Non-Gaussian Diffusion Near Surfaces.

Area of Science:

• Physics
• Physical Chemistry
• Statistical Mechanics

Background:

• Particle diffusion near surfaces exhibits complex behavior, deviating from simple Brownian motion.
• Local diffusivity is often dependent on the distance from confining boundaries.
• Understanding non-Gaussian diffusion is crucial for accurately modeling transport phenomena.

Purpose of the Study:

• To theoretically investigate particle diffusion in confined geometries (single and double walls).
• To analyze the non-Gaussian nature of displacement parallel to walls and its statistical properties.
• To establish a connection between particle diffusion and Taylor dispersion theory.

Main Methods:

• Development of a theoretical framework to calculate the fourth cumulant and displacement distribution tails.
• Incorporation of distance-dependent local diffusivities and external potentials (e.g., gravity).
• Comparison of theoretical predictions with experimental and numerical data for colloidal particle motion.

Main Results:

• Particle displacement parallel to walls is Brownian in variance but non-Gaussian due to a nonzero fourth cumulant.
• The theory successfully predicts experimentally measured fourth cumulants for colloidal motion.
• Displacement distribution tails are Gaussian, contradicting models predicting exponential tails for non-Gaussian diffusion.

Conclusions:

• The developed theory provides accurate predictions for particle diffusion near surfaces.
• Results offer new constraints for inferring surface force maps and local transport properties.
• The Gaussian nature of displacement tails has significant implications for modeling diffusion processes.