State-dependent diffusion of Brownian particles near a boundary wall

Brownian motion refers to the erratic random movement of microscopic particles suspended in a fluid. In a simple fluid, Brownian motion exhibits two key properties: the mean-squared displacement (MSD) increases linearly with time (the proportionality constant is the diffusivity D) and the displacement distribution is Gaussian. Although a linear MSD was initially assumed to always imply Gaussian displacements, recent experiments show that non-Gaussian displacements can coexist with a linear MSD in complex environments. Chubynsky et al. [PRL 113, 098302, 2014] have argued that such behavior arises when D has temporal and/or spatial fluctuations that are convolved together and form a non-Gaussian distribution. Experiments to date have been in complex settings where direct measurements of D(x, t) have not been possible. Here, we report experiments on a simple system where D(x, t) is known: the Brownian motion of a colloidal sphere near a boundary wall. By choosing the particle size carefully, we ensure that the bead explores a wide range of D. We observe a linear MSD curve and non-Gaussian displacements for vertical motion and directly confirm the proposed mechanism of Chubynsky et al. for such “diffusing diffusivity.”