Advances in numerical methods for the solution of population balance equations for disperse phase systems

Accurate prediction of the evolution of particle size distribution is critical to determining the dynamic flow structure of a disperse phase system. A population balance equation (PBE), a non-linear hyperbolic equation of the number density function, is usually employed to describe the micro-behavior (aggregation, breakage, growth, etc.) of a disperse phase and its effect on particle size distribution. Numerical solution is the only choice in most cases. In this paper, three different numerical methods (direct discretization methods, Monte Carlo methods, and moment methods) for the solution of a PBE are evaluated with regard to their ease of implementation, computational load and numerical accuracy. Special attention is paid to the relatively new and superior moment methods including quadrature method of moments (QMOM), direct quadrature method of moments (DQMOM), modified quadrature method of moments (M-QMOM), adaptive direct quadrature method of moments (ADQMOM), fixed pivot quadrature method of moments (FPQMOM), moving particle ensemble method (MPEM) and local fixed pivot quadrature method of moments (LFPQMOM). The prospects of these methods are discussed in the final section, based on their individual merits and current state of development of the field. Supported by the National Basic Research Program of China (Grant No. 2004CB720208), the National Natural Science Foundation of China (Grant Nos. 40675011 & 10872159), and the Key Laboratory of Mechanics on Disaster and Environment in Western China     

Numerical and similarity solutions for reversible population balance equations with size-dependent rates

Population balance equations (PBEs) for reversible aggregation-fragmentation processes are important to particle agglomeration and dissolution, polymerization and degradation, liquid droplet coalescence and breakup, and floc coagulation and disintegration. Moment solutions provide convenient solutions to the PBEs, including steady state and similarity solutions, but may not be feasible for complex forms of size-dependent rate coefficients and stoichiometric kernels. Numeric solutions are thus necessary not only for applications, but also for the study of the mathematics of PBEs. Here we propose a numerical method to solve PBEs and compare the results to moment solutions. The numeric results are consistent with known steady state and asymptotic long-time similarity solutions and show how processes can be approximated by self-similar formulations.     

A discretization method for computing chain length distributions

The method of Kumar and Ramkrishna is a numerical technique to solve population balance equations (PBEs) by discretization while preserving two moments of the distribution. When the method is used to calculate chain length distributions in polymerization reactions, the polydispersity, which depends on the first three moments of the distribution, cannot be estimated correctly. This work presents a modification of the method that allows to preserve three moments and thus calculate the polydispersity correctly, independently of the number of grid points. The modified method is applied to a model of controlled radical polymerization via RAFT and compared with the original one.     

A dynamical Lie algebraic mehtod for quantum reactive scattering

Ｒａｐｉｄｐｒｏｇｒｅｓｓｉｎｔｈｅｔｈｅｏｒｙｏｆｑｕａｎｔｕｍｒｅａｃｔｉｖｅｓｃａｔｔｅｒｉｎｇｈａｓｂｅｅｎｍａｄｅｉｎｔｈｅｐａｓｔｆｅｗｙｅａｒｓ.Ａｓａｒｅｓｕｌｔｏｆｔｈｅｐｒｏｇｒｅｓｓｏｎｅｃａｎｎｏｗｃａｌｃｕｌａｔｅｅｘａｃｔｓｔａｔｅ＿ｔｏｓｔａｔｅｒｅａｃｔｉｏｎｃｒｏｓｓｓｅｃｔｉｏｎｓｆｏｒａｆｅｗｆｕｎｄａｍｅｎｔａｌｒｅａｃｔｉｏｎｓ.Ａｍｏｎｇｖａｒｉｏｕｓｆｏｒｍｕｌａｔｉｏｎｓｏｆｔｈｅｔｈｅｏｒｅｔｉｃａｌａｐｐｒｏａｃｈ,ｔｈｅＳｍａｔｒｉｘＫｏｈｎｖ…     

Honeycomb-patterned films of polystyrene/poly(ethylene glycol): preparation,surface aggregation and protein adsorption

Highly ordered honeycomb-patterned polystyrene (PS)/poly(ethylene glycol) (PEG) films were prepared by a water-assisted method using an improved setup, which facilitated the formation of films with higher regularity, better reproducibility, and larger area of honeycomb structures. Surface aggregation of hydrophilic PEG and adsorption of bovine serum albumin (BSA) on the honeycomb-patterned films were investigated. Field emission scanning electron microscopy (FESEM) and atomic force microscopy (AFM) were used to observe the surface morphologies of the films before and after being rinsed with water. As confirmed by the FESEM images and the AFM phase images, PEG was enriched in the pores and could be gradually removed by water. The adsorption of fluorescence-labeled BSA on the films was studied in visual form using laser scanning confocal microscopy. Results clearly demonstrated that the protein-resistant PEG was selectively enriched in the pores. This water-assisted method may be a latent tool to prepare honeycomb-patterned biofunctional surfaces. Supported by the National Natural Science Foundation of China (Grant No. 50803053), the National Natural Science Foundation of China for Distinguished Young Scholars (Grant No. 50625309), the National Postdoctoral Science Foundation of China (Grant Nos. 20070421172 & 20081466) and the National Undergraduate Innovative Test Program     

Vapor Nucleation and Droplet Growth: Cluster Distribution Kinetics for Open and Closed Systems

A theory based on cluster distribution kinetics for single-monomer addition and dissociation is presented as a framework for homogeneous and heterogeneous vapor nucleation and growth dynamics. For continuous cluster and monomer distributions in a well-mixed non-steady-state flow system, population (mass) balance equations yield moment equations for the cluster mass moments. Nuclei are either homogeneously generated or heterogeneously seeded, and subsequent cluster growth occurs by reversible condensation of vapor monomers. The zeroth moment is the number (or moles) of clusters, the first moment is cluster mass, and the second moment gives cluster-size variance. Solutions are proposed for steady-state flow (open) and non-steady-state batch (closed) systems. Experimental data are interpreted by recognizing that droplets typically observed in nucleation experiments have grown much larger than their nuclei. This allows resolution of the large temperature-dependent discrepancy between experiment and classical nucleation theory. Copyright 2000 Academic Press.     

Population Balance Modeling with Coupled Agglomeration and Disintegration Processes for TiO2 Nanoparticles Formation and Experimental Validation

Particle size distribution of nanoparticles plays an important role in modelling many scientific and engineering problems. In this article, we proposed a Finite Volume Method (FVM) to model TiO₂ nanoparticles formation using population balance equations (PBEs) by incorporating the simultaneous agglomeration and disintegration processes. The superposition of the PBEs for agglomeration and disintegration with different kernels leads to a system of partial-integro differential equations, which are numerically solved by using FVM. The precipitation of TiO₂ nanoparticles in the batch reactor is studied experimentally as well as by numerical simulations based on Austin and Diemer disintegration kernels and Shear agglomeration kernel. Finally, the capability of the precipitation model is evaluated and the experimental results on particle sizes are compared with the numerical results.

     

Adsorptive desulfurization of diesel with mesoporous aluminosilicates

Mesoporous aluminosilicates (MAS) bearing microporous zeolite units and mesoporous structures were synthesized by the hydrothermal method. Adsorptive desulfurization ability of model oil and hydrotreated diesel was studied. The effects of template concentration, crystalization time and calcination time were investigated. The desulfurization ability of adsorbents was improved by transitional metal ion-exchanging. The adsorptive desulfurization of diesel was carried out on a fixed-bed system. The results show that the adsorptive capacity is MAS>MCM-41>NaY. The improvement of desulfurization ability of MAS by Cu⁺ is more significant than that of Ag⁺. Supported by National Basic Research Program of China (Grant No. 2006CB202507), National High-tech R&D Program (Grant No. 2006AA02Z209), and the National Natural Science Foundation of China (Grant No. 20806086)     

Unprecedented synthesis of chiral calix[4](aza)crowns and its potent encapsulating methanol

Unprecedented synthesis of chiral (aza)crown ethers of calix[4]arene derivatives bearing a carboxyl amide bridge was described. The synthesis proceeds through condensation of the corresponding dinitriles with optically active 1,2-aminoalcohols,and is catalyzed by the ZnCl2 Lewis acid at elevated temperature in a very efficient one-pot process. The cavity of calix[4](aza)crowns can encapsulate methanol molecules by O—H...π interaction,which has been confirmed by X-ray crystal structures and ESI-MS.     

In situ synthesis of DNA micro-arrays using typography technique

A novel typography technique was developed to in situ synthesize oligonucleotide arrays on glass slide, which has the celerity, high spatial resolution, lower cost, reliable operation, and high synthetic efficiency. The principle and process of the typography technique for fabricating gene-chips have been described in detail. A suit of poly(terafluoroethylene) devices for synthesizing oligonucleotide arrays were designed and prepared, and the fiber tubes with a number of nano-or micron-channels were employed. The oligonucleotide arrays of 16 and 160 features with four different probes were synthesized using the typography technique. The four specific oligonucleotide probes including the matched and the mismatched by the fluorescent target sequence gave obviously different hybridization fluorescent signals. It was indicated that the gene-chip fabricated by the typography method could be used to rapidly screen single-nucleotide polymorphisms (SNP) and to detect mutations. Supported by the National Natural Science Foundation of China (Grant Nos. 60571032, 60571001, 90606027 and 60121101), the National Hi-Tech Research and Development Program of China (Grant No. 2006AA03Z357), the Natural Science Foundation of Hunan Province (Grant Nos. 04jj40023 and 06JJ4012) and the Natural Science Foundation of Guangdong Province (Grant No. 04008782)     

Preparation of electrolyte membranes for micro tubular solid oxide fuel cells

Yttria-stabilized zirconia (YSZ) micro tubular electrolyte membranes for solid oxide fuel cells (SOFCs) were prepared via the combined wet phase inversion and sintering technique. The as-derived YSZ mi- cro tubes consist of a thin dense skin layer and a thick porous layer that can serve as the electrode of fuel cells. The dense and the porous electrolyte layers have the thickness of 3-5 μm and 70-90 μm, respectively, while the inner surface porosity of the porous layer is higher than 28.1%. The two layers are perfectly integrated together to preclude the crack or flake of electrolyte film from the electrode. The presented method possesses distinct advantages such as technological simplicity, low cost and high reliability, and thus provides a new route for the preparation of micro tubular SOFCs.     

Recent developments in intelligent biomedical polymers

Intelligent polymers or stimuli-responsive polymers may exhibit distinct transitions in physical-chemical properties, including conformation, polarity, phase structure and chemical composition in response to changes in environmental stimuli. Due to their unique 'intelligent' characteristics, stimuli-sensitive polymers have found a wide variety of applications in biomedical and nanotechnological fields. This review focuses on the recent developments in biomedical application of intelligent polymer systems, s...     

Sulfonate-based fluorescent probes for imaging hydrogen peroxide in living cells

Based on the mechanism of H₂O₂-mediated hydrolysis of sulfonates, two fluorescein disulfonates compounds (FS-1 and FS-2) were designed and synthesized as the highly selective and sensitive fluorescent probes for imaging H₂O₂ in living cells. The probes were detected with elemental analysis, IR, ¹H NMR and ¹³C NMR. Upon reaction with H₂O₂, the probes exhibit strong fluorescence responses and high selectivity for H₂O₂ over other reactive oxygen species and some biological compounds. Furthermore, the sulfonate-based probes, as novel fluorescent reagents, are cell-permeable and can detect micromolar changes in H₂O₂ concentrations in living cells by using confocal microscopy. Supported by the National Basic Research Program of China (Grant No. 2007CB936000), the National Natural Science Funds for Distinguished Young Scholar (Grant No. 20725518), Major Program of the National Natural Science Foundation of China (Grant No. 90713019), the National Natural Science Foundation of China (Grant No. 20875057), the Natural Science Foundation of Shandong Province, China (Grant No. Y2007B02), and the Science and Technology Development Programs of Shandong Province, China (Grant No. 2008GG30003012)     

Intrinsic oxidation kinetics of sulfite catalyzed by peracetic acid under different water quality and light conditions

Oxidation of sulfite is an important process in wet flue gas desulfurization. Using highly purified water or distilled water as a reaction medium and a transparent or an opaque intermittent reaction apparatus, the intrinsic oxidation kinetics of sulfite catalyzed by peracetic acid was investigated under four different conditions. The reaction order of the reagents and the activation energy were obtained. The results indicate that water quality and light have no obvious effects on the reaction order and activation energy, but have an influence on the reaction rate constant. The mechanism of the intrinsic reaction is proposed. The results derived with this mechanism are in good agreement with the experimental results. Supported by the National Basic Research Program of China (Grant No. JK00020), the Doctor Research Fund from North China Electric Power University (Grant No. 200612008), and the National High Technology Research and Development Program of China (Grant No. 2007AA061703)     

A three-dimensional vortex microsystem designed and fabricated for controllable mixing

A three-dimensional micromixer is designed and fabricated by using glass-poly(dimethylsiloxane) (PDMS) hybridized materials. The improvement of the fabrication process makes the micromixer endure much higher flow rate. Based on the self-rotation effect of the fluid, the fast mixing can be achieved. The mixing process is evaluated by connecting the micromixer to a UV-Vis detector. The results show that by adjusting the infuse flow rate, the mixing process can be accurately controlled. Supported by the National Natural Science Foundation of China (Grant Nos. 20735002 & 29877019) and the Key Natural Science Foundation of Fujian Province, China (Grant No. D0520001)     

Research of the relationship of intracellular acidification and apoptosis in Hela cells based on pH nanosensors

In this paper,the relationship of intracellular acidification and apoptosis in Hela cells induced by vin-cristine sulfate has been studied by use of the ratiometric pH nanosensors that have been developed by our group,employing fluorescein isothiocyanate(FITC) doped as the pH-sensitive dye and Tris(2,2'-bipyidyl) dichlororuthenium(II) hexahydrate(RuBpy) doped as reference dye. The pH change of the Hela cells induced by vincristine sulfate has been monitored in vivo,in situ and real time by use of the ratiometric pH nanosensors. The experimental results show that the pH of the apoptotic Hela cells induced by vincristine sulfate has been acidified from 7.11 to 6.51,and the percentage of intra-cellular acidification is correlated with the induced concentration and incubation time of the vincristine sulfate. The further study of the percentage of intracellular acidification and the percentage of apop-tosis of Hela cells at the same time reveals that apoptosis of Hela cells induced by vincristine sulfate is preceded by intracellular acidification. These results would provide theoretical foundation for the therapy of cancer through interfering the pH of cells by use of vincristine sulfate or other anti-cancer drugs.     

Peptidomimetics and metalloprotease inhibitors as anticancer drugs

Peptidomimetics with three types, as the structural or functional mimetics of natural active peptides, can preserve the bioactivity and improve the bioavailability and the specificity towards the targets of the lead peptides. Peptidomimetics of high bioactivity can be designed through various ways including conformation restriction, modification and non-peptide design. Recently the concentration on the development of cancer chemotherapeutic drugs was transferred from cytotoxic drugs to target-based drugs, and many proteases and peptidases that play key roles in the process of tumor genesis and development was discovered, which means that peptidomimetics as potential cancer chemotherapeutic drugs should be paid close attention to. Our laboratory has focused on the development of small-molecule peptidomimetic inhibitors of APN, MMPs and HDACs as target-based anticancer agents. These three zinc-dependent metalloproteinases play very important roles in the process of tumor genesis, invasion, metastasis, angiogenesis and matrix degradation, so small-molecule peptidomimetic inhibitors based on them would be quite potential in the development of chemotherapeutic drugs with high selectivity. Supported by the National High Technology Research and Development Program of China (863 Project) (Grant No. 2007AA02Z314), the National Natural Science Foundation of China (Grant Nos. 90713041 & 30772654), and the Doctoral Fund of Ministry of Education of China (Grant No. 20060422029)     

Statistical theory for hydrogen bonding fluid system of AaDd type (Ⅱ): Properties of hydrogen bonding networks

Making use of the invariant property of the equilibrium size distribution of the hydrogen bonding clusters formed in hydrogen bonding system of A_aD_d type, the analytical expressions of the free energy in pregel and postgel regimes are obtained. Then the gel free energy and the scaling behavior of the number of hydrogen bonds in gel phase near the critical point are investigated to give the corresponding scaling exponents and scaling law. Meanwhile, some properties of intermolecular and intramolecular hydrogen bonds in the system, sol and gel phases are discussed. As a result, the explicit relationship between the number of intramolecular hydrogen bonds and hydrogen bonding degree is obtained. Supported by the National Natural Science Foundation of China (Grant Nos. 20303006 and 20574016), the Natural Science Foundation of Hebei Province (Grant Nos. B2006000959 and B2004000093) and the Natural Science Foundation of Education Committee of Hebei Province (Grant No. 2003101)     

Application of the ABEEM/MM model in studying the properties of the water clusters (H2O) n ( n =7?10)

ABEEM/MM model has been applied to compute the various properties characterizing water clusters (H₂O) _n (n = 7−10), such as optimized geometries, the hydrogen bonds number, cluster interaction energies, stabilities, ABEEM charge distributions, dipole moments, structural parameters, and so on, and to describe the transition reflected by the hexamer region from two-dimensional (from dimer to pentamer) to three-dimensional structures (for clusters larger than the hexamer). Supported by the National Natural Science Foundation of China (Grant No. 20373021)     

Highly sensitive and selective ratiometric fluorescent copper sensors: Different binding affinities modulated by three separate side chains of naphthalimide

A series of compounds 1-11 with different side chains of naphthalimide as fluorescent copper sensors were designed and synthesized. Compounds 1, 9, 10 and 11 presented a high selectivity to Cu2+ in a neutral aqueous environment. Here 1, 9 and 10 showed selectivity and affinity to Cu2+ with an association constant of about ～106. It gave somewhat response to Ag+, Co2+, Ni2+ and Fe2+ while 1 detected copper. 9 and 10 displayed better selectivity by changing their hydrophobic side chains to the hydrophilic ones...