Diffusion and Brownian motion in Lagrangian coordinates

In this paper we consider the convection-diffusion problem of a passive scalar in Lagrangian coordinates, i.e., in a coordinate system fixed on fluid particles. Both the convection-diffusion partial differential equation and the Langevin equation are expressed in Lagrangian coordinates and are shown to be equivalent for uniform, isotropic diffusion. The Lagrangian diffusivity is proportional to the square of the relative change of surface area and is related to the Eulerian diffusivity through the deformation gradient tensor. Associated with the initial value problem, we relate the Eulerian to the Lagrangian effective diffusivities (net spreading), validate the relation for the case of linear flow fields, and infer a relation for general flow fields. Associated with the boundary value problem, if the scalar transport problem possesses a time-independent solution in Lagrangian coordinates and the boundary conditions are prescribed on a material surface/interface, then the net mass transport is proportional to the diffusion coefficient. This can be also shown to be true for large Peclet number and time-periodic flow fields, i.e., closed pathlines. This agrees with results for heat transfer at high Peclet numbers across closed streamlines.     

Pyridylazulenes: synthesis, color changes, and structure of the colored product

A facile method for the synthesis of 1- and 2-pyridylazulenes, and of 1,3-dipyridylazulenes, is described. Color and spectral changes of these pyridylazulenes upon the addition of either acid or metal ions were investigated in detail. The color changed from blue to red upon the addition of trifluoroacetic acid or soft metal ions, depending on the substitution patterns of the pyridyl group on the azulene skeleton. The structures of the protonated or coordinated products were examined on the basis of the spectral data. It was found that the protonation or coordination of metal ions occurred on the nitrogen atom of the pyridine ring, but not on the carbon atom of azulene ring. The transition intervals of several pyridylazulenes for use as pH indicators were also determined.     

Unsupervised Image Segmentation Using Hierarchical Clustering

In the analysis of a medical image database aimed at formulating useful knowledge for image diagnosis requires an unsupervised image processing technique without preconceived knowledge. In this paper, we propose a method for unsupervised image segmentation, which is suitable for finding the features contained in an image. A small region around each pixel is considered as a pattern vector, and the set of pattern vectors acquired from the whole image is classified using the hierarchical clustering technique. In hierarchical clustering, the classification of pattern vectors is divided into two clusters at each node according to the statistical criterion based on the entropy in thermodynamics. Results of the test image generated by the Markov random field (MRF) model and real medical images photomicrographs of a colon tumor are shown.     

Simulation of an ultrafiltration process of bovine serum albumin in hollow-fiber membranes

This work presents a numerical simulation of an ultrafiltration process of bovine serum albumin in solution, using hollow-fiber membranes. Such membranes are constituted of tiny polymer cylinders disposed in a tube-and-shell arrangement. The concentrate flows through the interior of the fibers and the pure solvent is recovered in the shell, assuming perfect solute rejection. In modeling the process, the flow of concentrate inside the fibers was considered to be laminar, with constant density, viscosity and solute diffusivity. Axial diffusion and angular effects were ignored. The model combines the effect of concentration polarization and adsorption, which are the two main limiting phenomena in ultrafiltration processes. The pressure on the shell side was considered constant and inside the fibers a linear pressure profile, dependent on the axial position, was adopted. The solution of the problem was achieved with the method of orthogonal collocation, with adequate choice of the weight function in the radial direction. In the axial direction, a finite-difference method was used. The numerical results were compared with experimental data available in the literature.     

Synthesis of polymers in aqueous solutions: Synthesis of polysulfide by reaction of bis(4‐mercaptophenyl) sulfide with bis(4‐chloro‐3‐nitrophenyl) sulfone using various bases in aqueous solutions

The polycondensation of bis(4‐mercaptophenyl) sulfide (BMPS) with bis(4‐chloro‐3‐nitrophenyl) sulfone (BCNPS) was examined using various organic or inorganic bases in mixed solvents of N‐methyl‐2‐pyrrolidone (NMP) with water or in plain water. The reaction of BMPS with BCNPS proceeded smoothly to give the corresponding polysulfide in mixed solvents of NMP with water at 60 °C using 1,8‐diazabicyclo[5.4.0]undecene‐7 as a base, although the rate of the reaction decreased gradually as the water in the solvent increased. Polysulfide can also be obtained by reaction in plain water using appropriate organic bases such as tripropylamine (TPA) or quinoline. The polysulfide with a number‐average molecular weight of 45,100 was synthesized in 62% yield when the reaction of BMPS with BCNPS was performed using TPA as a base at 60 °C for 48 h in plain water. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 3399–3404, 2000     

Synthesis of polysulfonates containing reactive pendant chloromethyl groups by the polyaddition of bisepoxides with disulfonyl chlorides

Polysulfonates with reactive pendant chloromethyl groups were synthesized by polyadditions of bisepoxides with disulfonyl chlorides. The polyaddition of bisphenol A diglycidyl ether (BPGE) with m-benzene disulfonyl chloride (m-BDSC) occurred in anisole without any catalyst at 130°C for 24 h. However, polymer with high molecular weight was not obtained. On the other hand, the polyadditions of BPGE with m-BDSC proceeded very smoothly with high yield (81–91%) to give polymers with relatively high molecular weights in anisole at 130°C for 24 h when quaternary phosphonium salts were used as catalysts. The polyaddition was also enhanced by the addition of certain crown ether complexes. However, the catalytic activity of these compounds was less than those of quaternary phosphonium salts. Furthermore, polyadditions of certain bisepoxides with disulfonyl chlorides were also carried out to produce the corresponding polymers under the same reaction conditions. © 1998 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 36: 249–256, 1998     

Controlled polymerization of an AB2 monomer using a chloromethylarene as comonomer: branched polymers from activated methylene compounds

Hyperbranched and branched polymers were synthesized by one-pot reaction of the AB₂ monomer 4-(4′-chloromethylbenzyloxy)phenylacetonitrile (1 ). The polymerization of 1 was controlled by adding a chloromethylarene (A₁ comonomer) such as methoxybenzyl chloride and by adding TBAC (tetrabutylammonium chloride). Copolymerization of 1 with A₂ comonomers, bis(chloromethyl)arenes, gives the corresponding copolymers.     

Synthesis of silicon-containing vinyl ether monomers and oligomers and their photoinitiated polymerization

Silicon-containing divinyl ether monomers were synthesized by the addition reaction of glycidyl vinyl ether ( 1 ) with various silyl dichlorides using tetra-n-butylammonium bromide (TBAB) as a catalyst. The reaction of 1 with diphenyl dichlorosilane gave bis-[1-(chloromethyl)-2-(vinyloxy)-ethyl]diphenyl silane ( 3a ) in 89% yield. Polycondensations of 3a with terephthalic acid were also carried out using 1,8-Diazabicyclo[5.4.0]-7-undecene (DBU) to afford silicon-containing polyfunctional vinyl ether oligomers ( 5 ). A multifunctional Si-monomer with both vinyl ether and methacrylate groups ( 7 ) was prepared by the reaction of 3a with potassium methacrylate using TBAB as a phase transfer catalyst. Photoinitiated cationic polymerizations of these vinyl ether compounds proceeded rapidly using the sulfonium salt, bis-[4-(diphenyl-sulfonio)phenyl]sulfide-bis-hexafluorophoshate (DPSP), as the cationic photoinitiator in neat mixtures upon UV irradiation. Multifunctional monomer 7 with both vinyl ether and methacrylate groups showed “hybrid curing properties” using both DPSP and the radical photoinitiator, 2,4,6-trimethylbenzoyl diphenylphoshine oxide (TPO). © 1997 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 35: 3217–3225, 1997     

Synthesis of polymers in aqueous solutions: Polyaddition of bis(oxazolines) with dithiol in aqueous solutions

Polyaddition of bis(4-mercaptophenyl) sulfide ( BMPS ) with m-phenylenebis(2-oxazoline) ( MPBO ) proceeded very smoothly in the mixtures of aprotic ploar solvents such as N-methyl-2-pyrrolidone ( NMP ) with water to produce the corresponding poly(amide–sulfide) with high molecular weights at 90°C under nitrogen. The reaction of BMPS with MPBO , p-phenylenebis(2-oxazoline), and 1,4-butylenebis(2-oxazoline) was also examined in water under the same conditions, and it was found that the reaction proceeds successfully to give the corresponding poly(amide–sulfide)s with high molecular weights. These results mean that water along as well as the mixed solvents of aprotic polar solvents such as NMP with water can be uses as suitable reaction media for the polyaddition of bis(oxazolines) with dithiol to synthesize poly(amide—sulfide)s with high molecular weights. © 1997 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 35 : 2711–2717, 1997     

General and efficient method for the synthesis of alkoxymethylsilanes

Although alkoxymethylsilanes serve as useful building blocks, various efforts to synthesize them by substitution reaction with an alkoxide ion at the carbon adjacent to the silicon failed. To solve this synthetic problem a new route which is very simple to perform was developed. Bromination of (methoxymethyl)trimethylsilane by using N‐bromosuccinimide/2,2′‐azobisisobutyronitrile (NBS/AIBN) was followed by a substitution by alcohols in the presence of triethylamine to give the corresponding [alkoxy‐­(methoxy)methyl]trimethylsilanes. These acetals can be used directly for the next reduction with di‐isobutylaluminium hydride (DIBAL‐H) or Et₃SiH/BF₃·OEt₂ to give alkoxymethylsilanes in good to moderate yields. The success of the substitution reaction with the alcohols suggests that the mechanism is of somewhat S_N1 by nature and formation of the cationic intermediate seems to release the steric hindrance around the carbon, allowing the attack of alcohols. Copyright © 1999 John Wiley & Sons, Ltd.