Trapping of diffusive particles by rough absorbing surfaces: boundary smoothing approach

Area of Science:

• Physics
• Statistical Mechanics
• Physical Chemistry

Background:

• Understanding particle diffusion near complex boundaries is crucial in various scientific fields.
• Traditional models often simplify boundary conditions, potentially overlooking significant effects.

Purpose of the Study:

• To develop an analytical method for studying first-passage statistics of Brownian particles near a comblike absorbing boundary.
• To provide insights into diffusive transport phenomena influenced by complex boundary geometries.

Main Methods:

• Employing the method of boundary homogenization (or boundary smoothing) to approximate a rough boundary with an equivalent flat one.
• Utilizing the conformal invariance of the Laplace equation to derive an analytical expression for the equivalent boundary's position.
• Analyzing steady-state systems to understand trapping time statistics.

Main Results:

• Derived an analytic expression for the equivalent flat boundary's position based on the original boundary's spatial period and amplitude.
• Obtained insights into the statistical characteristics of diffusive transport near rough boundaries.
• Characterized high-order moments of trapping time statistics.

Conclusions:

• Boundary homogenization provides an effective analytical approach for studying diffusion near complex absorbing boundaries.
• The derived analytical expressions offer valuable tools for predicting particle behavior in systems with rough interfaces.
• The findings enhance the understanding of diffusion-controlled processes influenced by boundary geometry.