Unbiased diffusion in two-dimensional channels with corrugated walls.

Area of Science:

• Physics
• Physical Chemistry
• Materials Science

Background:

• Particle diffusion in confined geometries is crucial for understanding transport phenomena.
• Linearly corrugated channels present complex diffusion pathways.
• Existing analytical models may lack accuracy for certain geometric parameters.

Purpose of the Study:

• To derive and validate an analytical expression for effective diffusivity of point particles in 2D linearly corrugated channels.
• To identify the limitations of the initial analytical model.
• To propose and verify an improved model incorporating empirical corrections.

Main Methods:

• Development of an approximate analytical expression for effective diffusivity.
• Validation using Brownian dynamics simulations.
• Introduction of an empirical correction to refine the analytical model.

Main Results:

• The initial analytical expression accurately predicts effective diffusivity for long channel periods.
• The model shows deficiencies when the channel period is short relative to its width.
• The corrected analytical expression demonstrates excellent agreement with simulation results for all tested channel periods.

Conclusions:

• The proposed empirical correction effectively extends the applicability of the analytical model.
• Accurate prediction of effective diffusivity in corrugated channels is achievable across a wide range of geometric parameters.
• The findings are valuable for designing and analyzing microfluidic devices and porous materials.