Trapping of diffusing particles by small absorbers localized in a spherical region

Area of Science:

• Physics
• Physical Chemistry
• Statistical Mechanics

Background:

• Particle diffusion and trapping are fundamental processes in various physical and chemical systems.
• Understanding particle interactions with boundaries and internal structures is crucial for modeling complex phenomena.
• Previous studies, like Krapivsky and Redner (2017), explored particle trapping in cavities but often with simpler geometries or absorber distributions.

Purpose of the Study:

• To derive an analytical expression for particle trapping probability in a spherical cavity with a central absorbing region.
• To investigate the competition between central absorbers and the cavity wall for diffusing particles.
• To generalize previous work by considering a localized central absorber region rather than absorbers filling the entire cavity.

Main Methods:

• Development of a steady-state approach to model particle diffusion and trapping.
• Derivation of an analytical expression for particle trapping probability.
• Analysis of the trapping probability as a function of dimensionless parameters.

Main Results:

• An expression for particle trapping probability was derived, depending on absorber transparency and the relative size of the absorber region.
• The study provides a more generalized model compared to previous work considering absorbers throughout the cavity.
• The steady-state approach offers a simpler alternative to time-dependent methods for this problem.

Conclusions:

• The derived expression accurately describes particle trapping in a spherical cavity with a central absorber region.
• The findings highlight the interplay between internal absorbers and boundary absorption in controlling particle fate.
• This work provides a valuable tool for analyzing diffusion-limited processes in structured environments.