A comparison of the gas-blast and centrifugal-accelerator erosion testers: The influence of particle dynamics

The gas-blast and centrifugal-accelerator testers are the two most commonly used erosion testers. An experimental and analytical study was made of the effect of particle characteristics (size, shape and concentration) on particle dynamics in each of these testers. Analysis showed that in the gas-blast tester both particle velocity and the dispersion angle of the particle jet were relatively sensitive to the particle characteristics. Particle characteristics, within the ranges studied, had little influence in the centrifugal accelerator tester. Consequently, during an erosion test, the range of particle velocities and dispersion angles in the gas-blast tester ismuch wider than in the centrifugal-accelerator tester. It was concluded that the centrifugal-accelerator tester gave closer control of the important erosion test parameters and therefore more consistent erosion test measurements. However, one drawback of the centrifugal-accelerator tester is the need to account for erosion effects associated with the impact of rotating particles, an inherent feature of this tester.

Utilising computational fluid dynamics (CFD) for the modelling of granular material in large-scale engineering processes

In this paper, the framework is described for the modelling of granular material by employing Computational Fluid Dynamics (CFD). This is achieved through the use and implementation in the continuum theory of constitutive relations, which are derived in a granular dynamics framework and parametrise particle interactions that occur at the micro-scale level. The simulation of a process often met in bulk solids handling industrial plants involving granular matter, (i.e. filling of a flat-bottomed bin with a binary material mixture through pneumatic conveying-emptying of the bin in core flow mode-pneumatic conveying of the material coming out of a the bin) is presented. The results of the presented simulation demonstrate the capability of the numerical model to represent successfully key granular processes (i.e. segregation/degradation), the prediction of which is of great importance in the process engineering industry.

Modelling meso-scale diffusion processes in stochastic fluid bio-membranes

The space–time dynamics of rigid inhomogeneities (inclusions) free to move in a randomly fluctuating fluid bio-membrane is derived and numerically simulated as a function of the membrane shape changes. Both vertically placed (embedded) inclusions and horizontally placed (surface) inclusions are considered. The energetics of the membrane, as a two-dimensional (2D) meso-scale continuum sheet, is described by the Canham–Helfrich Hamiltonian, with the membrane height function treated as a stochastic process. The diffusion parameter of this process acts as the link coupling the membrane shape fluctuations to the kinematics of the inclusions. The latter is described via Ito stochastic differential equation. In addition to stochastic forces, the inclusions also experience membrane-induced deterministic forces. Our aim is to simulate the diffusion-driven aggregation of inclusions and show how the external inclusions arrive at the sites of the embedded inclusions. The model has potential use in such emerging fields as designing a targeted drug delivery system.

Multigrid for American option pricing with stochastic volatility

The paper describes an implicit finite difference approach to the pricing of American options on assets with a stochastic volatility. A multigrid procedure is described for the fast iterative solution of the discrete linear complementarity problems that result. The accuracy and performance of this approach is improved considerably by a strike-price related analytic transformation of asset prices and adaptive time-stepping.

An improved result of exponential stability of stochastic semilinear evolution equations

Sufficient conditions for the exponential stability of a class ofnonlinear, non-autonomous stochastic differential equations in infinitedimensions are studied. The analysis consists of introducing a suitableapproximating solution systems and using a limiting argument to pass onstability of strong solutions to mild ones. As a consequence, the classicalcriteriaof stability in A. Ichikawa [8] are improved and extended to cover a class ofnon-autonomous stochastic evolution equations.Two examples are investigated to illustrate our theory.

Moment decay rates of solutions of stochastic differential equations

The objective of this paper is to investigate the p-ίh moment asymptotic stability decay rates for certain finite-dimensional Itό stochastic differential equations. Motivated by some practical examples, the point of our analysis is a special consideration of general decay speeds, which contain as a special case the usual exponential or polynomial type one, to meet various situations. Sufficient conditions for stochastic differential equations (with variable delays or not) are obtained to ensure their asymptotic properties. Several examples are studied to illustrate our theory.

Mathematical modelling of the behaviour of granular material in a computational fluid dynamics framework using micro-mechanical models

In this paper, a Computational Fluid Dynamics framework is presented for the modelling of key processes which involve granular material (i.e. segregation, degradation, caking). Appropriate physical models and sophisticated algorithms have been developed for the correct representation of the different material components in a granular mixture. The various processes, which arise from the micromechanical properties of the different mixture species can be obtained and parametrised in a DEM / experimental framework, thus enabling the continuum theory to correctly account for the micromechanical properties of a granular system. The present study establishes the link between the micromechanics and continuum theory and demonstrates the model capabilities in simulations of processes which are of great importance to the process engineering industry and involve granular materials in complex geometries.

Effect of fluid dynamics and device mechanism on biofluid behaviour in microchannel systems: modelling biofluids in a microchannel biochip separator

Biofluid behaviour in microchannel systems is investigated in this paper through the modelling of a microfluidic biochip developed for the separation of blood plasma. Based on particular assumptions, the effects of some mechanical features of the microchannels on behaviour of the biofluid are explored. These include microchannel, constriction, bending channel, bifurcation as well as channel length ratio between the main and side channels. The key characteristics and effects of the microfluidic dynamics are discussed in terms of separation efficiency of the red blood cells with respect to the rest of the medium. The effects include the Fahraeus and Fahraeus-Lindqvist effects, the Zweifach-Fung bifurcation law, the cell-free layer phenomenon. The characteristics of the microfluid dynamics include the properties of the laminar flow as well as particle lateral or spinning trajectories. In this paper the fluid is modelled as a single-phase flow assuming either Newtonian or Non-Newtonian behaviours to investigate the effect of the viscosity on flow and separation efficiency. It is found that, for a flow rate controlled Newtonian flow system, viscosity and outlet pressure have little effect on velocity distribution. When the fluid is assumed to be Non-Newtonian more fluid is separated than observed in the Newtonian case, leading to reduction of the flow rate ratio between the main and side channels as well as the system pressure as a whole.