Polymer-induced turbulence modifications in an impinging jet

This effort explores the impact of dilute polymer solutions on the turbulence characteristics in a submerged liquid impinging-jet configuration. Turbulent impinging jets are commonly used in technological applications such as drying, scouring, cooling, or heating due to an enhancement in transport characteristics in the impingement region under certain nozzle-to-wall configurations. Previous efforts have identified significant turbulence modifications in the presence of dilute concentrations of polymer in both bounded and unbounded flows, though the former has received considerably more attention. To this end, particle-image velocimetry measurements were taken for an axisymmetric turbulent impinging jet with a nozzle-to-wall distance H/D = 6.8 and nominal Reynolds number of 26,000. Measurements were performed for both plain water and dilute polymer solutions of polyethylene oxide at concentrations of 50 and 100 ppm. The mean and turbulence characteristics of these three flows are contrasted and it is observed that the two polymer solutions modify both the mean and turbulent characteristics of the jet in all three regions of interest (the free-jet, impingement, and wall-jet regions). Of interest, the 50 ppm case yielded a slight suppression of the turbulence in the free-jet region accompanied by a longer axial length of the potential core compared to the case of plain water. In contrast, the 100 ppm case exhibits clear enhancement of the turbulence in the free-jet region and a shortening of the potential core length. The effect of polymer was opposite in the impingement and wall-jet regions wherein the turbulence was slightly suppressed in the 100 ppm case in a manner consistent with the onset of the Toms effect in this wall-bounded region of the flow.     

Merging and splitting in cooperative games: some (im)possibility results

Allocation rules for cooperative games can be manipulated by coalitions merging into single players, or, conversely, players splitting into a number of smaller units. This paper collects some (im)possibility results on merging- and splitting-proofness of (core) allocation rules for cooperative games with side-payments.     

Microsoft Excel as a supplement in a high school statistics course

This study was conducted in the spring of 2002 at Arlington High School in a Probability and Statistics course for junior and senior level students. Two sections of the class were compared with respect to the use/non-use of EXCEL in the course. The experimental group (the one using EXCEL) outperformed the control group on five of the six teacher-created unit tests and on both of the criterion referenced assessments used by the district; however, the differences were not statistically significant at the 0.05 level. Furthermore, the experimental group expressed very positive feelings towards the use of the software in a survey administered at the conclusion of the course.     

Synthesis and characterization of polymethacrylates containing conjugated oligo(phenylene ethynylene)s as side chains

In order to form suitable systems designed for resonance energy transfer, a series of monodisperse methacrylate‐based monomers containing rigid π‐conjugated oligo(phenylene ethynylenes) with different sizes of the conjugated systems ( M1 – M3 ), and therefore different optoelectronic properties, were synthesized and subsequently polymerized using the reversible addition–fragmentation chain transfer polymerization technique ( P1 – P3 ). In addition, these oligomers were also copolymerized with methyl methacrylate. The obtained polymers were characterized by ¹H NMR spectroscopy, size exclusion chromatography, and analytical ultracentrifugation. The photophysical properties of the polymers were studied by UV–vis absorption and emission spectroscopy in diluted solutions as well as in thin films and compared to the photophysics of the corresponding monomers. Thereby, changes going from monomeric to polymeric systems could be detected in fluorescence quantum yields and lifetimes pointing to energy trapping, e.g., energy transfer. Donor–acceptor copolymers containing different numbers of monomeric units within the side chain exhibit differences in the emission spectra, indicating that energy trapping in polymers is very sensitive to structural properties such as the chain length. UV–vis absorption spectroscopy as well as time‐resolved lifetime studies indicate intrapolymer and interpolymer energy transfer. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012