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.

SCAPHOID AND LUNATE CARPAL MECHANICS OVER THE SPECTRUM OF HEALTHY FUNCTION

When ligaments within the wrist are damaged, the resulting loss in range of motion and grip strength can lead to reduced earning potential and restricted ability to perform important activities of daily living. Left untreated, ligament injuries ultimately lead to arthritis and chronic pain. Surgical repair can mitigate these issues but current procedures are often non-anatomic and unable to completely restore the wrist’s complex network of ligaments. An inability to quantitatively assess wrist function clinically, both before and after surgery, limits the ability to assess the response to clinical intervention. Previous work has shown that bones within the wrist move in a similar pattern across people, but these patterns remain challenging to predict and model. In an effort to quantify and further develop the understanding of normal carpal mechanics, we performed two studies using 3D in vivo carpal bone motion analysis techniques. For the first study, we measured wrist laxity and performed CT scans of the wrist to evaluate 3D carpal bone positions. We found that through mid-range radial-ulnar deviation range of motion the scaphoid and lunate primarily flexed and extended; however, there was a significant relationship between wrist laxity and row-column behaviour. We also found that there was a significant relationship between scaphoid flexion and active radial deviation range of motion. For the second study, an analysis was performed on a publicly available database. We evaluated scapholunate relative motion over a full range of wrist positions, and found that there was a significant amount of variation in the location and orientation of the rotation axis between the two bones. Together the findings from the two studies illustrate the complexity and subject specificity of normal carpal mechanics, and should provide insights that can guide the development of anatomical wrist ligament repair surgeries that restore normal function.