The Equilibrium Flux Method for the calculation of flows with non-equilbrium chemical reactions

The Equilibrium Flux Method [1] is a kinetic theory based finite volume method for calculating the flow of a compressible ideal gas. It is shown here that, in effect, the method solves the Euler equations with added pseudo-dissipative terms and that it is a natural upwinding scheme. The method can be easily modified so that the flow of a chemically reacting gas mixture can be calculated. Results from the method for a one-dimensional non-equilibrium reacting flow are shown to agree well with a conventional continuum solution. Results are also presented for the calculation of a plane two-dimensional flow, at hypersonic speed, of a dissociating gas around a blunt-nosed body.

A wavelet-based adaptive technique for adsorption problems involving steep gradients

A general, fast wavelet-based adaptive collocation method is formulated for heat and mass transfer problems involving a steep moving profile of the dependent variable. The technique of grid adaptation is based on sparse point representation (SPR). The method is applied and tested for the case of a gas–solid non-catalytic reaction in a porous solid at high Thiele modulus. Accurate and convergent steep profiles are obtained for Thiele modulus as large as 100 for the case of slab and found to match the analytical solution.

Computationally efficient solution techniques for adsorption problems involving steep gradients in bidisperse particles

A piecewise uniform fitted mesh method turns out to be sufficient for the solution of a surprisingly wide variety of singularly perturbed problems involving steep gradients. The technique is applied to a model of adsorption in bidisperse solids for which two fitted mesh techniques, a fitted-mesh finite difference method (FMFDM) and fitted mesh collocation method (FMCM) are presented. A combination (FMCMD) of FMCM and the DASSL integration package is found to be most effective in solving the problems. Numerical solutions (FMFDM and FMCMD) were found to match the analytical solution when the adsorption isotherm is linear, even under conditions involving steep gradients for which global collocation fails. In particular, FMCMD is highly efficient for macropore diffusion control or micropore diffusion control. These techniques are simple and there is no limit on the range of the parameters. The techniques can be applied to a variety of adsorption and desorption problems in bidisperse solids with non-linear isotherm and for arbitrary particle geometry.

A modified discrete random pore model allowing for different initial surface reactivity

We investigate here a modification of the discrete random pore model [Bhatia SK, Vartak BJ, Carbon 1996;34:1383], by including an additional rate constant which takes into account the different reactivity of the initial pore surface having attached functional groups and hydrogens, relative to the subsequently exposed surface. It is observed that the relative initial reactivity has a significant effect on the conversion and structural evolution, underscoring the importance of initial surface chemistry. The model is tested against experimental data on chemically controlled char oxidation and steam gasification at various temperatures. It is seen that the variations of the reaction rate and surface area with conversion are better represented by the present approach than earlier random pore models. The results clearly indicate the improvement of model predictions in the low conversion region, where the effect of the initially attached functional groups and hydrogens is more significant, particularly for char oxidation. It is also seen that, for the data examined, the initial surface chemistry is less important for steam gasification as compared to the oxidation reaction. Further development of the approach must also incorporate the dynamics of surface complexation, which is not considered here.

Adsorption in mesopores: A molecular-continuum model with application to MCM-41

The classical model of surface layering followed by capillary condensation during adsorption in mesopores, is modified here by consideration of the adsorbate solid interaction potential. The new theory accurately predicts the capillary coexistence curve as well as pore criticality, matching that predicted by density functional theory. The model also satisfactorily predicts the isotherm for nitrogen adsorption at 77.4 K on MCM-41 material of various pore sizes, synthesized and characterized in our laboratory, including the multilayer region, using only data on the variation of condensation pressures with pore diameter. The results indicate a minimum mesopore diameter for the surface layering model to hold as 14.1 Å, below which size micropore filling must occur, and a minimum pore diameter for mechanical stability of the hemispherical meniscus during desorption as 34.2 Å. For pores in-between these two sizes reversible condensation is predicted to occur, in accord with the experimental data for nitrogen adsorption on MCM-41 at 77.4 K.

Determination of coalescence kernels for high-shear granulation using DEM simulations

Discrete element method (DEM) modeling is used in parallel with a model for coalescence of deformable surface wet granules. This produces a method capable of predicting both collision rates and coalescence efficiencies for use in derivation of an overall coalescence kernel. These coalescence kernels can then be used in computationally efficient meso-scale models such as population balance equation (PBE) models. A soft-sphere DEM model using periodic boundary conditions and a unique boxing scheme was utilized to simulate particle flow inside a high-shear mixer. Analysis of the simulation results provided collision frequency, aggregation frequency, kinetic energy, coalescence efficiency and compaction rates for the granulation process. This information can be used to bridge the gap in multi-scale modeling of granulation processes between the micro-scale DEM/coalescence modeling approach and a meso-scale PBE modeling approach.

Dimensionless spray flux in wet granulation: Monte-Carlo simulations and experimental validation

Dimensionless spray flux Ψa is a dimensionless group that characterises the three most important variables in liquid dispersion: flowrate, drop size and powder flux through the spray zone. In this paper, the Poisson distribution was used to generate analytical solutions for the proportion of nuclei formed from single drops (fsingle) and the fraction of the powder surface covered by drops (fcovered) as a function of Ψa. Monte-Carlo simulations were performed to simulate the spray zone and investigate how Ψa, fsingle and fcovered are related. The Monte-Carlo data was an excellent match with analytical solutions of fcovered and fsingle as a function of Ψa. At low Ψa, the proportion of the surface covered by drops (fcovered) was equal to Ψa. As Ψa increases, drop overlap becomes more dominant and the powder surface coverage levels off. The proportion of nuclei formed from single drops (fsingle) falls exponentially with increasing Ψa. In the ranges covered, these results were independent of drop size, number of drops, drop size distribution (mono-sized, bimodal and trimodal distributions), and the uniformity of the spray. Experimental data of nuclei size distributions as a function of spray flux were fitted to the analytical solution for fsingle by defining a cutsize for single drop nuclei. The fitted cutsizes followed the spray drop sizes suggesting that the method is robust and that the cutsize does indicate the transition size between single drop and agglomerate nuclei. This demonstrates that the nuclei distribution is determined by the dimensionless spray flux and the fraction of drop controlled nuclei can be calculated analytically in advance.

The importance of wet-powder dynamic mechanical properties in understanding granulation

Granule impact deformation has long been recognised as important in determining whether or not two colliding granules will coalesce. Work in the last 10 years has highlighted the fact that viscous effects are significant in granulation. The relative strengths of different formulations can vary with strain rate. Therefore, traditional strength measurements made at pseudo-static conditions give no indication, even qualitatively, of how materials will behave at high strain rates, and hence are actually misleading when used to model granule coalescence. This means that new standard methods need to be developed for determining the strain rates encountered by granules inside industrial equipment and also for measuring the mechanical properties of granules at these strain rates. The constitutive equations used in theoretical models of granule coalescence also need to be extended to include strain-rate dependent components.

Dissolution of a solid sphere in an unbounded, stagnant liquid

An exact analytical solution is obtained for the transient dissolution of solid spheres in a diffusion-controlled environment. This result provides a useful reference point for drug testing in humans. The dimensionless solution is expressed in terms of a single parameter, which accounts for solubility, bulk flow, and stagnant fluid composition. A simple, explicit and exact expression was found to predict time-to-complete dissolution (TCD). An approximate solution was also found which tracks the exact case for low solubility conditions.

Optical study of a light diaphragm rupture process in an expansion tube

Rupture of a light cellophane diaphragm in an expansion tube has been studied by an optical method. The influence of the light diaphragm on test flow generation has long been recognised, however the diaphragm rupture mechanism is less well known. It has been previously postulated that the diaphragm ruptures around its periphery due to the dynamic pressure loading of the shock wave, with the diaphragm material at some stage being removed from the flow to allow the shock to accelerate to the measured speeds downstream. The images obtained in this series of experiments are the first to show the mechanism of diaphragm rupture and mass removal in an expansion tube. A light diaphragm was impulsively loaded via a shock wave and a series of images was recorded holographically throughout the rupture process, showing gradual destruction of the diaphragm. Features such as the diaphragm material, the interface between gases, and a reflected shock were clearly visualised. Both qualitative and quantitative aspects of the rupture dynamics were derived from the images and compared with existing one-dimensional theory.

Stimulated Raman adiabatic passage from an atomic to a molecular Bose-Einstein condensate

The process of stimulated Raman adiabatic passage (STIRAP) provides a possible route for the generation of a coherent molecular Bose-Einstein condensate (BEC) from an atomic BEC. We analyze this process in a three-dimensional mean-field theory, including atom-atom interactions and nonresonant intermediate levels. We find that the process is feasible, but at larger Rabi frequencies than anticipated from a crude single-mode lossless analysis, due to two-photon dephasing caused by the atomic interactions. We then identify optimal strategies in STIRAP allowing one to maintain high conversion efficiencies with smaller Rabi frequencies and under experimentally less demanding conditions.

Diagnostics of A Range of Highly Superorbital Carbon Dioxide Flows

Expansion tubes are impulse facilities capable of generating highly energetic hyper-sonic flows. This work surveys a broad range of flow conditions produced in the facility X1 with carbon dioxide test gas, for simulation of spacecraft entry into the Martian atmosphere. Conditions with nominal flow speeds of 7, 9, 11 and 13 km/s were tested. The freestream conditions were calibrated using static/Pitot pressure measurements and advanced optical diagnostics. An extensive set of holographic interferometry experiments was performed on flows over wedges for quantitative study of freestream and post-shock densities, and post-shock ionisation. A one-dimensional code with frozen and equilibrium chemistry capabilities was used to estimate the freestream conditions. An equilibrium chemistry model produced a good match to measured freestream quantities at the high enthalpy conditions which are a major aim of this facility's operation. The freestream in the lower enthalpy conditions was found to be heavily influenced by chemical non-equilibrium. Non-equilibrium in the final unsteady expansion process of flow generation was accounted for by switching from equilibrium to frozen chemistry at a predetermined point. Comparison between the freestream density results of holographic interferometry, pressure measurements and computations shows good agreement.

Workgroup emotional intelligence: Scale development and relationship to team process effectiveness and goal focus

Over the last decade, ambitious claims have been made in the management literature about the contribution of emotional intelligence to success and performance. Writers in this genre have predicted that individuals with high emotional intelligence perform better in all aspects of management. This paper outlines the development of a new emotional intelligence measure, the Workgroup Emotional Intelligence Profile, Version 3 (WEIP-3), which was designed specifically to profile the emotional intelligence of individuals in work teams. We applied the scale in a study of the link between emotional intelligence and two measures of team performance: team process effectiveness and team goal focus. The results suggest that the average level of emotional intelligence of team members, as measured by the WEIP-3, is reflected in the initial performance of teams. In our study, low emotional intelligence teams initially performed at a lower level than the high emotional intelligence teams. Over time, however, teams with low average emotional intelligence raised their performance to match that of teams with high emotional intelligence.

Spectral properties of the tandem Jackson network, seen as a quasi-birth-and-death process

Quasi-birth-and-death (QBD) processes with infinite “phase spaces” can exhibit unusual and interesting behavior. One of the simplest examples of such a process is the two-node tandem Jackson network, with the “phase” giving the state of the first queue and the “level” giving the state of the second queue. In this paper, we undertake an extensive analysis of the properties of this QBD. In particular, we investigate the spectral properties of Neuts’s R-matrix and show that the decay rate of the stationary distribution of the “level” process is not always equal to the convergence norm of R. In fact, we show that we can obtain any decay rate from a certain range by controlling only the transition structure at level zero, which is independent of R. We also consider the sequence of tandem queues that is constructed by restricting the waiting room of the first queue to some finite capacity, and then allowing this capacity to increase to infinity. We show that the decay rates for the finite truncations converge to a value, which is not necessarily the decay rate in the infinite waiting room case. Finally, we show that the probability that the process hits level n before level 0 given that it starts in level 1 decays at a rate which is not necessarily the same as the decay rate for the stationary distribution.