Dynamics of lumped chemically reacting systems near singular bifurcation points

The systematic method of locating and classifying complex dynamical regimes of lumped reactors involves analysis of dynamics near singular bifurcation points at multiple eigenvalues. Amplitude expansion in the proximity of a singular bifurcation combined with multiple time scaling are used to derive universal equations that, though valid quantitatively only in a narrow patch of the parametric space, give full qualitative information on dynamics of a system possessing the respective highest singularity. The principal general result is that an algebraic singularity of a certain order is required to obtain dynamics of a certain dimensionality. In the lowest order, this is cusp singularity for two-dimensional dynamics in the proximity of bifurcation at double zero eigenvalue, and swallowtail singularity for three-dimensional dynamics at triple zero eigenvalue. The basic equation of two-dimensional dynamics describes various transitions between stationary and periodic states as observed, for example, in a first-order exothermic reaction. The equation of three-dimensional dynamics generates more complex phenomena, in particular, chaotic regimes.     

The law of the algebraic sum of stationary points of vapor-liquid equilibrium diagrams of multicomponent mixtures

The article provides a rationale for nonlocal laws governing dynamic systems, using vapor-liquid equilibrium diagrams as an example.     

多元水盐体系冰盐共晶点的测定和图形表达

水盐体系共晶点的数据可以为盐湖卤水低温加工工艺开发提供必要的理论依据,采用低温冷却法,针对四元同离子体系K⁺//Cl^-,SO₄^2-,NO₃^--H₂O和四元交互体系Na⁺,K⁺//SO₄^2-,NO₃^--H₂O及其相关的6个三元子体系,测定研究了其冰点、共晶点以及析盐规律,绘制出了共晶点温度-液相组成图。研究结果表明:通过测定多元水盐体系降温过程中的时间-温度图,可以判断盐类析出规律、测定冰和盐的共晶点温度;上述体系中,常温下存在的复盐钾芒硝,在共晶点温度下均不再出现,水盐体系相关系得以简化;用棱柱图可以简单直观地表达三元体系、四元同离子体系和四元交互体系的相、冰点或共晶点的温度和溶液组成的关系;在三元体系的共晶点温度-液相组成图中,存在两条单盐与冰的共晶线、一个两种盐与冰的共晶点、一个冰析出面;在四元同离子体系和四元交互体系共晶点温度-液相组成图中,分别有3个和4个单盐与冰的共晶面、3条和5条两种盐与冰的共晶线、1个和2个3种盐与冰的共晶点。     

Power law models as descriptors of the kinetics of complex systems: Temperature effects

The effects of temperature on power law models for the kinetics of parallel first order systems are studied. The variation of the empirical power law parameters with temperature provides information on the relationship between the rate constant and activation energy distributions; in particular. if the power law exponent increases with temperature, there is a positive correlation between the rate constants and the activation energies; if the power law exponent decreases with temperature, there is a negative correlation between the rate constants and the activation energies; Arrhenius plots will always be concave unless the activation energies for all the reactions are equal. Application of the techniques described here to data from the catalytic cracking of gas oil over LaY zeolite reveals a compensation effect among the reacting hydrocarbon species.     

On the prediction of diffusivities in multicomponent liquid systems

A method of prediction of diffusion coefficients in binary and multicomponent liquid systems is proposed. Comparative calculations, carried out for binary, ternary and quaternary systems have shown a significantly better agreement of the results obtained on the ground of the suggested method with the experimental data available than in the case of the method based on the theory of ultimate volume[6].     

Formation and aging of colloidal multicomponent systems

The influence of the cationic surfactant, n-dodecylamine nitrate, on negative silver iodide sols has been studied in a range of qualitative and quantitative changes in surfactant aqueous solutions (in the neighbourhood of the c.m.c.). Silver iodide was formed and aged from concentration to concentration under different conditions. The role of surfactant in silver iodide formation and aging are discussed.     

An empirical method for calculating vapor-liquid critical points of multicomponent mixtures

The critical temperatures and critical pressures of binary mixtures involving nitrogen, carbon dioxide, hydrogen sulfide, and paraffinic hydrocarbons ranging from methane through n-heptane as calculated from the Peng—Robinson equation of state have been correlated using a modified compositional function of the Wilson equation in conjunction with the pseudo-critical properties. The resulting parameters have been used to predict the critical properties of sixty-one multicomponent systems. The empirically calculated critical temperatures and critical pressures deviate from the rigorously calculated values by an average of less than 1 K and 100 kPa, respectively.     

Folds on the temperature surfaces of heterogeneous multicomponent liquid-vapor systems

Regularities in the behavior of folds on the surface of equilibrium temperatures for multicomponent two-phase mixtures are studied. The concept of the multiplicity of a fold on the surface of temperatures is introduced.     

Dimensional analysis of the detergency process for systems containing multicomponent soils

Dimensional analysis of the detergency process has been extended from soil-surfactant systems which contain a single polar soil to those with binary and ternary component soils which contain a nonpolar ingredient. This was made possible by replacement of the soil dipole moment variable by the proportional square root of orientation polarization (P_o) and by establishment of the validity of the empirical volume fraction additivity of the ingredient P₀ values of binary polar—polar mixtures by using the classical dilute solution—solute (P₂) extrapolation procedure with a chemical oscillometer.     

Development of multisensor systems based on chalcogenide thin film chemical sensors for the simultaneous multicomponent analysis of metal ions in complex solutions

A new type of thin film chemical microsensors based on chalcogenide glass-sensitive materials was developed by means of silicon planar technology and pulsed laser deposition technique. These miniaturised ion-selective electrodes (ISEs) exhibit Nernstian responses over five concentration decades with detection limits of 1×10⁻⁷ mol/l towards the primary ions Cu and Pb, and 4×10⁻⁷ and 3×10⁻⁵ mol/l towards Cd and Tl, respectively. The thin film microsensors have been shown to be perspective instruments for the simultaneous multicomponent analysis of complex liquid media based on the principles of an ‘electronic tongue’ device. Incorporating the thin film sensors into a sensor array allowed the multicomponent analysis of heavy metal-ion species (Pb²⁺, Cd²⁺, Zn²⁺ and Fe³⁺). The concentrations of Pb²⁺-, Cd²⁺- and Zn²⁺-ions can be determined simultaneously by direct potentiometric measurements using a sensor array of seven all-solid-state thin film chemical microsensors with an accuracy of 15–30%. The sensor array allows overcoming the problem of an insufficient selectivity of single sensors. The suggested microsystem-compatible fabrication technique favours a further miniaturisation, aimed to a fully integrated electrochemical microsystem.     

Non-additive voltammetric currents from multicomponent systems of redox-active substances

Mixtures of two redox-active compounds with dissimilar diffusion coefficients produce non-additive mass-transfer limited currents. Similarly, in the potential range where three redox-active species, decamethylferrocene (dMeFc), ferrocene (Fc) and N-methylphenothiazine (MePTZ), are oxidized simultaneously with rates controlled by linear diffusion, electrogenerated radicals diffusing outwards from the electrode react with original species diffusing towards the electrode from the bulk; thus, Fc⁺ reacts with dMeFc producing Fc and dMeFc⁺, while MePTZ⁺ reacts with both Fc and dMeFc producing MePTZ together with Fc⁺ and dMeFc⁺. These processes replace the flux of dMeFc with Fc at the second current plateau (referring to normal pulse voltammetry), and the fluxes of both dMeFc and Fc with MePTZ at the third plateau. Analogous results have been obtained and analyzed with two other multicomponent systems undergoing multiple sequential electron transfers, namely dMeFc/Fc/TPTA and dMeFc/TTF (TPTA: tri-N-p-tolylamine; TTF: tetrathiafulvalene). Since the diffusion coefficients of the three species are different, the mass-transfer limited currents of the second and third oxidation waves are not equal to the sum of the currents that each component would have produced if it were in the solution alone. Numerical simulations of the experimental voltammograms using diffusion coefficients measured independently support this mechanism. Multicomponent systems are encountered frequently in practice and our results identify one significant (∼10%) source of error in quantitative voltammetric analysis. Ways around the problem are summarized in the conclusions section.     

复合凝聚法制备双相核材料纳米胶囊

以明胶-阿拉伯树胶为壁材,采用复合凝聚法制备了双相核材料的纳米胶囊,其内包覆改性TiO2/四氯乙烯双相分散体系。讨论了制备过程中,各参数对纳米胶囊粒径的影响,并采用扫描电镜及透射电镜观察了纳米胶囊的粒径分布及形貌。结果表明,制备的纳米胶囊囊壁光滑、均匀,具有窄的粒径分布。双相分散体系被包覆于纳米胶囊内,且TiO2纳米颗粒粒径约为50 nm。所制备的纳米胶囊平均粒径约为0.96μm,囊壁厚度约为18 nm。     

Behaviour of sulphonated EPDM in multicomponent/multiphase systems

The interactions of polymers containing low levels of ionic groups in selected environments has been a relatively unexplored area. For selected applications, it is important to understand how these polymers interact with a variety of cosolvents and/or solid substrates. The purpose of this study is aimed towards gaining an insight into these interactions. The solution behaviour of various inorganic salts (calcium, magnesium and zinc) of sulphonated ethylene-propylene diene monomers (EPDM) was investigated in order to determine the relative strength of interactions between sulphonate groups, cosolvents of varying structure and substrates possessing a specific chemistry. Viscosity-time-temperature relationships show that the properties of the polymer-cosolvent solutions are controlled to a large extent by ionic forces. The magnitude of these forces is dependent upon the nature of the cation and the specific molecular structure of the cosolvent. The weakest interaction was found to occur between the calcium neutralized polymer and cosolvent, while magnesium and zinc neutralized samples showed progressively stronger interactions. The extent to which these ionic forces can interact with their ‘environment’ depends upon the molecular structure of the cosolvent, in particular the structure of the polar ‘head’ is of paramount importance. These become even more apparent when the polymer and polymer-cosolvent complex is permitted to adsorb onto insoluble, solid substrates possessing a specific surface chemistry (in this instance, metal sulphate substrates). The results show that if the cation on the sulphonated polymer is identical to the cation contained in the metal sulphate, the adsorption of polymer is maximized (i.e., like prefers like). In addition, the nature of the cation is very important in determining the extent and, most probably, the mechanism of adsorption.     

多组分精馏分离过程中的最佳回流比控制

针对１,２,４－三氯苯的精制过程,建立以产品质量为控制目标的状态控制模型,采用动态回流比控制技术,实现了多组分分离的最佳回汉比操作及最小能耗优化控制。     

Percolation estimation of the conductivity and elasticity of heterogeneous two-phase systems

Physical and mechanical properties of binary composites estimated by the percolation method, which takes into account the particle-size ratio of the filler and the matrix phase and the dispersity and particle shape of the filler.     

Use of functional transformations in the solution of systems of nonlinear equations having singular or near singular jacobians

A functional transformation method has been developed for use with the Newton's method for solving single algebraic equations [f(x) = 0] and systems of algebraic equations (f(x) = 0] having either maxima, minima, turning points, or singular (or near singular) Jacobians. The functional transformation method is used to trace the path of a function through a maximum or minimum. If in the course of searching for the x that makes f(x) = 0 an x_k is found for which f'(x_k) = 0 or for which /f(x_k)/ > /f(xk−1)/, a new function F(x) having the same solution as f(x) but a different slope is defined such that /F(x_k)/ < /F(x_k−1/. After having passed through the maximum or minimum, the trial proceduce returns to the original function f(x). For the numerical examples presented herein, the performance of the functional transformation method was found to be superior to that of several other well known numerical methods.     

Application of the concentration-dependent surface diffusion model on the multicomponent fixed-bed adsorption systems

The ability of bone char to adsorb three metal ions, namely, cadmium, copper and zinc, from effluents in fixed beds has been studied. Two binary metal ion sorption systems, Cd+Cu and Cu+Zn, have been investigated. The variables studied include metal ion solution flowrate, initial metal ion concentration, and bone char particle size bed height. The experimental breakthrough curves for each binary system were measured at five bed heights.A multicomponent film-surface diffusion model has been developed to predict the breakthrough curves by incorporating the IAS for both the Langmuir and the Sips equations, since they both correlate the single component equilibrium isotherm data well. A novel development is the modification of the solution methodology, previously restricted to a constant diffusivity, to incorporate a variable diffusivity correlated with adsorbent coverage by the constant self-diffusivity. The self-diffusivities for the metal ions have been evaluated.