Tracer diffusion length scale

Bulk path at moderate to high overpotential. Studies of impedance time scales, tracer diffusion profiles, and electrode microstructure suggest that at moderate to high cathodic over potential, LSM becomes sufficiently reduced to open up a parallel bulk transport path near the three-phase boundary (like the perovskite mixed conductors). This effect may explain the complex dependence of electrode performance on electrode geometry and length scale. To date, no quantitative measurements or models have provided a means to determine the degree to which surface and bulk paths contribute under an arbitrary set of conditions. 

Here, the putative length scale represents some kind of mean displacement, or some Lagrangian decorrelation scale that is evidenced by a granularity in the tracer distribution (see Armi and Stommel, 1983 Jenkins, 1987 Joyce and Jenkins, 1993). The uf term is usually characterized as a turbulent diffusion coefficient k, because of its functional similarity to the molecular diffusion coefficient ... 

An important characteristic of a property distribution is encapsulated in the Peclet number, Pe = ULIk, which is the ratio of diffusive time-scale to advective timescale of the system. In this definition, U and L are the characteristic velocity and length scales of the flow. The Peclet number is a measure of the relative importance of advection versus diffusion, where a large number indicates an advectively dominated distribution, and a small number indicates a diffuse flow. Numerical modeling indicates that certain tracer distributions, in particular tracer-tracer relationships, are significantly affected by the Peclet number, and consequently can be used to determine the nature of the fluid flow (Jenkins, 1988 Musgrave, 1985, 1990). 

Fig. 14 Simulation of the trajectory of a tracer which can reversibly bind to polymer in a dilute polymer solution. When bound, the diffusion is strongly hindered whereas free diffusion is assumed in the non-bound periods. Panel (a) shows the case when the two length scales of the volumes with bound and unbound tracer are greater than the focal spot dimension, w, while panel (b) shows the opposite situation. In case (a), two distinct diffusion processes are resolved by PCS. In case (b), a single average process is observed, (adapted from Physical Review Letters [4b] Copyright (2013) American Physical Society)...

In practical applications we are often interested in the early stages of a mixing process, before the process becomes controlled by diffusion (i.e., when striations reach the length scale of diffusion). Short-term mixing dynamics have been extensively studied in the past by tracer dispersion simulations. Consider the sine flow... 

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