Facile modifications of a polyimide via chloromethylation. I. Novel synthesis of a new photosensitive polyimide

A soluble aromatic polyimide was chloromethylated via a reaction with chloromethyl methyl ether in the presence of tin(IV) chloride to produce a new starting material for the modification of aromatic polyimides. The chemical structure of the resulting polymer was confirmed by ¹H NMR and Fourier transform infrared spectroscopy. The maximum number of chloromethyl groups per repeat unit was 1.81. The chloromethylated polyimide was stable up to 250 °C and soluble in both chloroform and tetrahydrofuran. So that its utilization for further modification could be demonstrated, cinnamic acid was reacted with the formed polyimide, and it produced a new photosensitive polyimide with a cinnamoyl side chain. The photosensitivity of the resulting polyimide was investigated with ultraviolet spectroscopic methods. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 22–29, 2003     

D. Liu and X. Zhu,Erratum to: “Fractional chromatic number and circular chromatic number for distance graphs with large clique size”. Journal of Graph Theory47(2) 2004, 129–146

The original article to which this Erratum refers was published in Journal of Graph Theory 47:129–146,2004 .     

Computations of two passing‐by high‐speed trains by a relaxation overset‐grid algorithm

This paper presents a relaxation algorithm, which is based on the overset grid technology, an unsteady three‐dimensional Navier–Stokes flow solver, and an inner‐ and outer‐relaxation method, for simulation of the unsteady flows of moving high‐speed trains. The flow solutions on the overlapped grids can be accurately updated by introducing a grid tracking technique and the inner‐ and outer‐relaxation method. To evaluate the capability and solution accuracy of the present algorithm, the computational static pressure distribution of a single stationary TGV high‐speed train inside a long tunnel is investigated numerically, and is compared with the experimental data from low‐speed wind tunnel test. Further, the unsteady flows of two TGV high‐speed trains passing by each other inside a long tunnel and at the tunnel entrance are simulated. A series of time histories of pressure distributions and aerodynamic loads acting on the train and tunnel surfaces are depicted for detailed discussions. Copyright © 2004 John Wiley & Sons, Ltd.     

Numerical simulations of a filament in a flowing soap film

Experiments concerning the properties of soap films have recently been carried out and these systems have been proposed as experimental versions of theoretical two‐dimensional liquids. A silk filament introduced into a flowing soap film, was seen to demonstrate various stable modes, and these were, namely, a mode in which the filament oscillates and one in which the filament is stationary and aligns with the flow of the liquid. The system could be forced from the oscillatory mode into the non‐ oscillatory mode by varying the length of the filament. In this article we use numerical and computational techniques in order to simulate the strongly coupled behaviour of the filament and the fluid. Preliminary results are presented for the specific case in which the filament is seen to oscillate continuously for the duration of our simulation. We also find that the filament oscillations are strongly suppressed when we reduce the effective length of the filament. We believe that these results are reminiscent of the different oscillatory and non‐oscillatory modes observed in experiment. The numerical solutions show that, in contrast to experiment, vortices are created at the leading edge of the filament and are preferentially grown in the curvature of the filament and are eventually released from the trailing edge of the filament. In a similar manner to oscillating hydrofoils, it seems that the oscillating filaments are in a minimal energy state, extracting sufficient energy from the fluid to oscillate. In comparing numerical and experimental results it is possible that the soap film does have an effect on the fluid flow especially in the boundary layer where surface tension forces are large. Copyright © 2004 John Wiley & Sons, Ltd.     

A numerical and experimental investigation of the interactions between a non‐uniform planar array of incompressible free jets

The interaction between multiple incompressible air jets has been studied numerically and experimentally. The numerical predictions have been first validated using experimental data for a single jet configuration. The spreading features of five unequal jets in the configuration of one larger central jet surrounded by four smaller equi‐distant jets, have been studied, for different lateral spacing ratios of 1.5, 2.0 and 2.5 and a central jet Reynolds number of 1.24×105 (corresponding to a Mach number of 0.16). Flow of five equal jets has also been simulated, for the sake of comparison. The jet interactions commence at an axial distance of about 3–4 diameters and complete by an axial distance of about 10 diameters for the lowest spacing ratio of 1.5. For larger spacing ratios, the length required for the start and completion of jet interaction increase. Peripheral jets bend more towards the central jet and merge at a smaller distance, when their sizes are smaller than that of the central jet. The entrainment ratio for multiple jets is higher than that for a single jet. Excellent agreement is observed between the experimental data and theoretical predictions for both mean flow field and turbulent quantities, at regions away from the jet inlet. The potential core length and initial jet development, however, are not predicted very accurately due to differences in the assumed and actual velocity profiles at the jet inlet. Copyright © 2004 John Wiley & Sons, Ltd.     

A time‐accurate pseudo‐compressibility approach based on an unstructured hybrid finite volume technique applied to unsteady turbulent premixed flame propagation

A preconditioning approach based on the artificial compressibility formulation is extended to solve the governing equations for unsteady turbulent reactive flows with heat release, at low Mach numbers, on an unstructured hybrid grid context. Premixed reactants are considered and a flamelet approach for combustion modelling is adopted using a continuous quenched mean reaction rate. An overlapped cell‐vertex finite volume method is adopted as a discretisation scheme. Artificial dissipation terms for hybrid grids are explicitly added to ensure a stable, discretised set of equations. A second‐order, explicit, hybrid Runge–Kutta scheme is applied for the time marching in pseudo‐time. A time derivative of the dependent variable is added to recover the time accuracy of the preconditioned set of equations. This derivative is discretised by an implicit, second‐order scheme. The resulting scheme is applied to the calculation of an infinite planar (one‐dimensional) turbulent premixed flame propagating freely in reactants whose turbulence is supposed to be frozen, homogeneous and isotropic. The accuracy of the results obtained with the proposed method proves to be excellent when compared to the data available in the literature. Copyright © 2004 John Wiley & Sons, Ltd.     

Least‐squares meshfree method for incompressible Navier–Stokes problems

A least‐squares meshfree method based on the first‐order velocity–pressure–vorticity formulation for two‐dimensional incompressible Navier–Stokes problem is presented. The convective term is linearized by successive substitution or Newton's method. The discretization of all governing equations is implemented by the least‐squares method. Equal‐order moving least‐squares approximation is employed with Gauss quadrature in the background cells. The boundary conditions are enforced by the penalty method. The matrix‐free element‐by‐element Jacobi preconditioned conjugate method is applied to solve the discretized linear systems. Cavity flow for steady Navier–Stokes problem and the flow over a square obstacle for time‐dependent Navier–Stokes problem are investigated for the presented least‐squares meshfree method. The effects of inaccurate integration on the accuracy of the solution are investigated. Copyright © 2004 John Wiley & Sons, Ltd.     

Synthesis and association of poly(N,N‐dimethylacrylamide) copolymers with perfluorocarbon pendent groups connected through polyethylene‐glycol tethers

The synthesis is reported of copolymers of N,N‐dimethylacrylamide (DMA) and methacrylates containing 2,2′‐dihydroperfluorodecanoyl (RF) groups separated from the methacrylate by long polyethylene glycol (PEG) tether groups (between 1000 and 14,000 Da). At concentrations of between 1 and 8 wt % the copolymers with macromonomer contents of 1 mol % or less give gels in organic solvents such as dioxane, THF, or methanol, as well as in water. Given the low molecular weights, this indicates very efficient association of very low numbers of RF groups. Association and gel formation is enormously enhanced in the presence of longer PEG tethers. This is consistent with smaller poly(N,N,‐dimethylacrylamide) (PDMA) intermolecular excluded volume effects that are mediated by the longer PEG tethers and possibly by the incompatibility of PEG and PDMA that may lead to the formation of PEG microdomains. This increases the local concentrations of the RF groups in the PEO domains that are not diluted by the PDMA chains, as would be the case in the absence of PEG tethers. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 360–373, 2004