A new wavelet-based method for the solution of the population balance equation

A new wavelet-based method for solving population balance equations with simultaneous nucleation, growth and agglomeration is proposed, which uses wavelets to express the functions. The technique is very general, powerful and overcomes the crucial problems of numerical diffusion and stability that often characterize previous techniques in this area. It is also applicable to an arbitrary grid to control resolution and computational efficiency. The proposed technique has been tested for pure agglomeration, simultaneous nucleation and growth, and simultaneous growth and agglomeration. In all cases, the predicted and analytical particle size distributions are in excellent agreement. The presence of moving sharp fronts can be addressed without the prior investigation of the characteristics of the processes. (C) 2001 Published by Elsevier Science Ltd.

Design, modelling and analysis of a six component force balance for hypervelocity wind tunnel testing

A combination of modelling and analysis techniques was used to design a six component force balance. The balance was designed specifically for the measurement of impulsive aerodynamic forces and moments characteristic of hypervelocity shock tunnel testing using the stress wave force measurement technique. Aerodynamic modelling was used to estimate the magnitude and distribution of forces and finite element modelling to determine the mechanical response of proposed balance designs. Simulation of balance performance was based on aerodynamic loads and mechanical responses using convolution techniques. Deconvolution was then used to assess balance performance and to guide further design modifications leading to the final balance design. (C) 2001 Elsevier Science Ltd. All rights reserved.

Mass balance characterisation of Al-7Si-Mg alloy microstructures as a function of solution treatment time

Mass balance calculations were performed to model the effect of solution treatment time on A356 and A357 alloy microstructures. Image analysis and electron probe microanalysis were used to characterise microstructures and confirm model predictions. In as-cast microstructures, up to 8 times more Mg is tied up in the pi-phase than in Mg2Si. The dissolution of pi is accompanied by a corresponding increase in the amount of beta-phase. This causes the rate of pi dissolution to be limited by the rate of beta formation. It is predicted that solution treatments of the order of tens of minutes at 540degreesC produce near-maximum T6 yield strengths, and that Mg contents in excess of 0.52 wt% have no advantage.

Stay-green: A consequence of the balance between supply and demand for nitrogen during grain filling?

Retention of green leaf area in grain sorghum under post-anthesis drought, known as stay-green, is associated with greater biomass production, lodging resistance and yield. The stay-green phenomenon can be examined at a cell, leaf, or whole plant level. At a cell level, the retention of chloroplast proteins such as LHCP2, OEC33 and Rubisco until late in senescence has been reported in sorghum containing the KS19 source of stay-green, indicating that photosynthesis may be maintained for longer during senescence in these genotypes. At a leaf level, longevity of photosynthetic apparatus is intimately related to nitrogen (N) status. At a whole plant level, stay-green can be viewed as a consequence of the balance between N demand by the grain and N supply during grain filling. To examine some of these concepts, nine hybrids varying in the B35 and KS19 sources of stay-green were grown under a postanthesis water deficit. Genotypic variation in delayed onset and reduced rate of leaf senescence were explained by differences in specific leaf nitrogen (SLN) and N uptake during grain filling. Matching N supply from age-related senescence and N uptake during grain tilling with grain N demand found that the shortfall in N supply for grain filling was greater in the senescent than stay-green hybrids, resulting in more accelerated leaf senescence in the former. We hypothesise that increased N uptake by stay-green hybrids is a result of greater biomass accumulation during grain filling in response to increased sink demand (higher grain numbers) which, in turn, is the result of increased radiation use efficiency and transpiration efficiency due to higher SLN. Delayed leaf senescence resulting from higher SLN should, in turn, allow snore carbon and nitrogen to be allocated to the roots of stay-green hybrids during grain filling, thereby maintaining a greater capacity to extract N from the soil compared with senescent hybrids.

Population balance modelling of granulation with a physically based coalescence kernel

It was previously published by the authors that granules can either coalesce through Type I (when granules coalesce by viscous dissipation in the surface liquid layer before their surfaces touch) or Type II (when granules are slowed to a halt during rebound, after their surfaces have made contact) (AIChE J. 46 (3) (2000) 529). Based on this coalescence mechanism, a new coalescence kernel for population balance modelling of granule growth is presented. The kernel is constant such that only collisions satisfying the conditions for one of the two coalescence types are successful. One constant rate is assigned to each type of coalescence and zero is for the case of rebound. As the conditions for Types I and II coalescence are dependent on granule and binder properties, the coalescence kernel is thus physically based. Simulation results of a variety of binder and granule materials show good agreement with experimental data. (C) 2002 Elsevier Science Ltd. All rights reserved.

The influence of a concurrent cognitive task on the compensatory stepping response to a perturbation in balance-impaired and healthy elders

This study investigated the influence of a concurrent cognitive task on the compensatory stepping response in balance-impaired elders and the attentional demand of the stepping response. Kinetic, kinematic and neuromuscular measures of a forward recovery step were investigated in 15 young adults, 15 healthy elders and 13 balance-impaired elders in a single task (postural recovery only) and dual task (postural recovery and vocal reaction time task) situation. Results revealed that reaction times were longer in all subjects when performed concurrently with a compensatory step, they were longer for a step than an in-place response and longer for balance-impaired older adults compared with young adults. An interesting finding was that the latter group difference may be related to prioritization between the two tasks rather than attentional demand, as the older adults completed the step before the reaction time, whereas the young adults could perform both concurrently. Few differences in step characteristics were found between tasks, with the most notable being a delayed latency and reduced magnitude of the early automatic postural response in healthy and balance-impaired elders with a concurrent task. (C) 2002 Elsevier Science B.V. All rights reserved.

Young children's performance on the balance scale: The influence of relational complexity

Three experiments investigated the effect of complexity on children's understanding of a beam balance. In nonconflict problems, weights or distances varied, while the other was held constant. In conflict items, both weight and distance varied, and items were of three kinds: weight dominant, distance dominant, or balance (in which neither was dominant). In Experiment 1, 2-year-old children succeeded on nonconflict-weight and nonconflict-distance problems. This result was replicated in Experiment 2, but performance on conflict items did not exceed chance. In Experiment 3, 3- and 4-year-olds succeeded on all except conflict balance problems, while 5- and 6-year-olds succeeded on all problem types. The results were interpreted in terms of relational complexity theory. Children aged 2 to 4 years succeeded on problems that entailed binary relations, but 5- and 6-year-olds also succeeded on problems that entailed ternary relations. Ternary relations tasks from other domains-transitivity and class inclusion-accounted for 93% of the age-related variance in balance scale scores. (C) 2002 Elsevier Science (USA).

Modelling the activated sludge flocculation process combining laser light diffraction particle sizing and population balance modelling (PBM)

A technique based on laser light diffraction is shown to be successful in collecting on-line experimental data. Time series of floc size distributions (FSD) under different shear rates (G) and calcium additions were collected. The steady state mass mean diameter decreased with increasing shear rate G and increased when calcium additions exceeded 8 mg/l. A so-called population balance model (PBM) was used to describe the experimental data, This kind of model describes both aggregation and breakage through birth and death terms. A discretised PBM was used since analytical solutions of the integro-partial differential equations are non-existing. Despite the complexity of the model, only 2 parameters need to be estimated: the aggregation rate and the breakage rate. The model seems, however, to lack flexibility. Also, the description of the floc size distribution (FSD) in time is not accurate.

A new wavelet-based adaptive method for solving population balance equations

A new wavelet-based adaptive framework for solving population balance equations (PBEs) is proposed in this work. The technique is general, powerful and efficient without the need for prior assumptions about the characteristics of the processes. Because there are steeply varying number densities across a size range, a new strategy is developed to select the optimal order of resolution and the collocation points based on an interpolating wavelet transform (IWT). The proposed technique has been tested for size-independent agglomeration, agglomeration with a linear summation kernel and agglomeration with a nonlinear kernel. In all cases, the predicted and analytical particle size distributions (PSDs) are in excellent agreement. Further work on the solution of the general population balance equations with nucleation, growth and agglomeration and the solution of steady-state population balance equations will be presented in this framework. (C) 2002 Elsevier Science B.V. All rights reserved.