A grid‐free upwind relaxation scheme for inviscid compressible flows

A new grid‐free upwind relaxation scheme for simulating inviscid compressible flows is presented in this paper. The non‐linear conservation equations are converted to linear convection equations with non‐linear source terms by using a relaxation system and its interpretation as a discrete Boltzmann equation. A splitting method is used to separate the convection and relaxation parts. Least squares upwinding is used for discretizing the convection equations, thus developing a grid‐free scheme which can operate on any arbitrary distribution of points. The scheme is grid free in the sense that it works on any arbitrary distribution of points and it does not require any topological information like elements, faces, edges, etc. This method is tested on some standard test cases. To explore the power of the grid‐free scheme, solution‐based adaptation of points is done and the results are presented, which demonstrate the efficiency of the new grid‐free scheme. Copyright © 2005 John Wiley & Sons, Ltd.     

Hybrid free radical/cationic frontal photopolymerizations

The irradiation of hybrid photopolymer systems consisting of a free radically polymerizable multifunctional acrylate monomer and a cationically polymerizable epoxide or oxetane monomer was conducted under conditions where only the free radical polymerization takes place. This results in the formation of a free‐standing polyacrylate network film containing quiescent oxonium ions along with the unreacted cyclic ether monomer. The subsequent application of a point source of heat to the film ignites a cationic ring‐opening frontal polymerization that emanates from that site and propagates to all portions of the irradiated sample. This article examines the impact of various molecular structural and experimental parameters on these novel hybrid frontal polymerizations that produce interpenetrating network polymers. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 4331–4340, 2007     

Atomistic packing models for experimentally investigated swelling states induced by CO2 in glassy polysulfone and poly(ether sulfone)

Atomistic packing models have been created, which help to better understand the experimentally observed swelling behavior of glassy polysulfone and poly (ether sulfone), under CO₂ gas pressures up to 50 bar at 308 K. The experimental characterization includes the measurement of the time‐dependent volume dilation of the polymer samples after a pressure step and the determination of the corresponding gas concentrations by gravimetric gas‐sorption measurements. The models obtained by force‐field‐based molecular mechanics and molecular dynamics methods allow a detailed atomistic analysis of representative swelling states of polymer/gas systems, with respect to the dilation of the matrix. Also, changes of free volume distribution and backbone mobility are accessible. The behavior of gas molecules in unswollen and swollen polymer matrices is characterized in terms of sorption, diffusion, and plasticization. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1874–1897, 2006     

The effect of crystallinity on chain mobility and free volume in the amorphous regions of a miscible polycarbonate/polyester blend

Homopolymers and blends of polycarbonate/ThermX have been investigated by differential scanning calorimetry, dynamic mechanical analysis, density measurements, and positron annihilation lifetime spectroscopy. The study focuses on the chain mobility and free volume in the amorphous miscible regions of the blends and how this mobility and free volume are affected by increasing crystallinity. It is proposed that judicious annealing, which results in increasing crystallinity (while avoiding ageing or transesterification), induces a constraint on the amorphous region leading to an increase in T_g and coalescence of free volume sites. © 1994 John Wiley & Sons, Inc.     

Transient free‐surface flow of a viscoelastic fluid in a narrow channel

The interplay between inertia and elasticity is examined for transient free‐surface flow inside a narrow channel. The lubrication theory is extended for the flow of viscoelastic fluids of the Oldroyd‐B type (consisting of a Newtonian solvent and a polymeric solute). While the general formulation accounts for non‐linearities stemming from inertia effects in the momentum conservation equation, and the upper‐convected terms in the constitutive equation, only the front movement contributes to non‐linear coupling for a flow inside a straight channel. In this case, it is possible to implement a spectral representation in the depthwise direction for the velocity and stress. The evolution of the flow field is obtained locally, but the front movement is captured only in the mean sense. The influence of inertia, elasticity and viscosity ratio is examined for pressure‐induced flow. The front appears to progress monotonically with time. However, the velocity and stress exhibit typically a strong overshoot upon inception, accompanied by a plug‐flow behaviour in the channel core. The flow intensity eventually diminishes with time, tending asymptotically to Poiseuille conditions. For highly elastic liquids the front movement becomes oscillatory, experiencing strong deceleration periodically. A multiple‐scale solution is obtained for fluids with no inertia and small elasticity. Comparison with the exact (numerical) solution indicates a wide range of validity for the analytical result. Copyright © 2004 John Wiley & Sons, Ltd.     

A new VOF‐based numerical scheme for the simulation of fluid flow with free surface. Part II: application to the cavity filling and sloshing problems

Finite element analysis of fluid flow with moving free surface has been performed in 2‐D and 3‐D. The new VOF‐based numerical algorithm that has been proposed by the present authors (Int. J. Numer. Meth. Fluids, submitted) was applied to several 2‐D and 3‐D free surface flow problems. The proposed free surface tracking scheme is based on two numerical tools; the orientation vector to represent the free surface orientation in each cell and the baby‐cell to determine the fluid volume flux at each cell boundary. The proposed numerical algorithm has been applied to 2‐D and 3‐D cavity filling and sloshing problems in order to demonstrate the versatility and effectiveness of the scheme. The proposed numerical algorithm resolved successfully the free surfaces interacting with each other. The simulated results demonstrated applicability of the proposed numerical algorithm to the practical problems of large free surface motion. It has been also demonstrated that the proposed free surface tracking scheme can be easily implemented in any irregular non‐uniform grid systems and can be extended to 3‐D free surface flow problems without additional efforts. Copyright © 2003 John Wiley & Sons, Ltd.     

A hybrid finite-element–volume-of-fluid method for simulating free surface flows and interfaces

A numerical technique is developed for the simulation of free surface flows and interfaces. This technique combines the strength on the finite element method (FEM) in calculating the field variables for a deforming boundary and the versatility of the volume-of-fluid (VOF) technique in advection of the fluid interfaces. The advantage of the VOF technique is that it allows the simulation of interfaces with large deformations, including surface merging and breaking. However, its disadantage is that is solving the flow equations, it cannot resolve interfaces smaller than the cell size, since information on the subgrid scale is lost. Therefore the accuracy of the interface reconstruction and the treatment of the boundary conditions (i.e. viscous stresses and surface tension forces) become grid-size-dependent. On the other hand, the FEM with deforming interface mesh allows accurate implementation of the boundary conditions, but it cannot handle large surface deformations occurring in breaking and merging of liquid regions. Combining the two methods into a hybrid FEM-VOF method eliminates the major shortcomings of both. The outcome is a technique which can handle large surface deformations with accurate treatment of the boundary conditions. For illustration, two computational examples are presented, namely the instability and break-up of a capillary jet and the coalescence collision of two liquid drops.     

Measurement and prediction of solubilities and diffusion coefficients of carbon dioxide in starch–water mixtures at elevated pressures

The solubility and diffusion coefficient of carbon dioxide in intermediate‐moisture starch–water mixtures were determined both experimentally and theoretically at elevated pressures up to 16 MPa at 50 °C. A high‐pressure decay sorption system was assembled to measure the equilibrium CO₂ mass uptake by the starch–water system. The experimentally measured solubilities accounted for the estimated swollen volume by Sanchez–Lacombe equation of state (S‐L EOS) were found to increase almost linearly with pressure, yielding 4.0 g CO₂/g starch–water system at 16 MPa. Moreover, CO₂ solubilities above 5 MPa displayed a solubility increase, which was not contributed by the water fraction in the starch–water mixture. The solubilities, however, showed no dependence on the degree of gelatinization (DG) of starch. The diffusion coefficient of CO₂ was found to increase with concentration of dissolved CO₂, which is pressure‐dependent, and decrease with increasing DG in the range of 50–100%. A free‐volume‐based diffusion model proposed by Areerat was employed to predict the CO₂ diffusivity in terms of pressure, temperature, and the concentration of dissolved CO₂. S‐L EOS was once more used to determine the specific free volume of the mixture system. The predicted diffusion coefficients showed to correlate well with the measured values for all starch–water mixtures. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 607–621, 2006     

Freezing temperatures and densities of solutions of some hydrocarbons and sodium oleate inN-methylacetamide. Evidence for a solvophobic interaction

The freezing temperatures and densities (at 31°C) of solutions of octane, nonane, decane, 3,3-diethylpentane, and sodium oleate inN-methylacetamide (NMA) have been measured. The molality of the freezing solution was calculated from the density. The solubilities of octane, nonane, and decane inN-methylacetamide are also reported. Apparent molal volumes calculated from the densities are close to the values in the pure hydrocarbons and are not strong functions of the concentration. This indicates the absence of any unusual packing effect. The calculated free energies of transfer of the hydrocarbons from pure hydrocarbon to NMA solution are much less negative than the corresponding values for water, showing that the bulk solvophobic interaction inN-methylacetamide is smaller than in water. This is consistent with the freezing temperatures of sodium oleate which show that micelles do not form below 0.1 mole-kg^–1. The osmotic coefficients of the hydrocarbons calculated from the freezing temperatures showed negative deviations from ideality that were larger for the hydrocarbons with the higher molecular weights. Two estimates of the pairwise solvophobic interaction inN-methylacetamide indicate that it is also smaller than in water. The solvophobic effect in this solvent does not include the large entropy and enthalpy effects found in aqueous solutions.     

THE PARAMETER KERNELS FOR THE LINEAR INVERSION OF THE FREE OSCILLATION OF THE EARTH (Ⅰ)

In the linear inversion of the radial variation of the parameters of the Earth by usingthe observed frequencies of various normal modes of free oscillation of the earth, it is neces-sary to know the values of the kernels of the parameters ρ, μ and λ. This paper describesthe methods of the derivation of the formulas of these kernels. This is the first part of thepaper in which only the toroidal oscillations are considered. They are much simpler thanthose of the spheroidal ones, that we will consider in the second part of the paper. The data of the two types of oscillations are equally important in the solution of theinversion problem, and should be employed simultaneously, and we know that the toroidaloscillations are much simpler than the spheroidal ones, it seems wise to divide the whole programof the inversion problem into steps: first, by employing the toroidal data to correct the twoparameters ρ and μ in the mantle, then by using the spheroidal data to correct the remain-ing parameters, i.e. th