Effective diffusion coefficient in 2D periodic channels.

Area of Science:

• Physics
• Physical Chemistry
• Applied Mathematics

Background:

• Calculating effective diffusion coefficients D(x) in complex geometries is crucial for understanding transport phenomena.
• Previous methods for 2D channels with periodically corrugated walls involved scaling transverse lengths and homogenization techniques.
• Brownian simulations by Dagdug et al. observed specific behaviors of D(x) in short-period channels.

Purpose of the Study:

• To revisit the calculation of the effective diffusion coefficient D(x) in 2D channels with periodically corrugated walls.
• To propose a novel algorithm based on formulating the problem in the complex plane.
• To explain the observed behavior of D(x) in channels with short periods L.

Main Methods:

• Formulation of the diffusion problem in the complex plane.
• Development of a new algorithm avoiding transverse length scaling and standard homogenization.
• Solving a simple model to analyze D(x) behavior.

Main Results:

• The proposed complex plane algorithm provides a new approach to calculating D(x).
• The algorithm successfully explains the diffusion coefficient behavior observed in short-period corrugated channels.
• The method offers an alternative to traditional scaling and homogenization techniques.

Conclusions:

• The complex plane formulation offers an effective method for analyzing diffusion in corrugated channels.
• This approach clarifies the underlying mechanisms for D(x) behavior in specific channel geometries.
• The study provides a valuable tool for predicting transport properties in microfluidic and porous media.