Confined Diffusion of a Colloidal Particle Between Two Parallel Walls: Quantifying Diffusing Diffusivity

"Anomalous yet Brownian" diffusion has been observed in numerous physical and biological systems over the last few years, both experimentally and in simulations. The concept of Diffusing Diffusivity, which we proposed to explain such phenomena, has also been studied extensively. As shown by the Bechhoefer group (PRE 96, 042604, 2017), the simplest experimental system is possibly that of a particle confined to a slit since its diffusion coefficient does depend on the distance to a wall. We revisit this problem using Lattice Boltzmann simulations of a particle between two walls in the absence of external forces, a simpler situation since no external force is present. Instead of using the Kurtosis as a measure of the non-ideality of the diffusion motion, we introduce a new empirical fitting function with a tunable exponent and a critical time scale. We test our results with an alternative Monte Carlo simulation and discuss the implications.