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Search for a small hole in a cavity wall by intermittent bulk and surface diffusion
Alexander M Berezhkovskii1, Alexander V Barzykin
1Mathematical and Statistical Computing Laboratory, Division of Computational Bioscience, Center for Information Technology, National Institutes of Health, Bethesda, Maryland 20892, USA. berezh@mail.nih.gov
The Journal of Chemical Physics
|February 11, 2012
Summary
This study models particle search for a hole in a spherical cavity, considering both bulk and surface diffusion. Approximate formulas accurately predict mean search time and surface passage probability.
Area of Science:
- Physics
- Physical Chemistry
- Chemical Engineering
Background:
- Particles diffusing within cavities can interact with surfaces, influencing their search dynamics.
- Understanding particle search behavior is crucial in fields like drug delivery and microfluidics.
Purpose of the Study:
- To develop a coarse-grained model for particle search in a spherical cavity with a small hole.
- To derive analytical approximations for mean first passage time and surface vs. bulk search pathways.
- To validate model predictions against numerical simulations.
Main Methods:
- Coarse-grained modeling of particle diffusion and reversible binding.
- Derivation of approximate analytical formulas for key search metrics.
- Numerical solution of the mixed bulk-surface diffusion problem using the finite difference method.
Main Results:
- Accurate approximate formulas were derived for mean first passage time.
- The probability of the particle reaching the hole via the surface channel was determined.
- Analytical results showed excellent agreement with numerical simulations for both volume and surface starting distributions.
Conclusions:
- The proposed coarse-grained model effectively captures particle search dynamics in a spherical cavity.
- The derived analytical formulas provide reliable predictions for particle search efficiency.
- This work offers a simplified yet accurate approach to studying complex diffusion-reaction processes.
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