Towards a non-Fickian diffusion model using fractal geometric techniques

Most fluid diffusion models exhibit Fickian superdiffusive behavior due to the use of either a particle-tracking technique or an advective-diffusion equation on a computational grid. However, a new particle-tracking technique where each particle have fractional Brownian motion (fBm) has been shown to produce no Fickian diffusion. The 'non-Fickianess' of the fBm technique is inherent within the trajectories themselves, which eliminates the need for time-dependent diffusion coefficients. However, it is limited by the Hurst exponent to a maximum of unity.