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.

Maternal and paternal growth regulatory factor expression in hybrid sunfish.

Unidirectional hybridization between bluegill (Lepomis macrochirus) and pumpkinseed (L. gibbosus) sunfish enables researchers to explore the relative expression of paternal and maternal alleles in hybrids. Past studies have found that the metabolic dysfunction in bluegill-pumpkinseed hybrids may be due to incompatibilities between nuclear and mitochondrial genomes. However, the consequences of hybridization on body size and muscle growth have not been examined. This topic is particularly interesting because hybrids grow larger than parentals despite the fact that they are often sired by smaller, precociously mature bluegills. In order to improve our understanding of growth dynamics in hybrid sunfish, I conducted real-time quantitative PCR using species-specific primers on the white muscle tissue of bluegills, pumpkinseeds, and hybrids collected from Lake Opinicon, ON. Five growth factors that have been linked to muscle growth and body size demonstrated similar expression for maternal and paternal alleles. While about half of the hybrids showed the same pattern with myogenin, about half showed very low levels of mRNA for the paternal (bluegill) gene. While this did not explain the heterosis seen in hybrids, it may explain the small body phenotype of the cuckholding bluegill males. I explored the upstream genetic structure of bluegill myogenin and established that four alleles exist within the population. Furthermore, I uncovered a relationship in hybrids between the proximal promoter/ 5’ UTR of myogenin and its transcript level. I found that the hybrids demonstrating low paternal myogenin expression unfailingly possessed A3 or A4 alleles, but future studies will be needed to reveal the molecular links between the genotype and the growth phenotype. A similar genotype-phenotype association was not obvious in parentals, even those that were homozygous for these alleles. Whether this relationship can provide insight into the genetic determinants of bluegill alternative mating strategies has yet to be determined.