Calibrated X-ray micro-tomography for mineral ore quantification

Scanning Electron Microscopy (SEM) based assessments are the most widely used and trusted imaging technique for mineral ore quantification. X-ray micro tomography (XMT) is a more recent addition to the mineralogy toolbox, but with the potential to extend the measurement capabilities into the three dimensional (3D) assessment of properties such as mineral liberation, grain size and textural characteristics. In addition, unlike SEM based assessments which require the samples to be sectioned, XMT is non-invasive and non-destructive. The disadvantage of XMT, is that the mineralogy must be inferred from the X-ray attenuation measurements, which can make it hard to distinguish from one another, whereas SEM when coupled with Energy-Dispersive X-ray Spectroscopy (EDX) provides elemental compositions and thus a more direct method for distinguishing different minerals. A new methodology that combines both methods at the mineral grain level is presented. The rock particles used to test the method were initially imaged in 3D using XMT followed by sectioning and the 2D imaging of the slices using SEM-EDX. An algorithm was developed that allowed the mineral grains in the 2D slice to be matched with their 3D equivalents in the XMT based images. As the mineralogy of the grains from the SEM images can be matched to a range of X-ray attenuations, this allows minerals which have similar attenuations to one another to be distinguished, with the level of uncertainty in the classification quantified. In addition, the methodology allowed for the estimation of the level of uncertainty in the quantification of grain size by XMT, the assessment of stereological effects in SEM 2D images and ultimately obtaining a simplified 3D mineral map from low energy XMT images. Copper sulphide ore fragments, with chalcopyrite and pyrite as the main sulphide minerals, were used to demonstrate the effectiveness of this procedure

Characterisation, modification and mathematical modelling of sudsing

A programme of research is outlined which considers the foaming performance and foam behaviour of surfactant systems commonly encountered in hand-wash laundry detergent applications. An experimental study of the physical chemistry of foam generation indicates that precipitation of a typical anionic surfactant with calcium forms mesophase particles and causes a marked reduction in the rate of transport of surfactant to air–water surfaces and a concomitant reduction in foaming. Oily soil antifoam effects are however insensitive to the presence of calcium, being equally effective regardless of pH and calcium content. They may be reproduced by a simple particle–oil mixture of a saturated and an unsaturated triglyceride (e.g. tristearin and triolein respectively). A detailed foam rheometry study is performed using foam flowing through a constriction. Bubble shapes are used to deduce the normal and shear stresses across the foam flow field. Broad agreement between the experimental stress field and that obtained from quasistatic simulations is demonstrated. As foam flow-rate increases, a different model, which takes explicit account of viscous dissipative forces within the foam flow field is required. The dissipative foam flow model predicts differential shrinkage and stretch rates of foam films. Coupled to a model for surfactant transport, this shows the extent to which surfactant concentration accumulates in shrinking films and is depleted in stretching films. In addition to film stretching, it is also important to know about film bursting or failure rates. Here failure rates are estimated using capillary suction pressures exerted on the films by Plateau border channels around film edges. The failure rates can then be employed to predict the evolution of bubble size at various spatial locations in a foam: reasonable agreement with experimental bubble size distributions is obtained

Multi-scale quantification of leaching performance using X-ray tomography

The performance of heap leaching is dictated by a large number of processes acting at a wide range of length scales. One important scale is that of the individual particles, where the interaction between the rate kinetics at the surfaces of the individual mineral grains and the mass transport through the particle combine to give the overall apparent particle scale kinetics. It has been recognised for a long time that variability in the mineralogy, size and spatial distribution of the mineral grains within the particle are likely to have a large effect on the leach performance and its variability and thus, ultimately, the performance of the heap. In this paper a new method for quantifying this behaviour and its variability at scales from the particle through to the grain and down to the surface kinetics is presented. This method is based on the use of a series of XMT (also called micro-CT) images of a column taken at regular intervals over 168 days of leaching. The key development in the analysis of this data is an algorithm that has allowed every single one of the hundreds of thousands of mineral grains within the column to be individually tracked across all the time points as they undergo dissolution. This has allowed the dependency of the mineral grain leach rate on its size and position in the particle to be decoupled from one another. It also meant that the variability in the surface kinetics of the grains could be assessed, with mineralogical variability being the key source of this variability. We demonstrate that understanding and quantifying this underlying kinetic variability is important as it has a major impact on the time evolution of the average kinetics of the leaching

Iterative approach to weir drainage

Understanding liquid drainage in foam is an important step in determining the performance of a froth flotation system. The geometry of the flotation vessel has a major impact on drainage and thereby performance. In particular it is known that in a vessel geometry with sloping walls, a thin boundary layer of wet foam can appear near the wall, containing a high speed liquid jet that is sliding downwards. Although a zeroth order theory exists describing this liquid jet (Eur. Phys. J. E 8 (2002) 517), it has a number of unsatisfactory features which need to be rectified. The jet structure predicted does not match correctly onto the known state of the foam far from the wall. Also important physical mechanisms influencing the speed and liquid content of the jet are neglected. These problems can be corrected by iteratively improving the zeroth order solutions. The iterative approach indicates that bulk foam motion is an important effect influencing the jet boundary layer, and indeed that the foam is wetter at the wall than previously predicted

Quasi-one-dimensional and two-dimensional drainage of foam

Foam drainage is considered in a froth flotation tank containing a flowing froth. A simplified theory (the quasi-one-dimensional theory) exists in which horizontal variations across the tank of the foam’s typical Plateau border area can be neglected. Moreover, drainage is shown to be gravity dominated over most of the froth. For weakly decelerated foam flows, the gravity dominated drainage equation admits constant Plateau border area solutions, both horizontally and vertically. For strongly decelerated flows there are two solution branches: one with constant Plateau border area, and another branch with kinked solutions. The kinked branch is the relevant one in the case of a foam with non-uniform bubble sizes. The gravity dominated solutions are required to match onto boundary layer solutions at the base of the foam. Capillary suction becomes important in this layer, and the solutions have a well-known structure: that of a soliton on an already wetted foam. The simple quasi-one-dimensional solutions are shown to have remarkable agreement with full two-dimensional drainage simulations

The growth, drainage and breakdown of foams

This paper examines the behaviour of growing and collapsing foams. In particular, it focuses on the drainage of the liquid, and thus the evolution of the liquid content, within the growing or collapsing foam. By assuming that the films fail when they are subjected to a pressure above a certain critical pressure, the collapse of the foam is modelled. The model predicts that the growing foam behaviour can be divided into two regimes: at low gas rates, the foams will asymptote towards an equilibrium height, while above a certain critical gas rate, the foams will continue to grow indefinitely. This behaviour was found experimentally as well. At the higher gas rates, there is a change in the slope of the foam height versus time plot, though with the exception of a transition region, this relationship remains a linear relationship one. The difference between these slopes can be used to estimate the pressure exerted on the films at the top surface of the foam. Since these bubbles are bursting, this is the critical pressure required to cause film failure within the foam. When compared to the stability of films in single film experiments, those in the foam, not unexpectedly, demonstrate lower stability. This is due to vibrations and other disturbances that are present within flowing foams

Quasi-one-dimensional foam drainage

Foam drainage is considered in a froth flotation cell. Air flow through the foam is described by a simple two-dimensional deceleration flow, modelling the foam spilling over a weir. Foam microstructure is given in terms of the number of channels (Plateau borders) per unit area, which scales as the inverse square of bubble size. The Plateau border number density decreases with height in the foam, and also decreases horizontally as the weir is approached. Foam drainage equations, applicable in the dry foam limit, are described. These can be used to determine the average cross-sectional area of a Plateau border, denoted A, as a function of position in the foam. Quasi-one-dimensional solutions are available in which A only varies vertically, in spite of the two-dimensional nature of the air flow and Plateau border number density fields. For such situations the liquid drainage relative to the air flow is purely vertical. The parametric behaviour of the system is investigated with respect to a number of dimensionless parameters: K (the strength of capillary suction relative to gravity), α (the deceleration of the air flow), and n and h (respectively, the horizontal and vertical variations of the Plateau border number density). The parameter K is small, implying the existence of boundary layer solutions: capillary suction is negligible except in thin layers near the bottom boundary. The boundary layer thickness (when converted back to dimensional variables) is independent of the height of the foam. The deceleration parameter α affects the Plateau border area on the top boundary: weaker decelerations give larger Plateau border areas at the surface. For weak decelerations, there is rapid convergence of the boundary layer solutions at the bottom onto ones with negligible capillary suction higher up. For strong decelerations, two branches of solutions for A are possible in the K = 0 limit: one is smooth, and the other has a distinct kink. The full system, with small but non-zero capillary suction, lies relatively close to the kinked solution branch, but convergence from the lower boundary layer onto this branch is distinctly slow. Variations in the Plateau border number density (non-zero n and h) increase individual Plateau border areas relative to the case of uniformly sized bubbles. For strong decelerations and negligible capillarity, solutions closely follow the kinked solution branch if bubble sizes are only slightly non-uniform. As the extent of non-uniformity increases, the Plateau border area reaches a maximum corresponding to no net upward velocity of foam liquid. In the case of vertical variation of number density, liquid content profiles and Plateau border area profiles cease to be simply proportional to one another. Plateau border areas match at the top of the foam independent of h, implying a considerable difference in liquid content for foams which exhibit different number density profiles