Diffusion toward non-overlapping partially reactive spherical traps: Fresh insights onto classic problems

Area of Science:

• Physical Chemistry
• Theoretical Physics
• Mathematical Modeling

Background:

• Understanding particle diffusion and reaction dynamics is crucial in various scientific fields.
• Existing models often face challenges with complex geometries and reactive boundaries.

Purpose of the Study:

• To revisit classic diffusion problems involving particles outside partially reactive spherical traps.
• To develop a robust semi-analytical method for analyzing diffusion-reaction characteristics.

Main Methods:

• Generalized method of separation of variables for modified Helmholtz equation.
• Derivation of a semi-analytical Green function solution.
• Numerical and asymptotic determination of eigenvalues and eigenfunctions.

Main Results:

• A semi-analytical Green function solution is derived for diffusion outside spherical traps.
• The method facilitates calculation of survival probability, first-passage time, and reaction rates.
• Eigenvalue and eigenfunction analysis is presented for perforated domains.

Conclusions:

• The generalized method offers a powerful tool for studying diffusion-reaction systems.
• Applications span chemical physics and biophysics, including mortal particle reactions.
• The findings enhance the understanding of particle behavior in complex environments.