial NC, while low proliferation described the trunk NC outcome of incomplete primary plexus and even more deficient secondary plexus. We conclude that cranial NC, relative to trunk NC, has a positionally-determined proliferation advantage favouring ENS formation. This has important implications for proposed NC stem cell therapy for Hirschsprungs disease, since such cells may need to be optimised for positional identity.

Model-based analysis of the likelihood of gene introgression from genetically modified crops into wild relatives

The proliferation of genetically modified crops has created a need for methods to predict the likelihood of gene introgression into related species in situ. We present a model of a modified crop and an associated unmodified plant population removed spatially from the modified crop but not completely isolated from it, reflecting standard practices for isolation of field trials. We develop models for two kinds of life histories, broadly based on Brassica and Gossypium, taxa that are targets for genetic modification. We find that current prescriptions for field trials are likely to lead to escape of transgenes into wild populations when outcrossing rates are moderate and hybrids are fertile. The results are sensitive to pollen rain within plausible bounds for model parameters, suggesting buffer widths are an important aspect of the design of field trials. When gene introgression requires the spontaneous development of a polyploid, the likelihood of gene introgression is lower but still appreciable in realistic circumstances. Events that are unlikely over periods of a few years become almost certain within scales of a few decades, emphasising the need for gene risk assessments to be set in specified time frames. The models serve to identify the parts of the system that are poorly known and that are important in determining outcomes, providing a focus for future research. There is a need for research on the consequences of changes in fitness due to the transgenes, competitive interactions between related species, and the broader ecological consequences of changes in agricultural practice resulting from the use of genetically modified crops.

Time-dependent batch settling of flocculated suspensions

The equations governing the settling and consolidation of flocculated fully networked suspensions under the influence of gravity, based on the assumption that the network possesses a compressive yield stress Py(oslash;) that is a function of local volume fraction (oslash;) only, are discussed. They are nonlinear partial differential equations with two moving boundaries, one at the top of the bed and the other marking the position of the consolidation region. A novel technique is used to solve these numerically. The time evolution of the volume fraction in the sedimenting column and the two moving boundaries are computed, and their dependence on the physical properties of the system are discussed. Analytic results for the steady state and the small time behavior are given.

Mathematical models of cell colonization of uniformly growing domains

During the development of vertebrate embryos, cell migrations occur on an underlying tissue domain in response to some factor, such as nutrient. Over the time scale of days in which this cell migration occurs, the underlying tissue is itself growing. Consequently cell migration and colonization is strongly affected by the tissue domain growth. Numerical solutions for a mathematical model of chemotactic migration with no domain growth can lead to travelling waves of cells with constant velocity; the addition of domain growth can lead to travelling waves with nonconstant velocity. These observations suggest a mathematical approximation to the full system equations, allowing the method of characteristics to be applied to a simplified chemotactic migration model. The evolution of the leading front of the migrating cell wave is analysed. Linear, exponential and logistic uniform domain growths are considered. Successful colonization of a growing domain depends on the competition between cell migration velocity and the velocity and form of the domain growth, as well as the initial penetration distance of the cells. In some instances the cells will never successfully colonize the growing domain. These models provide an insight into cell migration during embryonic growth, and its dependence upon the form and timing of the domain growth.

A cell migration device that maintains a defined surface with no cellular damage during wound edge generation.

Studying the rate of cell migration provides insight into fundamental cell biology as well as a tool to assess the functionality of synthetic surfaces and soluble environments used in tissue engineering. The traditional tools used to study cell migration include the fence and wound healing assays. In this paper we describe the development of a microchannel based device for the study of cell migration on defined surfaces. We demonstrate that this device provides a superior tool, relative to the previously mentioned assays, for assessing the propagation rate of cell wave fronts. The significant advantage provided by this technology is the ability to maintain a virgin surface prior to the commencement of the cell migration assay. Here, the device is used to assess rates of mouse fibroblasts (NIH 3T3) and human osteosarcoma (SaOS2) cell migration on surfaces functionalized with various extracellular matrix proteins as a demonstration that confining cell migration within a microchannel produces consistent and robust data. The device design enables rapid and simplistic assessment of multiple repeats on a single chip, where surfaces have not been previously exposed to cells or cellular secretions.

Filtration at large pressures for strongly flocculated suspensions

Filtration using large pressures is an effective method for removing liquids from a flocculated suspension and creating a high volume fraction filtercake. Recent experimental work exhibits phenomena that are unexplained by previous calculations with nonlinear models. These models are modified and now predict the region of clear liquid and the high concentration of the filtercake observed in filtration at large pressure. The governing equations are based on the assumption that, at sufficiently high volume fractions, a network forms through the aggregation of flocs and possesses a compressive yield stress Py(φ) that depends only on the local volume fraction φ.

On the role of differential adhesion in gangliogenesis in the enteric nervous system

A defining characteristic of the normal development of the enteric nervous system (ENS) is the existence of mesoscale patterned entities called ganglia. Ganglia are clusters of neurons with associated enteric neural crest (ENC) cells, which form in the simultaneously growing gut wall. At first the precursor ENC cells proliferate and gradually differentiate to produce the enteric neurons; these neurons form clusters with ENC scattered around and later lying on the periphery of neuronal clusters. By immunolabelling neural cell-cell adhesion molecules, we infer that the adhesive capacity of neurons is greater than that of ENC cells. Using a discrete mathematical model, we test the hypothesis that local rules governing differential adhesion of neuronal agents and ENC agents will produce clusters which emulate ganglia. The clusters are relatively stable, relatively uniform and small in size, of fairly uniform spacing, with a balance between the number of neuronal and ENC agents. These features are attained in both fixed and growing domains, reproducing respectively organotypic in vitro and in vivo observations. Various threshold criteria governing ENC agent proliferation and differentiation and neuronal agent inhibition of differentiation are important for sustaining these characteristics. This investigation suggests possible explanations for observations in normal and abnormal ENS development.