Extensional flow-induced crystallization of a polyethylene melt

Measurements of flow-induced orientation and crystallization have been made on a high-density polyethylene melt (HDPE) undergoing a planar extensional flow in a four-roll mill. The HDPE was suspended as a cylindrical droplet at the flow stagnation point in a linear low density polyethylene (LLDPE) carrier phase. Deformation and crystallization of the HDPE droplet phase were monitored using video imaging in conjunction with measurement of the birefringence and dichroism to quantify the in-situ transformation kinetics. Planar deformation rates along the symmetry axis of the molten HDPE phase were on the order of 0.03 s^?1. Measurements of the initial transformation rate following flow cessation at 131.5°C and 133.2°C show a dependence on initial amorphous phase orientation and the total Hencky strain achieved during flow. The flow-induced crystallization rate is enhanced over the quiescent transformation rate by orders of magnitude, however, the dependence on temperature is less dramatic than expected for a nucleation-controlled growth mechanism. Analysis demonstrates that the melting point elevation model cannot account either qualitatively or quantitatively for the phenomena observed, suggesting that alternative explanations for the strong orientation dependence of the transformation rate are needed.     

Conservative methods for the Toda lattice equations

We are concerned with the numerical integration of the Todalattice equations by using different conservative methods. Numericalexperiments suggest that the global error for isospectral schemesdecreases exponentially with time but it is almost constantfor either symplectic or more general integrators. We providea theoretical explanation for these experimental findings.     

Impact of fluorine on the phase behavior of bis-p-tolyl propane in supercritical CO2, 1,1-difluoroethane,and 1,1,1,2-tetrafluoroethane

Fluorine substitution on a solute can have a significant effect on solute solubility in a given solvent and fluorine substitution on a solvent can also have a significant effect on solvent quality. The effect of fluorine is demonstrated with the phase behavior data for bis(p-tolyl)propane (BTP) compared to bis(p-tolyl)hexafluoropropane (BTHFP) in supercritical carbon dioxide, 1,1-difluoroethane (F152a), and 1,1,1,2-tetrafluoroethane (F134a). Semifluorinated BTHFP is more soluble than non-fluorinated BTP in all three solvents, especially CO₂. The CO₂–BTP system exhibits solid solubility behavior while the CO₂–BTHFP system exhibits liquid–liquid–vapor (LLV) behavior near the critical point of CO₂. Although the two dipolar hydrofluorocarbons (HFC) are better solvents than CO₂ for these two aromatic solid compounds, F152a is the superior HFC solvent, especially for BTP, because F152a has a smaller molar volume and a larger effective dipole moment than F134a. LLV behavior is also observed for the F134a–BTP system near the critical point of F134a although the F134a–BTHFP, F152a–BTP, and F152a–BTHFP systems all appear to exhibit type-I phase behavior and no liquid–liquid immiscibility near the respective critical points.     

Using non-linear magneto-optic techniques to characterise particulate recording media

The concept of using comparison between magneto-optic measurements taken in the linear and second-harmonic reflected fields to address problems attending the development of ultra-high-density recording media as the limits of thermal stability are approached is presented. It is shown how magneto-optical measurements made routinely in the linear reflected field to access many of the bulk characteristics of such media may, by operating in the second-harmonic field, be fruitfully extended. To illustrate the techniques being explored, reference is made to initial measurements on a longitudinal recording medium under continuing development at Coventry. This medium, already shown to support recording at linear densities in excess of 100 kfci, is based on cobalt particles around 10 nm in diameter. Received: 16 October 2001 / Revised version: 14 March 2002 / Published online: 29 May 2002     

Flow-induced crystallization by surface growth of polyethylene fibers

A series of experiments has been carried out investigating several features of the surface growth method for observing longitudinal growth of polyethylene fibers in Couette geometry. Attempts to obtain limiting steady-state takeup rates using a Teflon rotor were hampered by fiber breakage; however, maximum growth rates before breakage were found to be considerably higher than those observed in previous studies. Growth rates were also obtained using a static method, and for the Teflon rotor indicated above a critical concentration a linear growth rate equal to the stirrer velocity with rates essentially independent of temperature. With a silanized glass rotor, the same method gave much lower growth rates at comparable stirrer speeds and temperatures and showed a temperature dependence suggestive of a nucleation-controlled mechanism. The implications of these results for other studies of the mechanisms of growth by the surface method are also discussed.     

Fully coupled finite volume solutions of the incompressible Navier–Stokes and energy equations using an inexact Newton method

An inexact Newton method is used to solve the steady, incompressible Navier–Stokes and energy equation. Finite volume differencing is employed on a staggered grid using the power law scheme of Patankar. Natural convection in an enclosed cavity is studied as the model problem. Two conjugate-gradient -like algorithms based upon the Lanczos biorthogonalization procedure are used to solve the linear systems arising on each Newton iteration. The first conjugate-gradient-like algorithm is the transpose-free quasi-minimal residual algorithm (TFQMR) and the second is the conjugate gradients squared algorithm (CGS). Incomplete lower-upper (ILU) factorization of the Jacobian matrix is used as a right preconditioner. The performance of the Newton- TFQMR algorithm is studied with regard to different choices for the TFQMR convergence criteria and the amount of fill-in allowed in the ILU factorization. Performance data are compared with results using the Newton-CGS algorithm and previous results using LINPACK banded Gaussian elimination (direct-Newton). The inexact Newton algorithms were found to be CPU competetive with the direct-Newton algorithm for the model problem considered. Among the inexact Newton algorithms, Newton-CGS outperformed Newton- TFQMR with regard to CPU time but was less robust because of the sometimes erratic CGS convergence behaviour.