Using two dimensional sectional distributions to infer three dimensional volumetric distributions - Validation using tomography

The critical process parameter for mineral separation is the degree of mineral liberation achieved by comminution. The degree of liberation provides an upper limit of efficiency for any physical separation process. The standard approach to measuring mineral liberation uses mineralogical analysis based two-dimensional sections of particles which may be acquired using a scanning electron microscope and back-scatter electron analysis or from an analysis of an image acquired using an optical microscope. Over the last 100 years, mathematical techniques have been developed to use this two dimensional information to infer three-dimensional information about the particles. For mineral processing, a particle that contains more than one mineral (a composite particle) may appear to be liberated (contain only one mineral) when analysed using only its revealed particle section. The mathematical techniques used to interpret three-dimensional information belong, to a branch of mathematics called stereology. However methods to obtain the full mineral liberation distribution of particles from particle sections are relatively new. To verify these adjustment methods, we require an experimental method which can accurately measure both sectional and three dimensional properties. Micro Cone Beam Tomography provides such a method for suitable particles and hence, provides a way to validate methods used to convert two-dimensional measurements to three dimensional estimates. For this study ore particles from a well-characterised sample were subjected to conventional mineralogical analysis (using particle sections) to estimate three-dimensional properties of the particles. A subset of these particles was analysed using a micro-cone beam tomograph. This paper presents a comparison of the three-dimensional properties predicted from measured two-dimensional sections with the measured three-dimensional properties.

Prediction of minimum spouting velocity in two-dimensional flat bottom spouted beds

Spouted beds have been used in industry for operations such as drying, catalytic reactions, and granulation. Conventional cylindrical spouted beds suffer from the disadvantage of scaleup. Two-dimensional beds have been proposed by other authors as a solution for this problem. Minimum spouting velocity has been studied for such two-dimensional beds. A force balance model has been developed to predict the minimum spouting velocity and the maximum pressure drop. Effect of porosity on minimum spouting velocity and maximum pressure drop has been studied using the model. The predictions are in good agreement with the experiments as well as with the experimental results of other investigators.

Erratum: Two-Dimensional Failure Modeling with Minimal Repair which appeared in this journal of April 2004, Volume 51:3 on pages 345–362

In this Erratum, we point out the reason for an error in the derivation of a result in our earlier paper, “Two-Dimensional Failure Modeling with Minimal Repair” [1], which appeared in the April 2004 issue of this journal, 51:3, on pages 345–362, and give the correct derivation.

Drying process of microcrystalline cellulose studied by attenuated total reflection IR spectroscopy with two-dimensional correlation spectroscopy and principal component analysis

Molecular interactions between microcrystalline cellulose (MCC) and water were investigated by attenuated total reflection infrared (ATR/IR) spectroscopy. Moisture-content-dependent IR spectra during a drying process of wet MCC were measured. In order to distinguish overlapping O–H stretching bands arising from both cellulose and water, principal component analysis (PCA) and, generalized two-dimensional correlation spectroscopy (2DCOS) and second derivative analysis were applied to the obtained spectra. Four typical drying stages were clearly separated by PCA, and spectral variations in each stage were analyzed by 2DCOS. In the drying time range of 0–41 min, a decrease in the broad band around 3390 cm−1 was observed, indicating that bulk water was evaporated. In the drying time range of 49–195 min, decreases in the bands at 3412, 3344 and 3286 cm−1 assigned to the O6H6cdots, three dots, centeredO3′ interchain hydrogen bonds (H-bonds), the O3H3cdots, three dots, centeredO5 intrachain H-bonds and the H-bonds in Iβ phase in MCC, respectively, were observed. The result of the second derivative analysis suggests that water molecules mainly interact with the O6H6cdots, three dots, centeredO3′ interchain H-bonds. Thus, the H-bonding network in MCC is stabilized by H-bonds between OH groups constructing O6H6cdots, three dots, centeredO3′ interchain H-bonds and water, and the removal of the water molecules induces changes in the H-bonding network in MCC.