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.

Analysis of Non-Stationary Flows Using Eulerian and Lagrangian Frameworks

Recent developments have made researchers to reconsider Lagrangian measurement techniques as an alternative to their Eulerian counterpart when investigating non-stationary flows. This thesis advances the state-of-the-art of Lagrangian measurement techniques by pursuing three different objectives: (i) developing new Lagrangian measurement techniques for difficult-to-measure, in situ flow environments; (ii) developing new post-processing strategies designed for unstructured Lagrangian data, as well as providing guidelines towards their use; and (iii) presenting the advantages that the Lagrangian framework has over their Eulerian counterpart in various non-stationary flow problems. Towards the first objective, a large-scale particle tracking velocimetry apparatus is designed for atmospheric surface layer measurements. Towards the second objective, two techniques, one for identifying Lagrangian Coherent Structures (LCS) and the other for characterizing entrainment directly from unstructured Lagrangian data, are developed. Finally, towards the third objective, the advantages of Lagrangian-based measurements are showcased in two unsteady flow problems: the atmospheric surface layer, and entrainment in a non-stationary turbulent flow. Through developing new experimental and post-processing strategies for Lagrangian data, and through showcasing the advantages of Lagrangian data in various non-stationary flows, the thesis works to help investigators to more easily adopt Lagrangian-based measurement techniques.