MULTIPLICITY AND STABILITY ANALYSIS OF AGGLOMERATION CONTROLLED PRECIPITATION

The possibility of multiplicity in continuous isothermal MSMPR precipitators has been explored for agglomeration controlled conditions and general criteria, independent of nucleation kinetics, are developed for stability and multiplicity of the steady states. For the Volmer model of primary nucleation and the magma dependent power law model of secondary nucleation, parameter regions are determined in which multiple steady states exist, and their linear stability is analyzed. The analysis holds in general for all types of agglomeration kernel. For the Volmer nucleation kinetics three steady states exist in the region of multiplicity with the “middle” one always being unstable. The analysis for magma dependent power law model showed multiplicity regions having as many as four steady states, the number depending on magma and kinetic order. Unlike the case of molecular growth control, limit cycle behaviour is not possible, and the approach to the steady state is always asymptotic     

MULTIPLICITY IN CONTINUOUS CRYSTALLIZERS: ADIABATIC REACTIVE PRECIPITATION

The application of the theory of both concentration and temperature multiplicities is extended to the case of a reactive precipitation system in a continuous mixed suspension mixed product removal (MSMPR) crystallizer. A process involving elementary homogeneous chemical reaction with first order reaction kinetics with respect to each of the reactive components and subsequent crystallization described by conventional power law growth and power law magma dependent nucleation models is considered; the temperature dependency of each of these kinetics is described by Arrhenius relations. Exact uniqueness and multiplicity (i.e. multiple steady states) criteria are developed. The stability of these steady states is analysed using small perturbations around the steady state     

MODELLING AND ANALYSIS OF PARTICLE FORMATION DURING AGGLOMERATIVE CRYSTAL PRECIPITATION PROCESSES

While nucleation and crystal growth are normally considered to be the primary particle formation processes during industrial crystallization, secondary processes including crystal agglomeration and breakage can have a determining effect on product form, especially of precipitates. In addition to the usual overall size distribution, primary and secondary particle size, particle structure and morphology then become important characteristics affecting both product quality and downstream processing performanc

In this paper, the kinetics of processes which determine the formation of both primary particles and crystal agglomerates are briefly reviewed together with established and recent population balance and simulation techniques for analysing and predicting primary and secondary particle size distributions and total specific surface area. These approaches are then illustrated by some experimental and modelling studies of agglomerative precipitation reported recently in the literature.     

AGGLOMERATION, BREAKAGE, POPULATION BALANCE, AND CRYSTALLIZATION KINETICS OF REACTIVE PRECIPITATION PROCESS

The agglomeration and breakage of particles play a significant role in determining final particle size distribution (PSD) and other qualities such as filtering characteristics and impurity content. In reactive precipitation processes, especially during the precipitation of fine particles, the agglomeration and breakage of particles normally cannot be neglected. In this study, the agglomeration and breakage of particles during the reactive precipitation process of procaine penicillin has been investigated experimentally through a continuous steady MSMPR crystallizer. Based on the population balance theory, a crystallization kinetics model including agglomeration and breakage is established, in which the breakage of particles is expressed by a two-body equal-volume birth function and a two-body power-law death function. The crystallization kinetics model is shown to be more suitable than size-dependent growth models as ASL and MJ2.     

ALKALI-INDUCED AGGLOMERATION OF SOLID PARTICLES IN COAL COMBUSTORS AND GASIFIERS

The effect of alkali adsorption on the agglomeration of particles of bauxite, kaolinite, emathlite, lime and two types of coal ash is studied. An agglomeration (adhesion) temperature is defined which characterizes the adhesion propensity of particles. An experimental technique is developed to measure this agglomeration point in situ and without sample quenching or removal. The effect of alkali adsorption on the agglomeration characteristics of the substrates is determined. The agglomeration temperature for all substrates decreases a:, alkali content increases. At low loadings the alkali adsorption enhances particle agglomeration by forming new compounds of lower melting points. At high concentrations, the agglomeration point of all substrates approaches the melting point of condensing alkali. Under these conditions, adhesion and agglomeration are caused by a layer of molten alkali which covers the exterior of the particles.     

MICROMIXING EFFECTS ON BARIUM SULFATE PRECIPITATION IN AN MSMPR REACTOR

The Effects of non-ideal and nonhomogeneous mixing on barium sulfate precipitation in an MSMPR reactor were observed experimentally and analyzed theoretically. To generate nonhomogeneous mixing the unmixed feed streams were fed to the reactor at the same location (joint feeding mode) or a plug flow reactor was connected to the MSMPR reactor. These nonhomogeneous mixing conditions resulted in significant reductions in particle size and increases in particle numbers. These non ideal mixing effects were dependent on the impeller speed, feed stream velocity and residence time in the connected plug flow reactor and are believed to result from elevated supersaturation levels in a premixing zone which are controlled by turbulent micromixing

To model the effect of nonhomogeneous mixing (premixing) in the MSM PR reactor a plug flow-stirred lank reactor series model was developed. The plug flow reactor represents the premixing region of the MSMPR reactor in which turbulent micromixing is important, and the stirred tank reactor describes the homogeneous mixing region of the MSMPR reactor where particle growth is important. The model predicts that the premixing effect is strongly dependent on micromixing of the feeds in the premixing region, and thus, as the turbulent mixing intensity in this region is increased, the particle size in the product suspension is reduced and the particle population is increased. These predictions of the model arc in good agreement with the experimental data. An interesting prediction of the model is that as the impeller speed increases, the precipitation of barium sulfate in an MSMPR reactor deviates increasingly from the precipitation in a perfectly mixed (ideal) reactor.     

DEPENDENCE OF THE MULTIPLICITY FEATURES OF AN ISOTHERMAL CATALYTIC REACTION ON EXTERNAL AND INTERNAL TRANSPORT RESISTANCES

A mathematical model (Robin) which accounts for both internal and external transport resistances is used to determine the multiplicity features of a porous catalytic pellet in which an isothermal Langmuir-Hinshelwood reaction occurs. At most three solutions exist for a slab, but an arbitrarily large number of solutions can be found for an infinite cylinder or a spherical pellet. The maximal number of solutions for any finite external mass transfer resistance is bounded between that existing for a model which ignores the external mass transfer resistance and one which ignores intra-particle concentration gradients. The approximate shape of the cross section of the bifurcation set and of the uniqueness boundary of the Robin model can be estimated from the knowledge of the multiplicity features of three simplified (lumped, Dirichlet and Neumann) models, each containing one less parameter.     

MULTIPLICITY OF STATES IN SYSTEMS OF INTERACTING CATALYST PARTICLES

Presented here are several case studies, both theoretical and experimental, of the steady-state features of an assembly of interacting catalyst particles in a CSTR. Ostensibly, the results of these studies, though bused on simple string arrangements of two and three particles in a uniform environment, have meaning in terms of the behavioral characteristics of more complicated situations, including fixed-bed reactors.

Theoretical results exhibit complex bifurcation patterns and multiplicity features for steady-state curves when the particles are described as individual interacting entities. The complexity increases when the catalytic activities of the particles are not all alike.

Observations from experiments with the oxidation of hydrogen on spherical pellets of supported platinum resemble the theoretical cases. Individual pellet states in the laboratory work are depicted by their temperature maps obtained by means of a thermal infrared imaging system.     

MULTIPLICITY OF STATES IN SYSTEMS OF INTERACTING CATALYST PARTICLES

Presented here are several case studies, both theoretical and experimental, of the steady-state features of an assembly of interacting catalyst particles in a CSTR. Ostensibly, the results of these studies, though bused on simple string arrangements of two and three particles in a uniform environment, have meaning in terms of the behavioral characteristics of more complicated situations, including fixed-bed reactors.

Theoretical results exhibit complex bifurcation patterns and multiplicity features for steady-state curves when the particles are described as individual interacting entities. The complexity increases when the catalytic activities of the particles are not all alike.

Observations from experiments with the oxidation of hydrogen on spherical pellets of supported platinum resemble the theoretical cases. Individual pellet states in the laboratory work are depicted by their temperature maps obtained by means of a thermal infrared imaging system.     

溶剂沉淀法制备的聚酰胺粉末之溶剂与粉末结构和热稳定性的关系

使用粒度分布仪、白度仪、电子显微镜和差热仪测定四种溶剂沉淀法制备的聚酰胺粉末发现：每种方法所获得的粉末粒径、比表面积、白度均不相同；以乙醇 氯化钙混合溶剂制备的粉末内部具有多孔结构；以乙醇 盐酸 水混合溶剂制备的粉末热稳定性较高     

一种SFEP丙烯酸酯聚合涂膜的稳定性分析

合成了一种丙烯酸酯SFEP的聚合产物,对其涂膜的稳定性进行了四个方面的分析测试。数据表明：其耐水性可达5％－65,吸水性为9％－10％,耐酸碱性小于4％,10％Ca^2 稳定性大于60mL。     

采用粒数衡算模型研究沉淀过程中粒子的聚结和破裂

通过采用MSMPR反应沉淀器,研究了普鲁卡因青霉素反应沉淀过程中粒子的聚结和破裂对过程的影响机理,并对用生死函数表征聚结和破裂的粒数衡算模型采用新的分析方法。结果表明,将二元破裂模型应用于该粒数衡算模型是可行的。     

EFFECT OF GAS-SIDE RESISTANCE ON STEADY STATE MULTIPLICITY IN GAS-LIQUID CSTRs

The effect of gas-side resistance to mass transfer on the existence and uniqueness of steady states in gas-liquid CSTRs is analyzed. It is shown that there exists an upper bound on gas-side resistance beyond which multiplicity cannot arise.     

NONLINEAR STABILITY ANALYSIS OF FILM FLOW WITH SMALL WEBER NUMBER

Nonlinear-kinematic equation for the film thickness with small surface tension at the interface is used to investigate the nonlinear stability of film flow down an inclined plane. The analysis shows that both supercritical stability and subcritical instability are possible for film flow system. It is also found that if the magnitude of Reynolds number is larger than a critical value, the nonlinear effects make the film flow system unstable in the region near the upper neutral stability curve.     

STABILITY ANALYSIS FOR THE PREDICTION OF THE MINIMUM TEMPERATURE OF FILM BOILING

The stability of film boiling on a vertical, constant temperature wall is analyzed by a steady-state small perturbation method. It was found that large amplifications of the perturbations in the downstream direction are predicted when the vapor Reynolds number falls below a critical value, indicating a great tendency to collapse the vapor film. Using a relatively simple model for the film thickness, the minimum wall temperature required to sustain the vapor film is calculated. The results show a tendency which is in agreement with experimental observation. It is suggested, however, that using a more accurate model for the film thickness can lead to a good prediction of the minimum wall temperature and explain the large effect of liquid subcooling, system pressure, surface tension and other fluid properties.     

ANALYSIS OF THE MULTIPLICITY PATTERNS OF A CSTR

Continuous changes in the residence time of a cooled continuously stirred tank reactor, in which a single, exothermic, first-order reaction occurs, may lead to one of six different multiplicity patterns. A simple technique is developed for the exact prediction of the multiplicity pattern existing for any set of parameter values and of the influence of changes in the parameter values on the transition from one pattern to another.     

FLOW OF SUPERSATURATED SOLUTIONS IN PIPES. MODELING BULK PRECIPITATION AND SCALE FORMATION

Pipe flow of supersaturated solutions of sparingly soluble salts is simulated in this work. Models from the literature are selected to represent individual processes, which may occur simultaneously, such as nucleation, particle growth, coagulation, and particulate and ionic deposition on the pipe wall. As regards formulation, a fairly comprehensive population balance equation is employed for the sol:d phase combined with mass balance for the ionic species. A sufficiently accurate, yet computationally convenient, discretization scheme is used in the simulation algorithm. Arbitrary parameters are avoided with the exception of surface reaction parameters which are determined from experimental data since no theoretical values are available. The PbS-water system (previously studied experimentally in this laboratory) serves as a test case. The PbS effective surface energy is estimated from experimental data. Predictions are quite encouraging, reproducing statisfactorily the measured “beH”-shaped deposition versus pH curves. The predicted particle size distributions and their evolution are physically realistic, qualitatively and quantitatively. Despite necessary future improvements, the proposed simulation algorithm is already considered a useful tool for scale up in industrial and other applications.     

帽型复合材料梁的稳定性分析与固有频率计算

根据经典层合板理论,结合纯弯曲状态下内力与应变的关系,推导了帽型复合材料梁的等效弯曲刚度计算公式,并利用等效弯曲刚度进一步推出了该类型梁的轴向临界载荷与固有频率计算公式,最后用有限元法进行验证,为帽型及其他截面类型的复合材料梁在工程中的应用提供参考。     

DYNAMIC BEHAVIOR OF PARTICLE AGGLOMERATION OF EUROPIUM OXALATE DURING REACTION CRYSTALLIZATION IN SEMI-BATCH REACTOR

During reaction crystallization of europium oxalate in a semi-batch reactor, a monotonical increase in the mean particle size and corresponding reduction in the total particle population were observed due to particle agglomeration occurring simultaneously with particle nucleation and growth. However, since particle agglomeration was achieved via particle aggregation and molecular growth, the mean particle size and total particle population in the product suspension were significantly influenced by the crystallization conditions of the feed concentration, agitation speed, and feeding time. A higher feed concentration and feeding time resulted in a larger mean particle size and smaller total particle population due to the higher supersaturation and longer holding time in the reactor. Meanwhile, agitation was found to exhibit a rather complicated influence on particle agglomeration because particle collision and a turbulent fluid shear were both promoted at the same time. In the semi-batch reactor, the reduction in total particle population during crystallization clearly reflected particle agglomeration.     

ON THE DYNAMICS OF THE COMBUSTION OF SINGLE CHAR PARTICLES

Diffusion and reaction models of varying complexity are used to study the stability of the combustion of single char particles. In contrast to past studies which have considered only the reaction of carbon with oxygen, both the heterogeneous reactions of carbon with oxygen and carbon dioxide and the homogeneous oxidation of carbon monoxide are taken into account in the formulation of the mathematical models. Emphasis is placed on the investigation of the feasibility of occurrence of oscillatory combustion. Our results show that high rates of the C-O₂ reaction and high concentration of O₂ in the ambient favor the occurrence of multiple steady states and oscillatory solutions, but the appearance of oscillatory instability is suppressed by the homogeneous reaction in the gas phase and the presence of CO and CO₂ in the ambient. The parametric investigation of the problem reveals, in agreement with the results of past studies, that the heat capacity of the porous solid, the Lewis number, and the thickness of the stagnant film are three key parameters for the occurrence of the oscillatory response of the system. Reasonably large values of solid heat capacity practically eliminate the possibility of oscillatory combustion, but an appropriate combination of large values of stagnant film thickness and small Lewis numbers may offset the effect of solid heat capacity