Polymer Fluid Dynamics: Continuum and Molecular Appoaches

To solve problems in polymer fluid dynamics, one needs the equation of continuity, motion, and energy. The last two equations contain the stress tensor and the heat-flux vector for the material. There are two ways to formulate the stress tensor: (1) one can write a continuum expression for the stress tensor in terms of kinematic tensors, or (2) one can select a molecular model that represents the polymer molecule, and then develop an expression for the stress tensor from kinetic theory. The advantage of the kinetic theory approach is that one gets information about the relation between the molecular structure of the polymers and the rheological properties. In this review, we restrict the discussion primarily to the simplest stress tensor expressions or “constitutive equations” containing from two to four adjustable parameters, although we do indicate how these formulations may be extended to give more complicated expressions. We also explore how these simplest expressions are recovered as special cases of a more general framework, the Oldroyd 8-constant model. The virtue of studying the simplest models is that we can discover some general notions as to which types of empiricisms or which types of molecular models seem to be worth investigating further. We also explore equivalences between continuum and molecular approaches. We restrict the discussion to several types of simple flows, such as shearing flows and extensional flows. These are the flows that are of greatest importance in industrial operations. Furthermore, if these simple flows cannot be well described by continuum or molecular models, then it is not necessary to lavish time and energy to apply them to more complex flow problems.

IMPACTS OF ENHANCED TEMPERATURE AND SNOW DEPOSITION ON SENESCENCE DATE, VEGETATION COVER, AND CO2 EXCHANGE IN A CANADIAN HIGH ARCTIC MESIC ECOSYSTEM

Arctic regions are expected to experience an increase in both temperature and precipitation over the coming decades, which is likely to impact vegetation dynamics and greenhouse gas exchange. To test this response, an experiment was installed at the Cape Bounty Arctic Watershed Observatory, on Melville Island, NU, in 2008 as part of the International Tundra Experiment (ITEX). Snow fences and open top chambers (OTCs) were used to manipulate snow depth and air temperature, respectively. Unlike most ITEX sites to date, enhanced temperature and snowfall were combined here in a factorial design with eight replicates. As an added control, four plots were established well outside the enhanced snow area. Senescence date was recorded at the end of the season, and at the peak of the growing season a vegetation survey was conducted within each plot in order to determine the total percent cover of each plot, as well as the percent cover of individual species. Carbon dioxide (CO2) exchange was also measured within each plot throughout the growing season. The date of senescence occurred significantly earlier in plots which had not been manipulated in any way, compared to all other treatments for all species. Salix arctica showed the greatest increase in cover over time at the species level. Lichen cover increased significantly in the deepened snow plots, and in general there were significant increases in percent cover in some functional groups over time. During June and into July the net CO2 flux was to the atmosphere. It was not until July 27 that these ecosystems became net carbon sinks. However, warming alone resulted in the ecosystem acting as a significant net carbon sink for the entire growing season. Plots exposed to warming alone were estimated to have removed approximately 19.94 g C m-2 from the atmosphere, whereas all other treatments were very similar to one another and estimated to have added approximately 3.12 g C m-2 to the atmosphere. Active layer depth and soil temperatures suggest that plots within the ambient snow zone may be receiving some additional snow due to their proximity to the fences. CO2 fluxes measured within the outer control plots suggest that the effect of warming alone could lead to this ecosystem being an even stronger net C sink under truly ambient snow conditions.