Applications where the diffusive and advective time scales are of similar order give rise to advection– diffusion phenomena that are inconsistent with the predictions of parabolic Fickian diffusion models. Non-Fickian diffusion relations can capture these phenomena and remedy the paradox of infinite propagation speeds in Fickian models. In this work, we implement a modified, frame-invariant for...

[1] Fickian models of diffusion often fail to describe transport phenomena in heterogeneous environments due to their inability to capture the sub-scale fluctuations. We present an effective description of non-Fickian behavior that reflects the dichotomy between the continuum nature of Fick’s law and the finite (effective) observation scale associated with experimental studies of transport phen...

Models of biological diffusion-reaction systems require accurate classification of the underlying diffusive dynamics (e.g., Fickian, subdiffusive, or superdiffusive). We use a renormalization group operator to identify the anomalous (non-Fickian) diffusion behavior from a short trajectory of a single molecule. The method provides quantitative information about the underlying stochastic process,...

Many electrochemical devices are formulated on conjugated polymer films. A model is presented for electrogenerated chemiluminescence in such systems. The resulting diffusion equation for ion transport has a standard Fickian form, but with a highly nonlinear diffusion coefficient. The asymptotic analysis of the equation involves both intermediate layers and logarithmic matching. The asymptotic r...

For the past few decades, researchers have been intrigued by glassy polymers, which applications ranging from gas separations to corrosion protection drug delivery systems. The techniques employed examine sorption and diffusion of small molecules in polymers are subject this review. Diffusion models regulated Fickian non-Fickian diffusion, with being more prevalent. characteristics determined i...

The asymptotic scaling behavior of the mixing region induced by a random velocity field is determined by applying Corrsin’s hypothesis in both the Eulerian and Lagrangian pictures. Both pictures lead to the same results for the asymptotic scaling exponent of the mixing region. Both longitudinal and transverse diffusion are asymptotically non-Fickian (Fickian) when the correlation function of th...