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 Poverty Dynamics in Canada (Working Paper 9)

While we know much about poverty (or “low income”) in Canada in a static context, our understanding of the underlying dynamics remains very limited. This is particularly problematic from a policy perspective and the country has been increasingly left out on an international level in this regard. The contribution of this paper is to report the results of an empirical analysis of low income (“poverty”) dynamics in Canada using the recently available “LAD” tax-based database. The paper first describes the general nature of individuals’ poverty profiles (how many are short-term versus longterm, etc.)., the breakdown of the poor population in any given year amongst these different types, and the characterisation of poverty profiles by sex and family type. It then reports the estimation of various econometric models, starting with a set which specifies entry into and exit from poverty in any given year as a function of a variety of personal attributes and situational characteristics, including family status and changes therein, province of residence, inter-provincial mobility, language, area size of residence and calendar year (to capture trend effects). A set of proper hazard models then adds duration effects to these specifications to see how exit and re-entry probabilities shift with the amount of time spent in a poverty spell or after having exited a previous spell. A final set of specifications then investigates “occurrence dependence” effects by including past poverty spells first in an entry model and then with respect to the probability of being poor in a given year. Policy implications are discussed.