Hydrodynamic fluctuations in quasi-two dimensional diffusion

A common feature of many biological systems is the diffusion of particles in a two-dimensional interface immersed in a three-dimensional fluid. Think for example of proteins diffusing in a lipid membrane. It is known that in these systems the interplay between hydrodynamic interactions and Brownian fluctuations leads to anomalous diffusion, in which the collective diffusion coefficient diverges like the inverse of the wavenumber. Here, we use particle simulations and fluctuating hydrodynamics to study the diffusion of colloids in a simplified system, ideal
particles at a fluid-fluid interface. We find that even if collective diffusion is enhanced the self-diffusion of a particle at thermal equilibrium is slow down at long times. We extend previous theories to account for a species labeling of the particles and use nonequilibrium fluctuating
hydrodynamics to show that when only a fraction of the particles in the system are tracked their density has giant fluctuations. These findings can be relevant to interpret results from fluorescent experiments.