Evaluation and comparison of a moist granulation technique to conventional methods

In the moist granulation technique (MGT), a minimum amount of liquid is used to activate a binder in a planetary mixer. Then, any excess moisture is absorbed by the addition of a moisture-absorbing substance. In the experiments described below, acetaminophen (APAP) was the model drug; polyvinylpyrrolidone (PVP) and microcrystalline cellulose (MCC) served as the binder and moisture-absorbing material, respectively. Water was used as the granulating fluid. Comparison of the MGT with direct compression (DC) and wet granulation (WG) methods was accomplished by sieve analysis (particle size) and density measurements. Moist granulation yielded an increase in particle size compared to direct compression; these results are comparable to those from the traditional wet granulation after drying and screening. Based only on the particle size, moist granulation appears comparable to conventional wet granulation for this formula. The moist granulation technique appears to have potential for the development of controlled-release formulations.     

Understanding production of fines in batch ball milling for mill scale-up design using the population balance model

The rate of production of fine material in the batch mode of grinding operation forms the basis for determination of the grindability parameter of the Bond approach and the breakage distribution function of the population balance model (PBM) approach to the mill scale-up design. For a given set of mill operating conditions, the rate of production of fines is determined by the breakage characteristics and production history of the material being ground. Another important aspect is the variation in the rate of production of fines with grinding time. With a view to developing a clear understanding of these aspects, a detailed analysis of variations in the rate of production of fines was carried out using the PBM framework and two well-known functional forms for the specific breakage rate and breakage distribution parameters. In this paper, it has been shown how the results of this analysis can be used for: (i) obtaining more accurate estimates of the breakage distribution parameters by performing just one short-duration batch grinding experiment, and (ii) explaining variation in the Bond Work index with the product size in terms of the exponent of particle size in the expression for the specific breakage rate function: $k_j=A^1{x}_j^{\alpha }$.     

A compartment based population balance model for the prediction of steady and induction granule growth behavior in high shear wet granulation

This paper presents a predictive modeling approach of the high shear wet granulation process, quantifying the difference between the steady and induction granule growth behavior. The spatial heterogeneity in liquid binder distribution and shear rate is simulated using a compartmental population balance model. The granulator is divided into two compartments based on particle motion, which consists of a circulation compartment, and an impeller compartment. In the circulation compartment, a viscous dissipation dependent coalescence kernel is adapted for the aggregation process. In the impeller compartment a shear rate dependent aggregation kernel is implemented. The model was calibrated and validated using the dynamic evolution of granule mean size (d₅₀). The granulation dynamics are studied with respect to change in impeller speed, liquid to solid ratio, wet massing time, initial porosity, and binder viscosity. The transition from induction growth to steady growth regime with changing process conditions is demonstrated using the model. It is observed that the model captures the effect of process parameters and spatial heterogeneity on the dynamic evolution of d₅₀.     

Closed-form and finite difference solutions to a population balance model of grinding mills

The wear of steel balls in continuously operated grinding mills, used in mineral processing to comminute metalliferous rocks, can be described by a simple population-balance model. This model gives rise to a scalar transport equation with a singular source term for the number density of balls as a function of size and time. Exact solutions to this equation are determined under the assumption of a simple power-law type wear law. It is shown that a particular term proposed in the engineering literature that describes the removal of used balls from the mill leads to negative solutions (Model 1). An alternative, more realistic term for the sieve action, which admits nonnegative solutions only, is introduced (Model 2). A working first-order finite-difference scheme for Model 2 and a second-order TVD variant are introduced and applied for numerical simulations along with an error study. A weak solution concept for Model 2 is proposed, uniqueness of weak solutions is shown, and convergence of the first-order scheme to a weak solution is established. These results hold for a general class of wear laws, not just power-law type.     

Integrated Population Balance Model Development and Validation of a Granulation Process

This study is concerned with the development of an integrated three-dimensional population balance model (PBM) that describes the combined effect of key granulation mechanisms that occur during the course of a granulation process. Results demonstrate the importance of simulating the different mechanisms within a population balance model framework to elucidate realistic granulation dynamics. The incorporation of liquid addition in the model also aids in demarcating the dynamics in different regimes such as premixing, granulation (during liquid addition) and wet massing (after liquid addition). For the first time, the effect of primary particle size distributions and mode of binder addition on key granule properties was studied using an integrated PBM. Experimental data confirms the validity of the overall model as compared to traditional models in the literature that do not integrate the different granulation mechanisms.     

An original approximate method for estimating the invariant probability distribution of a large class of multi-dimensional nonlinear stochastic oscillators

This paper proposes an original method for obtaining analytical approximations of the invariant probability density function of multi-dimensional Hamiltonian dissipative dynamic systems under Gaussian white noise excitations, with linear non-conservative parts and nonlinear conservative parts. The method is based on an exact result and a heuristic argument. Its pertinence is attested by numerical tests.     

An aggregation method of Markov graphs for the reliability analysis of hybrid systems

To meet always increasing safety requirements in car industry, design and safety assessment methods are developed in order to fit the complexity of new embedded mecatronic systems. Hybrid (discrete/continuous) and dynamic features, specific to these systems, require choosing a suitable formalism. These features should also be considered in safety studies made all through the system design. The aim of this paper is to propose a quantitative analysis method based on the construction of an aggregated Markov graph, which allows a limitation of the combinatorial expansion. This graph is directly deducted from the Petri net modelling of the system. It is composed by a set of functional modes and a set of transitions to which statistical information regarding the system dynamics has been added.     

Influence of process variable and physicochemical properties on the granulation mechanism of mannitol in a fluid bed top spray granulator

This study investigated the influence of specific process variables, including the hydroxypropyl cellulose (HPC) binder solution atomization, on the fluidized bed top spray granulation of mannitol. Special attention was given to the relationship between wetting and the granule growth profile. The atomization of the HPC binder solution using a binary nozzle arrangement produced droplets of decreasing size as the atomization pressure was increased, while changes in the spray rate had little effect on the mean droplet size. Increasing the HPC binder concentration from 2 to 8% w/w increased the binder droplet size and was most likely attributed to higher solution viscosity. The top spray granulation of mannitol showed induction type growth behavior. Process conditions like high spray rate, low fluidizing air velocity and binder solution concentration that promote the availability of HPC binder solution at the surface of the particles appeared to be key in enhancing nucleation and growth of the granules. Increasing the bed moisture level, up to a certain value, reduced the contribution of attrition to the overall growth profile of the granule and, more significantly, produced less granule breakage on drying. It was observed that the mean granule size could be reduced as much as 40% between the end of granulation and the end of drying for lower initial bed moisture level despite a shorter drying phase. High atomization pressure, especially when maintained during the drying phase, contributed substantially to granule breakage.     

On the impact of the scheme for solving the higher dimensional equation in coupled population balance systems

Population balance systems are models for processes in nature and industry that lead to a coupled system of equations (Navier–Stokes equations, transport equations, etc.) where the equations are defined in domains with different dimensions. This paper will study the impact of using different schemes for solving the three‐dimensional (3D) equation of a precipitation process in a two‐dimensional flow domain. The numerical schemes for the 3D equation are assessed with respect to the median of the volume fraction of the particle size distribution and the computational costs. It turns out that in the case of a structured flow field with small variations in time all schemes give qualitatively the same results. For a highly time‐ dependent flow field, the evolution of the median of the volume fraction differs considerably between first order and higher order schemes. Copyright © 2010 John Wiley & Sons, Ltd.     

General harmonic balance solution of a cracked rotor-bearing-disk system for harmonic and sub-harmonic analysis: Analytical and experimental approach

The effect of crack depth of a rotor-bearing-disk system on vibration amplitudes and whirl orbit shapes is investigated through a general harmonic balance technique and experimental verification. Two models of the crack, which are the breathing and the open crack models, are considered. Finite element models and general harmonic balance solutions are derived for breathing and open cracks which are valid for damped and undamped rotor systems. It is found via waterfall plots of the system with a breathing crack that there are large vibration amplitudes at critical values of crack depth and rotor speed for a slight unbalance in the system. The high vibration amplitudes at the backward whirl appear at earlier crack depths than those of the forward whirl for both crack models. Resonance peaks at the second, third and fourth subcritical speeds emerge as the crack depth increases. It is shown that the unique signature of orbits for the breathing crack model which have been verified experimentally can be used as an indication of a breathing crack in the shaft. In addition, the veering in the critical frequencies has been noticed in the open crack case.     

An aggregation method of Markov graphs for the reliability analysis of hybrid systems

To meet always increasing safety requirements in car industry, design and safety assessment methods are developed in order to fit the complexity of new embedded mecatronic systems. Hybrid (discrete/continuous) and dynamic features, specific to these systems, require choosing a suitable formalism. These features should also be considered in safety studies made all through the system design. The aim of this paper is to propose a quantitative analysis method based on the construction of an aggregated Markov graph, which allows a limitation of the combinatorial expansion. This graph is directly deducted from the Petri net modelling of the system. It is composed by a set of functional modes and a set of transitions to which statistical information regarding the system dynamics has been added.     

土压平衡式液压盾构推进系统的非线性动力学建模及分析

建立了土压平衡式盾构的液压推进系统的非线性动力学模型,分析了推进系统各个结构参数对盾构掘进作业的影响.通过动力学模型中的刚度矩阵,分析了各自由度方向的刚度特性,提出了推进系统液压缸数量的配置准则.在刚度分析的基础上,进一步探讨了系统的自振频率,提出了防止推进系统产生共振的方法.最后,分析了各固有频率下各阶模态向量元素的特性,确定了盾构扭矩设计原则.     

A mathematical model of subpopulation kinetics for the deconvolution of leukaemia heterogeneity

Acute myeloid leukaemia is characterized by marked inter- and intra-patient heterogeneity, the identification of which is critical for the design of personalized treatments. Heterogeneity of leukaemic cells is determined by mutations which ultimately affect the cell cycle. We have developed and validated a biologically relevant, mathematical model of the cell cycle based on unique cell-cycle signatures, defined by duration of cell-cycle phases and cyclin profiles as determined by flow cytometry, for three leukaemia cell lines. The model was discretized for the different phases in their respective progress variables (cyclins and DNA), resulting in a set of time-dependent ordinary differential equations. Cell-cycle phase distribution and cyclin concentration profiles were validated against population chase experiments. Heterogeneity was simulated in culture by combining the three cell lines in a blinded experimental set-up. Based on individual kinetics, the model was capable of identifying and quantifying cellular heterogeneity. When supplying the initial conditions only, the model predicted future cell population dynamics and estimated the previous heterogeneous composition of cells. Identification of heterogeneous leukaemia clones at diagnosis and post-treatment using such a mathematical platform has the potential to predict multiple future outcomes in response to induction and consolidation chemotherapy as well as relapse kinetics.     

An analytical stiffness derivative extended finite element technique for extraction of crack tip Strain Energy Release Rates

An analytical approach combined with the extended finite element method (XFEM) is proposed to extract the Strain Energy Release Rates within the classical stiffness derivative technique. The proposed idea hinges on the following two XFEM properties: (i) the crack is mesh independent, i.e. there is no need for mesh perturbations in the vicinity of the crack and (ii) the asymptotic crack tip field is embedded in the mathematical formulation of the stiffness matrix. By employing these properties we show that the derivative of the stiffness matrix with respect to the crack extension can be computed in a closed form and on the fly during the analysis. Thus the virtual crack extension, and the error inherent in the finite difference scheme of the classical stiffness derivative technique is completely avoided. Numerical results on few benchmark problems show that this method is comparable to the J-integral method.     

The dynamic balance of import and export of zinc in Escherichia coli suggests a heterogeneous population response to stress

Zinc is essential for life, but toxic in excess. Thus all cells must control their internal zinc concentration. We used a systems approach, alternating rounds of experiments and models, to further elucidate the zinc control systems in Escherichia coli. We measured the response to zinc of the main specific zinc import and export systems in the wild-type, and a series of deletion mutant strains. We interpreted these data with a detailed mathematical model and Bayesian model fitting routines. There are three key findings: first, that alternate, non-inducible importers and exporters are important. Second, that an internal zinc reservoir is essential for maintaining the internal zinc concentration. Third, our data fitting led us to propose that the cells mount a heterogeneous response to zinc: some respond effectively, while others die or stop growing. In a further round of experiments, we demonstrated lower viable cell counts in the mutant strain tested exposed to excess zinc, consistent with this hypothesis. A stochastic model simulation demonstrated considerable fluctuations in the cellular levels of the ZntA exporter protein, reinforcing this proposal. We hypothesize that maintaining population heterogeneity could be a bet-hedging response allowing a population of cells to survive in varied and fluctuating environments.     

60000m^3／h空分设备物料平衡及变负荷控制原理

文章以60000m^3／h空分设备为例，以理论计算为基础，从物料平衡角度出发，介绍空分设备的自动变负荷的控制原理和计算。实际运行证明，自动变负荷控制系统运行效果较好。     

60000m~3/h空分设备物料平衡及变负荷控制原理

文章以60000m3/h空分设备为例,以理论计算为基础,从物料平衡角度出发,介绍空分设备的自动变负荷的控制原理和计算。实际运行证明,自动变负荷控制系统运行效果较好。     

An investment plan for preventing child injuries using risk priority number of failure mode and effects analysis methodology and a multi-objective, multi-dimensional mixed 0-1 knapsack model

In this paper, a general framework for child injury prevention and a multi-objective, multi-dimensional mixed 0-1 knapsack model were developed to determine the optimal time to introduce preventive measures against child injuries. Furthermore, the model maximises the prevention of injuries with the highest risks for each age period by combining preventive measures and supervision as well as satisfying budget limits and supervision time constraints. The risk factors for each injury, variable, and time period were based on risk priority numbers (RPNs) obtained from failure mode and effects analysis (FMEA) methodology, and these risk factors were incorporated into the model as objective function parameters. A numerical experiment based on several different situations was conducted, revealing that the model provided optimal timing of preventive measures for child injuries based on variables considered.     

Effects of heterogeneity in infection-exposure history and immunity on the dynamics of a protozoan parasite

Infection systems where traits of the host, such as acquired immunity, interact with the infection process can show complex dynamic behaviour with counter-intuitive results. In this study, we consider the traits ‘immune status’ and ‘exposure history’, and our aim is to assess the influence of acquired individual heterogeneity in these traits. We have built an individual-based model of Eimeria acervulina infections, a protozoan parasite with an environmental stage that causes coccidiosis in chickens. With the model, we simulate outbreaks of the disease under varying initial contaminations. Heterogeneity in the traits arises stochastically through differences in the dose and frequency of parasites that individuals pick up from the environment. We find that the relationship between the initial contamination and the severity of an outbreak has a non-monotonous ‘wave-like’ pattern. This pattern can be explained by an increased heterogeneity in the host population caused by the infection process at the most severe outbreaks. We conclude that when dealing with these types of infection systems, models that are used to develop or evaluate control measures cannot neglect acquired heterogeneity in the host population traits that interact with the infection process.