Diffusion profile, stability

Diffusion of the stable Zr tracer isotope in 12mol% poly crystalline scandia-stabilized zirconia was studied in air at 1200 to 1600C. Secondary ion mass spectroscopy was used to record the tracer diffusion profiles. The diffusivities for bulk and grain boundary diffusion were given by,... 

Chemical diffusion of the rare-earth element was measured in natural calcite under anhydrous conditions, using rare-earth carbonate powders as the sources. Experiments were run in sealed silica capsules together with finely ground calcite to ensure stability of the single-crystal samples during diffusion anneals. Rutherford back-scattering spectroscopy was used to measure diffusion profiles. The Arrhenius relationship at 600 to 850C was ... 

Flow in a Tube. Laminar flow with a flat velocity profile and slip at the walls can occur when a viscous fluid is strongly heated at the walls or is highly non-Newtonian. It is sometimes called toothpaste flow. If you have ever used Stripe toothpaste, you will recognize that toothpaste flow is quite different than piston flow. Although Vflr) = u and z(7) = 1, there is little or no mixing in the radial direction, and what mixing there is occurs by diffusion. In this situation, the centerline is the critical location with respect to stability, and the stability criterion is... 

A model and attendant computer code have been constructed to describe time-dependent void growth and stability for any processing cure cycle. Although the analysis is approximate, it does account for the moving void-resin boundary layer and its effect on the concentration profile and diffusion of water in the resin. It was found that for the duration of the cure cycle it makes little difference whether the initial small voids contain pure water or mixtures of air and water. 

The local stability of a given stationary-state profile can be determined by the same sort of test applied to the solutions for a CSTR. Of course now, when we substitute in a = ass + Aa etc., we have the added complexity that the profile is a function of position, as may be the perturbation. Stability and instability again are distinguished by the decay or growth of these small perturbations, and except for special circumstances the governing reaction-diffusion equation for SAa/dr will be a linear second-order partial differential equation. Thus the time dependence of Aa will be governed by an infinite series of exponential terms ... 

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