SCI Publications

In a previous article, we described how the frequency-dependent complex shear modulus and the time-dependent shear stress relaxation modulus for a highly entangled polybutadiene (PBD) melt can be obtained from molecular dynamics (MD) simulations of an unentangled PBD melt.1 In that work, we obtained from simulations of an unentangled melt all properties required for the prediction of the dynamic shear modulus with three reptation theories for the dynamics of entangled melts of linear, monodisperse polymers.2–5 More recently, we showed how the high-frequency (glassy) behavior of PBD can be obtained directly from MD simulations.6 The calculated complex and stress relaxation shear moduli for a PBD melt with a molecular weight of 1.3 · 10⁵ Da at 298 K were found to be in excellent agreement with experimental data.1, 6 In this work, we investigate the ability of MD simulations of the unentangled melt, in conjunction with reptation theory, to reproduce the molecular weight and temperature dependence of the viscoelastic properties of PBD. Here we concentrate on the low-frequency/long-time dynamics that determine the zero shear-rate viscosity, a property that has been extensively studied for PBD as a function of molecular weight and temperature.

Aromatics growth beyond 2-, 3-ring PAH is analyzed through a radical-molecule reaction mechanism which, in combination with a previously developed PAH model, is able to predict the size distribution of aromatic structures formed in rich premixed flames of ethylene at atmospheric pressure with C/O ratios across the soot threshold limit. Modeling results are in good agreement with experimental data and are used to interpret the ultraviolet absorption and the light scattering measured in flames before soot inception. The model shows that the total number concentration of high molecular mass aromatics and the different moments of the size distribution are functions of both the PAH and H-atom concentrations, two quantities which have different trends as functions of the residence time and the C/O ratio. Regimes of nearly stoichiometric or slightly rich premixed combustion are dominated by reactions between aromatics which lead to the formation of particles with sizes of the order of 3 to 4 nm. At higher C/O ratios the formation of nanoparticles is less efficient. Particles with sizes of the order of 2 nm are predicted in flames at the threshold of soot formation, whereas particles with sizes around 1 to 1.5 nm are predicted in fully sooting conditions.

This paper presents a hierarchical cluster analysis of the principal values of the 13C chemical shift tensors encountered in polycyclic aromatic hydrocarbons (PAHs). Because of the limited set of experimental data presently available, the analysis was performed using chemical shifts tensors calculated using the DFT (B3PW91) GIAO method with a D95 basis set on optimized molecular geometries obtained using the CVFF force field and the DISCOVER routine in MSI's InsightII package. The good correlation observed between the calculated and the available experimental values supports the use of calculated values in the analysis. The hierarchical cluster analysis was performed for two data sets of increasing size and the classification was found independent of the size of the sample, leading to the conclusion that the results presented here are valid for the types of PAHs reported. The classification of the tensors using hierarchical cluster analysis produces classes of chemical shift principal values that can be associated with intuitive chemical types of carbons present in PAHs.

Numerical solutions to elastohydrodynamic lubrication problems have been computed
for the last half century. Over the past decade multilevel techniques have been successfully
applied in several solvers and significant speed-ups achieved. The aim of numerical
research in this field is to develop techniques in order to calculate accurate solutions to
demanding industrial problems as efficiently as possible.

In this work the numerical solver, previously developed by Nurgat, is examined. Despite
being successful in achieving converged results on a single grid, there were some
unresolved issues relating to the multigrid performance. These problems are explained
and the necessary modifications to the method used are detailed.

There is much current interest in obtaining results to transient elastohydrodynamic
lubrication problems. These are examined in detail and the justification for the methods
used are discussed. Example results for industrially relevant cases, such as variation of
lubricant entrainment, oscillation of the applied load and the presence of surface defects
are considered.

In many other fields, adaptation in both space and time is used to increase performance
and accuracy. However, these techniques are not currently used for elastohydrodynamic
lubrication problems. It is shown that they can be successfully applied and substantial
benefits accrued.

A method of variable timestepping has been introduced and results are presented
showing that not only is it as accurate as fixed time stepping methods, but that the computational
work required to obtain these solutions is significantly reduced. Local error
control on each individual timestep is also implemented.

Adaptation of the spatial mesh is also developed. By developing a hierarchy of refined
meshes within the multigrid structure it is seen how significantly fewer computational
points are used in the most expensive numerical calculations. This, in turn, means that
the computational time required is reduced. Different criteria for adaptation are explained
and results presented showing the relative levels of accuracy and speed-up achieved.