Shear and extensional flow of polyacrylamide solutions

As part of an EEC Science Stimulation programme on extensional viscosity two major conferences were organised on the subject. The second of these was devoted to the results obtained on a standard fluid, M 1. The data obtained in shear flow was remarkably consistent from laboratory to laboratory. Extensional flow results presented quite a different picture. Using a series of nonequilibrium techniques such as the spinline rheometer, opposing jet, falling drop and converging flow, extensional viscosity results were obtained which differed by as much as two to three orders of magnitude. Nevertheless, it was apparent that consistancy did exist between similar techniques. It is in the context of this information that the measurements described below have been made.The shear and extensional flow properties of partially ionised polyacrylamide in solution at concentrations ranging from 5 ppm were measured. The method of solution preparation was found to have a profound effect on the behaviour of the solutions in shear flow. The influence of salt concentration and pH was investigated and is discussed in the context of molecular shape in solution.Extensional flow measurements, using the spinline rheometer, show that the solutions are strongly strain thickening even at concentrations as low as 5 ppm. These results are considered in the light of polymer entanglement and association in the strong flow field.Delivered as a Keynote Lecture at the Golden Jubilee Conference of the British Society of Rheology and Third European Rheology Conference, Edinburgh, 3–7 September, 1990.     

Sulfur K-edge XAS and DFT calculations on [Fe4S4]2+ clusters: effects of H-bonding and structural distortion on covalency and spin topology

Sulfur K-edge X-ray absorption spectroscopy of a hydrogen-bonded elongated [Fe4S4]2+ cube is reported. The data show that this synthetic cube is less covalent than a normal compressed cube with no hydrogen bonding. DFT calculations reveal that the observed difference in electronic structure has significant contributions from both the cluster distortion and from hydrogen bonding. The elongated and compressed Fe4S4 structures are found to have different spin topologies (i.e., orientation of the delocalized Fe2S2 subclusters which are antiferromagnetically coupled to each other). It is suggested that the H-bonding interaction with the counterion does not contribute to the cluster elongation. A magneto-structural correlation is developed for the Fe4S4 cube that is used to identify the redox-active Fe2S2 subclusters in active sites of HiPIP and ferredoxin proteins involving these clusters.     

A computational study of some rheological influences on the “splashing experiment”

In various attempts to relate the behaviour of highly-elastic liquids in complex flows to their rheometrical behaviour, obvious candidates for study have been the variation of shear viscosity with shear rate, the two normal stress differences N₁ and N₂, especially N₁, the extensional viscosity, and the dynamic moduli G′ and G″. In this paper, we shall confine attention to ‘constant-viscosity’ Boger fluids, and, accordingly, we shall limit attention to N₁, η_E, G′ and G″.We shall concentrate on the “splashing” problem (particularly that which arises when a liquid drop falls onto the free surface of the same liquid). Modern numerical techniques are employed to provide the theoretical predictions. We show that high η_E can certainly reduce the height of the so-called Worthington jet, thus confirming earlier suggestions, but other rheometrical influences (steady and transient) can also have a role to play and the overall picture may not be as clear as it was once envisaged. We argue that this is due in the main to the fact that splashing is a manifestly unsteady flow. To confirm this proposition, we obtain numerical simulations for the linear Jeffreys model.     

Iterated Point–Line Configurations Grow Doubly-Exponentially

Begin with a set of four points in the real plane in general position. Add to this collection the intersection of all lines through pairs of these points. Iterate. Ismailescu and Radoičić (Comput. Geom. 27:257–267, 2004) showed that the limiting set is dense in the plane. We give doubly exponential upper and lower bounds on the number of points at each stage. The proof employs a variant of the Szemerédi–Trotter Theorem and an analysis of the “minimum degree” of the growing configuration.     

Nachweis und Bestimmung des Chroms

Ohne Zusammenfassung     

Development of Molecular Mechanics Torsion Parameters for alpha,beta-Cyclopropyl Ketones and Conformational Analysis of Bicyclo[m.1.0]alkan-2-ones

Conformations of cyclopropyl methyl ketone have been studied using ab initio methods in an effort to quantify the effects of conjugative overlap between the cyclopropane ring and an adjacent ketone carbonyl. Results were comparable with previous experimental and theoretical studies. Cyclopropyl methyl ketone exhibits a global energy minimum in the s-cis conformer and a local energy minimum near the s-trans conformer. The potential energy curve obtained was used to derive torsion parameters which were employed in molecular mechanics studies of the conformations of the set of bicyclo[m.1.0]alkan-2-ones having larger ring sizes from five- to 16-membered. Similar conformations for the cyclopropyl ketone substructure are observed for all the medium and large ring systems examined. Possible synthetic ramifications of local conformational anchoring by this functional group array are discussed.     

ADAPTIVE MANAGEMENT OF HARVEST RATES IN THE PRESENCE OF A RISK AVERSE UTILITY FUNCTION

Previous research on adaptive harvest strategies has suggested that it should rarely be optimal to introduce deliberate, probing variations in harvest rates in order to reduce uncertainty about production parameters, when there is strong aversion to the risk of low catches. Here we show that this suggestion is incorrect for cases where the stock dynamics can be approximated by a simple power model and the objective is to maximize the sum over time of discounted logarithms of catches. In such cases, the objective function has a simple form that permits easy comparison between passively adaptive (certainty equivalent or cautious) versus actively adaptive policies involving probing variation in harvest rates. Probing is favored when there is high uncertainty about the power parameter that represents density dependence in the stock dynamics.