Stability of plane Poiseuille flow of slightly viscoelastic fluids

Summary The title subject has been examined by the author in a series of papers (Cousins, 1970, 1972a, b), and the assumptions and principal results of those papers are discussed here. The work is motivated by the phenomenon evinced in fluid flow situations, of turbulent drag reduction by certain polymer additives. From a survey of experimental work it is clear that molecular elongation plays an important role in reducing drag by suppressing transverse motions. This effect may be interpreted as a normal stress effect in a continuum theory. A second-order fluid, which is a simple model exhibiting such a property, is used in a linear analysis of disturbances to planePoiseuille flow. Unlike theNewtonin case Squire's theorem is not valid (Lockett, 1969a) and a three-dimensional analysis is required. The viscoelastic terms are in general destabilising. Under certain conditions the first growing disturbance will propagate at an angle to the basic flow, giving a longitudinal vortex structure close to the channel boundaries not present at the onset of instability in aNewtonian fluid. The analysis is extended to finite-amplitude disturbances by introducing a time-dependent amplitude, but calculations are here confined to the simpler two-dimensional case. Disturbances which would decay under linear theory may in fact grow provided the initial amplitude is sufficiently large. A threshold amplitude for instability is found as a function ofReynolds number. The viscoelastic terms are again found to be destabilising. Finally, a further viscoelastic property, that of stress relaxation, is introduced through an integral representation of the stress. A linear analysis is developed and stress relaxation is also shown to be a destabilising influence.With 6 figures     

Syntheses and reactions of some fluorinated dienes,cyclobutenes and furans

There are many reports¹ of the pyrolysis of fluorinated organic compounds, including the defluorination of cyclic fluorocarbons over iron to give aromatic compounds. Extending this technique we have investigated the flow pyrolysis of some readily accessible unsaturated fluorocarbons, such as I, II, and III, and found these to be synthetically

useful routes to fluorinated dienes, cyclobutenes, and furans. Pyrolyses were carried out using a nitrogen flow over platinum, iron or caesium fluoride heated at 430–700°. The various products can all be rationalized in terms of intermediate allylic radicals, and the solid substrate influences which allylic radicals are formed.We are also investigating the chemistry of those now accessible compounds, such as IV, V, and VI, and some of the preliminary results are described.

For example the fluoride ion induced dimerisation of IV gave two major products VII and VIII via a particular interesting mechanism.

     

Periodate oxidative decrystallization of cotton cellulose

Cotton cellulose is decrystallized by periodate oxidation to essentially zero crystallinity index (CI) at 100% oxidant consumption. The decrease in CI is pseudo zero-order over 60% of the reaction and consistent with a diffusion-controlled mechanism. The attack on regions of high order is indicated to be 100% in the latter phase of oxidation and 13% in the initial phase. Data allow an estimate that approximately 60% of the structural segments of the cotton cellulose under investigation lies in highly ordered arrangements.     

Conduction electron spin resonance in magnesium

We report on the observation of conduction electron spin resonance (CESR) in samples of specially purified magnesium. Measurements were made over the temperature range 4.2–300 K and at two frequencies, 9.27 and 21 GHz. It is found that in contrast with previous data, there is no upturn in the low temperature linewidth and little variation between samples.