Numerical Study of Extension Rheological Properties of Polymer Solutions using FENE Model

Dilute polymer solutions represent a complex rheological response. A finitely extensible nonlinear elastic (FENE) bead-spring chain model for dilute solutions of polymer molecules in a Newtonian solvent is employed to describe the bead-bead interaction within a molecule. Brownian dynamics simulation is used to capture the most important rheological properties of dilute polymer solutions. A program based on this model is developed to simulate the steady elongational flow and inception of elongational flow, and the flow situations and the rheological material functions are investigated. Semi-implicit predictor-corrector methods are introduced and the results qualitatively agree with rheological theory.     

Use of cake deposition to improve the efficiency of ultra- and microfiltration plants

Fundamental principles and topics of a new approach to designing ultra- and microfiltration plants in which cake deposition and its control are used to improve the membrane filtration efficiency are discussed. A general phenomenological mathematical model for the process of depth membrane filtration, which was suggested by the new approach, is formulated and methods of its numerical and approximate solutions are described. The available particular solutions to the DMF model are analyzed and classified, and recommendations for their practical use are given. The use of the new approach for increasing the efficiency of existing deadend outside-in hollow fiber membrane filters is also discussed. A general mathematical model is formulated for this type of deadend filters and methods of its numerical and approximate solutions are discussed. It is shown that the highest efficiency of outside-in hollow fiber membrane filters can be achieved when the collection efficiency of the membrane surface with respect to suspended particles is highest.     

Expression and analysis of pore fluids from hardened cement pastes and mortars

A device is described that has been used for several years for expression pf pore solution from hardened portland cement pastes and mortars. Particulars with respect to the design, fabrication, and operation of such equipment are given, and methods for the analysis of the resulting small volumes of pore solutions are briefly discussed. It is believed that the compositions of the pore solutions obtained are representative of that of the bulk of the pore solution within the paste or mortar from which the solutions have been obtained.     

SMB色谱分离过程计算机仿真

针对模拟移动床(SMB)综合速率模型，采用有限元法和正交配点法分别对柱向和颗粒径向模型进行离散化，利用MatLab ODE求解器对SMB过程进行数值求解。通过仿真，验证了该方法的可行性。     

Application of genetic algorithm in calculation of the phase behavior of binary and ternary polymer solutions

A genetic algorithm as an optimization procedure has been developed to predict the phase behavior of polymer solutions. The phase equilibrium diagrams of binary and ternary polymer solutions have been determined using the appropriate form of Flory–Huggins free-energy function for polymer solutions. A concentration and temperature dependent form of the interaction parameter has been used to reflect the effect of temperature and polymer properties in the free-energy form. The proposed genetic algorithm is applied to compare the phase behavior results of some typical polymer solutions with the results of the classical determination methods and then applied to some conventional ternary polymer solutions as polymer–solvent–nonsolvent systems. The proposed algorithm use a set of individual states as the initial chromosomes and uses the general rules as crossover, mutation, and with use of a fractional objective function determines the binodal points or the phase diagram boundaries of polymer solutions. The properties of an industrially relevant polymer solution, a polystyrene–cyclohexane solution, have been used to emphasize on the industrial application of the proposed algorithm. The algorithm has been used to predict the phase behavior of the two polymer–solvent–nonsolvent systems as polystyrene-butanone-methanol and polystyrene-butanone-propanol at three different temperatures and results show good agreement with the experimental observations. The algorithm also has the capability to predict both the concentration-independent and concentration-dependent interaction parameters among the different components. The genetic algorithm is an easy-to-use, state-of-art, and very fast optimization tool, and has very strong capability to solve nonlinear systems in chemical and polymer engineering topics.     

On the measurement of the real values of individual ionic activities: A chemical engineering perspective

This work demonstrates the perfect analogy between the standard method for determining activities in non-electrolyte mixtures and the method used for the determination of ionic activities in electrolyte solutions. For the case of electrolyte solutions, the general procedure of solving three equations with three unknowns is discussed and the reasons why this procedure failed to work for the case of KCl solutions are recapitulated. A modified iteration procedure implemented in this work gives convergence of the solution after three iterations. The crucial difference between eliminating the junction potential, by combination of independent equations, and the use of a proper estimate of its value is emphasized. A new model-free calibration procedure is proposed and sample calculations of K⁺ and Cl⁻ activities in KCl aqueous solutions are presented. Values of K⁺ and Cl⁻ activities in KCl aqueous solutions obtained by this new procedure and by a variety of other methods and researchers are compared.     

COMPOSITE NUMERICAL SOLUTIONS OF PARTIAL DIFFERENTIAL EQUATIONS Part I. Global Extrapolation

Composite techniques are developed for numerical solutions of partial differential equations (PDE's) by the combinations of different solutions. The combination can be global or local depending on the usage of the composite. A global composite is one in which the composite solution is not utilized in any continued calculations of the different numerical solutions. Global composites are space by space combinations, i.e., the solutions are obtained over the entire space of independent variables. For local combinations, on the other hand, the composite is used in the continued calculations of the different solutions. Therefore, the local procedure is a line by line algorithm where the different solutions are combined and become the initial values for the continued calculations of the different solutions.

Composites considered are (i) global extrapolation, (ii) local extrapolation and local stabilization, (iii) alternating direction methods, and (iv) acceleration. By extrapolation the solution over the space of independent variables is calculated and combined with solutions for successively smaller grid spacings, characterized by h_m. Global extrapolation is applied to the finite difference solution of PDE's and shown to be effective for reducing the truncation error (TE) of fixed difference methods. On the basis of computation time the spacing sequence h₀(m + 1) is shown to reduce the TE more efficiently than fco/2m for more than two extrapolations, where /i0 characterizes the largest spacing.     

A MATHEMATICAL MODEL CHARACTERIZING THE DIFFUSION PROPERTIES OF MICROCAPSULES

Composite techniques are developed for numerical solutions of partial differential equations (PDE's) by the combinations of different solutions. The combination can be global or local depending on the usage of the composite. A global composite is one in which the composite solution is not utilized in any continued calculations of the different numerical solutions. Global composites are space by space combinations, i.e., the solutions are obtained over the entire space of independent variables. For local combinations, on the other hand, the composite is used in the continued calculations of the different solutions. Therefore, the local procedure is a line by line algorithm where the different solutions are combined and become the initial values for the continued calculations of the different solutions.

Composites considered are (i) global extrapolation, (ii) local extrapolation and local stabilization, (iii) alternating direction methods, and (iv) acceleration. By extrapolation the solution over the space of independent variables is calculated and combined with solutions for successively smaller grid spacings, characterized by h_m . Global extrapolation is applied to the finite difference solution of PDE's and shown to be effective for reducing the truncation error (TE) of fixed difference methods. On the basis of computation time the spacing sequence h₀ (m + 1) is shown to reduce the TE more efficiently than fco/2m for more than two extrapolations, where /i0 characterizes the largest spacing.     

The crystallization of magnesium hydroxide

The thermodynamic association constant for the formation of the ion-pair MgOH⁺ in solutions of magnesium hydroxide has been studied by potentiometric and conductometric methods.The growth of magnesium hydroxide seed crystals in supersaturated solutions over a range of concentrations of magnesium and hydroxide ions and in the presence of phosphonate additives has been investigated by a precision conductance method. After a rapid initial surge of growth, an equation first order with respect to supersaturation can be used to explain the experimental data. A surface diffusion process is proposed as the controlling step in the crystallization process.     

Objects for MWR

A computational framework has been developed for step-by-step implementation of global spectral projection methods used for solving boundary-value problems and for subsequent analysis of solutions produced using the numerical techniques of this framework. A set of matlab-based functions corresponding to each step in a Galerkin discretization procedure has been developed with emphasis on simplifying the implementation of discretization methods for nonlinear, distributed-parameter system models in up to three-dimensional physical domains. A key feature of this computational approach is that a set of object classes were developed to facilitate implementation of the weighted residual methods (MWR) in an effort to make the connection between the solution procedures and modeling equations as clear as possible. The utility of the computational procedures is demonstrated through applications to two-dimensional reaction-diffusion and fluid flow problems, and a three-dimensional heat transfer model relevant to semiconductor manufacturing.     

Ion-resistive effect in surface layers of glasses and glass-ceramics in the Cu-As-Se and Cu-As-Te systems

A linear logarithmic dependence of the electrical resistance of glasses and glass-ceramics in semiconductor chalcogenide systems in cupric salt solutions on the cation content in the solution is established for the first time. The revealed effect can be used in chemical analysis for both fundamental and practical applications, in particular, for the development of chemical analysis methods.     

Several basic and practical aspects related to electrochemical deionization of water

We examine water desalination processes based on the electrosorption of ions onto activated carbon electrodes (capacitive deionization, CDI). A flow‐by operation mode was used (solutions flows within channels in the separator, parallel to the electrodes) in both continuous and stopped flow experiments. The different response of solutions containing more than 5000 ppm NaCl and dilute solutions (e.g., 1000 ppm NaCl) to the applied potential is discussed. The electrical current transients on potential steps were faster by two orders of magnitude than the resulting concentration transients due to the dynamics of these deionization processes and the properties of the cells used herein. Guidelines for the practical development of capacitive water deionization processes are discussed herein. It is assumed that for brackish water containing several thousands ppms of NaCl, CDI may be advantageous over competitive methods (e.g., reverse osmosis). © 2009 American Institute of Chemical Engineers AIChE J, 2010     

Additivity rules for the prediction of the density of aqueous solutions containing mixed-type solutes

Densities of ternary aqueous solutions of mixed-type solutes have been measured at 25°C to high concentration. Two methods, the one isopycnotic (same density) and the other based on ionic strength, have been used to predict the densities of these solutions. The isopycnotic method proved to be the more accurate. The two methods have been applied in reverse to calculate densities of supersaturated binary aqueous solutions of NaCl and KCl. The methods give concordant results for each salt Deviation parameters for the methods are presented, with a discussion of their use.     

Additivity rules for the prediction of the density of aqueous solutions containing mixed-type solutes

Densities of ternary aqueous solutions of mixed-type solutes have been measured at 25°C to high concentration. Two methods, the one isopycnotic (same density) and the other based on ionic strength, have been used to predict the densities of these solutions. The isopycnotic method proved to be the more accurate. The two methods have been applied in reverse to calculate densities of supersaturated binary aqueous solutions of NaCl and KCl. The methods give concordant results for each salt Deviation parameters for the methods are presented, with a discussion of their use.     

Applications of set theoretic methods to color systems

A vector-space approach to color systems has been shown to be useful in describing metameric effects and producing metamers under different illuminations. The vector-space approach has also been used to describe color scanning and reproduction systems. This article extends the applications presented in previous work by introducing set theoretic concepts which allow the addition of realistic constraints. The set theoretic methods allow the full range of solutions of color problems to be explored by allowing a set of solutions to a particular problem formulation. The applications discussed here include producing realizable metamers and the design of scanning filters.     

Numerical methods for the simulation of the settling of flocculated suspensions

For one space dimension, the phenomenological theory of sedimentation of flocculated suspensions yields a model that consists of an initial-boundary value problem for a second order partial differential equation of mixed hyperbolic–parabolic type. Due to the mixed hyperbolic-parabolic nature of the model, its solutions may be discontinuous and difficulties arise if one tries to construct these solutions by classical numerical methods. In this paper we present and elaborate on numerical methods that can be used to correctly simulate this model, i.e. conservative methods satisfying a discrete entropy principle. Included in our discussion are finite difference methods and methods based on operator splitting. In particular, the operator splitting methods are used to simulate the settling of flocculated suspensions.     

Dissolution of a Stationary Bubble in a Glassmelt with a Reversible Chemical Reaction: Rapid Forward Reaction Rate Constant

The effects of a reversible chemical reaction on the dissolution of a stationary gas bubble in a glassmelt are considered. The governing equations for a model system are presented and analyzed for a variety of the controlling parameters. Approximation methods are used to obtain analytical results for the bubble radius shrinkage rate. These results are compared to numerical solutions of the complete governing equations. A comparison is made between the influence of reversible and irreversible reactions on gas bubble dissolution behavior.     

A novel algorithm for solving population balance equations: the parallel parent and daughter classes. Derivation, analysis and testing

A novel numerical method, the parallel parent and daughter classes (PPDC) technique, for solving population balance equations (PBEs) is presented in this paper. In many practical applications, the PBE of particles under investigation is coupled with the thermo-fluid dynamics of the surrounding fluid. Hence, the PBE needs to be implemented in a computational fluid dynamics (CFD) code, which leads to an additional computational load. The computational cost becomes intractable when techniques such as methods of classes (CM) or Monte Carlo method are used. Quadrature method of moments (QMOM) and direct quadrature method of moments (DQMOM) are accurate and require a relatively low additional computational cost when applied to CFD. The PPDC is shown to be as accurate as QMOM and DQMOM, and even more accurate in some cases, when the same number of classes is used. In the present work, the PPDC technique has been derived and tested. This technique can be used for solving a wide class of problems involving PBE such as polymerization, aerosol dynamics, bubble columns, etc. Numerical simulations have been carried out on aggregation processes with different kernels and on simultaneous aggregation and breakage processes. The numerical predictions are compared either with analytical solutions, when available, or with the numerical solutions obtained by methods of classes.     

Medical hydrogels based on bioactive compounds. Synthesis,properties, and possible application for preparing bactericidal materials

Several physicochemical analytical methods were used to study aqueous solutions and hydrogels based on L-cysteine and silver nitrate. It was found that anions played a decisive role in forming the threedimensional gel-network in dilute silver-cysteine solutions. The ability to use silver-cysteine solutions and hydrogels to prepare bactericidal fibers and fabrics was examined.     

On nonaqueous electrochemical behavior of titanium and Ti compounds

In this study, we examined the electrochemical behavior of titanium and Ti⁴⁺ compounds in THF solutions. Tetra butyl ammonium chloride (TBACl) was used as supporting electrolyte in order to increase the ionic conductivity of the solutions. Electrodeposition of pure titanium could not be obtained. A variety of analytical techniques have been used in conjunction with electrochemical methods in order to analyze the reduction process of Ti⁴⁺. These included Raman and UV-vis spectroscopy, ICP and CHNS elemental analyses. Ti⁴⁺ is being reduced to Ti³⁺ in TiCl₄/THF/TBACl solutions.In addition we show that metallic titanium can be electrochemically dissolved from an organo-metallic electrolyte solution comprising EtAlCl₂ and LiCl in THF. The product is Ti⁴⁺. While LiCl is insoluble in THF it reacts with EtAlCl₂ to form ionic species. Hence, these solutions possessed reasonable ionic conductivity.We could not obtain electroactive Ti⁴⁺ with TiBr₄ or TiI₄ as starting materials, in similar solutions.