A mathematical model of concentrate solids content for the wet drum magnetic separator

Low concentrate density from wet drum magnetic separators in dense medium circuits can cause operating difficulties due to inability to obtain the required circulating medium density and, indirectly, high medium solids losses. The literature is almost silent on the processes controlling concentrate density. However, the common name for the region through which concentrate is discharged-the squeeze pan gap-implies that some extrusion process is thought to be at work. There is no model of magnetics recovery in a wet drum magnetic separator, which includes as inputs all significant machine and operating variables. A series of trials, in both factorial experiments and in single variable experiments, was done using a purpose built rig which featured a small industrial scale (700 mm lip length, 900 turn diameter) wet drum magnetic separator. A substantial data set of 191 trials was generated in this work. The results of the factorial experiments were used to identify the variables having a significant effect on magnetics recovery. It is proposed, based both on the experimental observations of the present work and on observations reported in the literature, that the process controlling magnetic separator concentrate density is one of drainage. Such a process should be able to be defined by an initial moisture, a drainage rate and a drainage time, the latter being defined by the volumetric flowrate and the volume within the drainage zone. The magnetics can be characterised by an experimentally derived ultimate drainage moisture. A model based on these concepts and containing adjustable parameters was developed. This model was then fitted to a randomly chosen 80% of the data, and validated by application to the remaining 20%. The model is shown to be a good fit to data over concentrate solids content values from 40% solids to 80% solids and for both magnetite and ferrosilicon feeds. (C) 2003 Elsevier Science B.V. All rights reserved.

A mathematical model of recovery of dense medium magnetics in the wet drum magnetic separator

Loss of magnetic medium solids from dense medium circuits is a substantial contributor to operating cost. Much of this loss is by way of wet drum magnetic separator effluent. A model of the separator would be useful for process design, optimisation and control. A review of the literature established that although various rules of thumb exist, largely based on empirical or anecdotal evidence, there is no model of magnetics recovery in a wet drum magnetic separator which includes as inputs all significant machine and operating variables. A series of trials, in both factorial experiments and in single variable experiments, was therefore carried out using a purpose built rig which featured a small industrial scale (700 mm lip length, 900 mm diameter) wet drum magnetic separator. A substantial data set of 191 trials was generated in the work. The results of the factorial experiments were used to identify the variables having a significant effect on magnetics recovery. Observations carried out as an adjunct to this work, as well as magnetic theory, suggests that the capture of magnetic particles in the wet drum magnetic separator is by a flocculation process. Such a process should be defined by a flocculation rate and a flocculation time; the latter being defined by the volumetric flowrate and the volume within the separation zone. A model based on this concept and containing adjustable parameters was developed. This model was then fitted to a randomly chosen 80% of the data, and validated by application to the remaining 20%. The model is shown to provide a satisfactory fit to the data over three orders of magnitude of magnetics loss. (C) 2003 Elsevier Science BY. All rights reserved.

Comparison of DEM and experiment for a scale model SAG mill

Predictions of flow patterns in a 600-mm scale model SAG mill made using four classes of discrete element method (DEM) models are compared to experimental photographs. The accuracy of the various models is assessed using quantitative data on shoulder, toe and vortex center positions taken from ensembles of both experimental and simulation results. These detailed comparisons reveal the strengths and weaknesses of the various models for simulating mills and allow the effect of different modelling assumptions to be quantitatively evaluated. In particular, very close agreement is demonstrated between the full 3D model (including the end wall effects) and the experiments. It is also demonstrated that the traditional two-dimensional circular particle DEM model under-predicts the shoulder, toe and vortex center positions and the power draw by around 10 degrees. The effect of particle shape and the dimensionality of the model are also assessed, with particle shape predominantly affecting the shoulder position while the dimensionality of the model affects mainly the toe position. Crown Copyright (C) 2003 Published by Elsevier Science B.V. All rights reserved.

An energy-based model for swing hammer mills

An energy-based swing hammer mill model has been developed for coke oven feed preparation. it comprises a mechanistic power model to determine the dynamic internal recirculation and a perfect mixing mill model with a dual-classification function to mimic the operations of crusher and screen. The model parameters were calibrated using a pilot-scale swing hammer mill at various operating conditions. The effects of the underscreen configurations and the feed sizes on hammer mill operations were demonstrated through the fitted model parameters. Relationships between the model parameters and the machine configurations were established. The model was validated using the independent experimental data of single lithotype coal tests with the same BJD pilot-scale hammer mill and full operation audit data of an industrial hammer mill. The outcome of the energy-based swing hammer mill model is the capability to simulate the impact of changing blends of coal or mill configurations and operating conditions on product size distribution. Alternatively, the model can be used to select the machine settings required to achieve a desired product. (C) 2003 Elsevier Science B.V. All rights reserved.

A unified model of flames as gasdynamic discontinuities

Viewed on a hydrodynamic scale, flames in experiments are often thin so that they may be described as gasdynamic discontinuities separating the dense cold fresh mixture from the light hot burned products. The original model of a flame as a gasdynamic discontinuity was due to Darrieus and to Landau. In addition to the fluid dynamical equations, the model consists of a flame speed relation describing the evolution of the discontinuity surface, and jump conditions across the surface which relate the fluid variables on the two sides of the surface. The Darrieus-Landau model predicts, in contrast to observations, that a uniformly propagating planar flame is absolutely unstable and that the strength of the instability grows with increasing perturbation wavenumber so that there is no high-wavenumber cutoff of the instability. The model was modified by Markstein to exhibit a high-wavenumber cutoff if a phenomenological constant in the model has an appropriate sign. Both models are postulated, rather than derived from first principles, and both ignore the flame structure, which depends on chemical kinetics and transport processes within the flame. At present, there are two models which have been derived, rather than postulated, and which are valid in two non-overlapping regions of parameter space. Sivashinsky derived a generalization of the Darrieus-Landau model which is valid for Lewis numbers (ratio of thermal diffusivity to mass diffusivity of the deficient reaction component) bounded away from unity. Matalon & Matkowsky derived a model valid for Lewis numbers close to unity. Each model has its own advantages and disadvantages. Under appropriate conditions the Matalon-Matkowsky model exhibits a high-wavenumber cutoff of the Darrieus-Landau instability. However, since the Lewis numbers considered lie too close to unity, the Matalon-Matkowsky model does not capture the pulsating instability. The Sivashinsky model does capture the pulsating instability, but does not exhibit its high-wavenumber cutoff. In this paper, we derive a model consisting of a new flame speed relation and new jump conditions, which is valid for arbitrary Lewis numbers. It captures the pulsating instability and exhibits the high-wavenumber cutoff of all instabilities. The flame speed relation includes the effect of short wavelengths, not previously considered, which leads to stabilizing transverse surface diffusion terms.

Phase equilibria and surface tension of pure fluids using a molecular layer structure theory (MLST) model

This paper presents a new model based on thermodynamic and molecular interaction between molecules to describe the vapour-liquid phase equilibria and surface tension of pure component. The model assumes that the bulk fluid can be characterised as set of parallel layers. Because of this molecular structure, we coin the model as the molecular layer structure theory (MLST). Each layer has two energetic components. One is the interaction energy of one molecule of that layer with all surrounding layers. The other component is the intra-layer Helmholtz free energy, which accounts for the internal energy and the entropy of that layer. The equilibrium between two separating phases is derived from the minimum of the grand potential, and the surface tension is calculated as the excess of the Helmholtz energy of the system. We test this model with a number of components, argon, krypton, ethane, n-butane, iso-butane, ethylene and sulphur hexafluoride, and the results are very satisfactory. (C) 2002 Elsevier Science B.V. All rights reserved.

A kinetic study of the thermally initiated free radical reactions of styrene with octanedithiol as a model for the reactions of multifunctional thiols with divinylbenzene

The kinetics of chain reactions of octanedithiol with styrene, thermally initiated with TX29B50 (a 50:50 wt% solution of TX29 diperoxy initiator in a phthalate plasticizer), have been studied over a range of initiator concentrations, a range of mixture formulations and a range of temperatures. This system has been investigated as a model system for the reactions of polyfunctional thiols with divinyl benzene. The reactions have been shown to follow first-order kinetics for both the thiol and the ene species and to be characterized by a dependence on the initiator concentration to the power of one half. The kinetic rate parameters have been shown to adhere to Arrhenius behaviour. A kinetic model for the chain reactions for this system has been proposed. (C) 2003 Society of Chemical Industry.

A high-throughput screening method for general cytotoxicity part I Chemical toxicity

Foi desenvolvido um método destinado a fazer a triagem rápida e o escalonamento da toxicidade geral exercida por xenobióticos tendo como modelo o Saccharomyces cerevisiae. Para padronizar as condições de experimentação foi estabelecida a relação entre a absorvência a 525 nm e o número de células em suspensão por mililitro de meio de cultura e calculadas uma curva padrão e respectiva equação definidora (Y=6,8219E-08X + 0,0327) Culturas de Saccharomyces cerevisiae em meio completo para leveduras (YPD - 1% de glucose 2%, de peptona 0,5% e extracto de levedura 1%) foram expostas a diferentes concentrações de nicotina e a inibição do crescimento avaliada.

Re-entrant phase behaviour of network fluids: A patchy particle model with temperature-dependent valence

We study a model consisting of particles with dissimilar bonding sites ("patches"), which exhibits self-assembly into chains connected by Y-junctions, and investigate its phase behaviour by both simulations and theory. We show that, as the energy cost epsilon(j) of forming Y-junctions increases, the extent of the liquid-vapour coexistence region at lower temperatures and densities is reduced. The phase diagram thus acquires a characteristic "pinched" shape in which the liquid branch density decreases as the temperature is lowered. To our knowledge, this is the first model in which the predicted topological phase transition between a fluid composed of short chains and a fluid rich in Y-junctions is actually observed. Above a certain threshold for epsilon(j), condensation ceases to exist because the entropy gain of forming Y-junctions can no longer offset their energy cost. We also show that the properties of these phase diagrams can be understood in terms of a temperature-dependent effective valence of the patchy particles. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3605703]

Three-dimensional patchy lattice model for empty fluids

The phase diagram of a simple model with two patches of type A and ten patches of type B (2A10B) on the face centred cubic lattice has been calculated by simulations and theory. Assuming that there is no interaction between the B patches the behavior of the system can be described in terms of the ratio of the AB and AA interactions, r. Our results show that, similarly to what happens for related off-lattice and two-dimensional lattice models, the liquid-vapor phase equilibria exhibit reentrant behavior for some values of the interaction parameters. However, for the model studied here the liquid-vapor phase equilibria occur for values of r lower than 1/3, a threshold value which was previously thought to be universal for 2AnB models. In addition, the theory predicts that below r = 1/3 (and above a new condensation threshold which is < 1/3) the reentrant liquid-vapor equilibria are so extreme that it exhibits a closed loop with a lower critical point, a very unusual behavior in single-component systems. An order-disorder transition is also observed at higher densities than the liquid-vapor equilibria, which shows that the liquid-vapor reentrancy occurs in an equilibrium region of the phase diagram. These findings may have implications in the understanding of the condensation of dipolar hard spheres given the analogy between that system and the 2AnB models considered here. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4771591]

Synechocystis ferredoxin/ferredoxin-NADP+-reductase/NADP+ complex: Structural model obtained by NMR-restrained docking

FEBS Letters 579 (2005) 4585–4590

Three-dimensial patchy lattice model: Ring formation and phase separation

We investigate the structural and thermodynamic properties of a model of particles with 2 patches of type A and 10 patches of type B. Particles are placed on the sites of a face centered cubic lattice with the patches oriented along the nearest neighbor directions. The competition between the self- assembly of chains, rings, and networks on the phase diagram is investigated by carrying out a systematic investigation of this class of models, using an extension ofWertheim's theory for associating fluids and Monte Carlo numerical simulations. We varied the ratio r epsilon(AB)/epsilon(AA) of the interaction between patches A and B, epsilon(AB), and between A patches, epsilon(AA) (epsilon(BB) is set to theta) as well as the relative position of the A patches, i.e., the angle. between the (lattice) directions of the A patches. We found that both r and theta (60 degrees, 90 degrees, or 120 degrees) have a profound effect on the phase diagram. In the empty fluid regime (r < 1/2) the phase diagram is reentrant with a closed miscibility loop. The region around the lower critical point exhibits unusual structural and thermodynamic behavior determined by the presence of relatively short rings. The agreement between the results of theory and simulation is excellent for theta = 120 degrees but deteriorates as. decreases, revealing the need for new theoretical approaches to describe the structure and thermodynamics of systems dominated by small rings. (C) 2014 AIP Publishing LLC.

Three-Dimensional patchy lattice model for empty fluids

The phase diagram of a simple model with two patches of type A and ten patches of type B (2A10B) on the face centred cubic lattice has been calculated by simulations and theory. Assuming that there is no interaction between the B patches the behavior of the system can be described in terms of the ratio of the AB and AA interactions, r. Our results show that, similarly to what happens for related off-lattice and two-dimensional lattice models, the liquid-vapor phase equilibria exhibit reentrant behavior for some values of the interaction parameters. However, for the model studied here the liquid-vapor phase equilibria occur for values of r lower than 1/3, a threshold value which was previously thought to be universal for 2AnB models. In addition, the theory predicts that below r = 1/3 (and above a new condensation threshold which is < 1/3) the reentrant liquid-vapor equilibria are so extreme that it exhibits a closed loop with a lower critical point, a very unusual behavior in single-component systems. An order-disorder transition is also observed at higher densities than the liquid-vapor equilibria, which shows that the liquid-vapor reentrancy occurs in an equilibrium region of the phase diagram. These findings may have implications in the understanding of the condensation of dipolar hard spheres given the analogy between that system and the 2AnB models considered here.

The nature of the ordered phase of the confined self-assembled rigid Rod model

We investigate the nature of the ordered phase and the orientational correlations between adjacent layers of the confined three-dimensional self-assembled rigid rod model, on the cubic lattice. We find that the ordered phase at finite temperatures becomes uniaxial in the thermodynamic limit, by contrast to the ground state (partial) order where the orientation of the uncorrelated layers is perpendicular to one of the three lattice directions. The increase of the orientational correlation between layers as the number of layers increases suggests that the unconfined model may also exhibit uniaxial ordering at finite temperatures.