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

Abstract

Several classic problems for particles diffusing outside an arbitrary configuration of non-overlapping partially reactive spherical traps in three dimensions are revisited. For this purpose, we describe the generalized method of separation of variables for solving boundary value problems of the associated modified Helmholtz equation. In particular, we derive a semi-analytical solution for the Green function that is the key ingredient to determine various diffusion-reaction characteristics such as the survival probability, the first-passage time distribution, and the reaction rate. We also present modifications of the method to determine numerically or asymptotically the eigenvalues and eigenfunctions of the Laplace operator and of the Dirichlet-to-Neumann operator in such perforated domains. Some potential applications in chemical physics and biophysics are discussed, including diffusion-controlled reactions for mortal particles.

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• Resonance scattering in a waveguide with identical thick barriers
• Reversible Target-Binding Kinetics of Multiple Impatient Particles
• An encounter-based approach to the escape problem
• First-encounter time of two diffusing particles in two- and three-dimensional confinement
• Accumulation time of diffusion in a 3D singularly perturbed domain
• A molecular relay race: sequential first-passage events to the terminal reaction centre in a cascade of diffusion controlled processes
• Survival in a nanoforest of absorbing pillars
• The Steklov problem for exterior domains: asymptotic behavior and applications
• Adsorption and permeation events in molecular diffusion
• Accumulation time of diffusion in a 2D singularly perturbed domain
• Enhancing search efficiency through diffusive echo