Diffusion-influenced reactions on non-spherical partially absorbing axisymmetric surfaces

Abstract

The calculation of the diffusion-controlled reaction rate for partially absorbing, non-spherical boundaries presents a formidable problem of broad relevance. In this paper we take the reference case of a spherical boundary and work out a perturbative approach to get a simple analytical formula for the first-order correction to the diffusive flux onto a non-spherical partially absorbing surface of revolution. To assess the range of validity of this formula, we derive exact and approximate expressions for the reaction rate in the case of partially absorbing prolate and oblate spheroids. We also present numerical solutions by a finite-element method that extend the validity analysis beyond spheroidal shapes. Our perturbative solution provides a handy way to quantify the effect of non-sphericity on the rate of capture in the general case of partial surface reactivity.

References in corpus (9)

• Phoretic Motion of Spheroidal Particles Due To Self-Generated Solute Gradients
• Spectral theory of imperfect diffusion-controlled reactions on heterogeneous catalytic surfaces
• Catalysis by metallic nanoparticles in solution: Thermosensitive microgels as nanoreactors
• Semi-analytical computation of Laplacian Green functions in three-dimensional domains with disconnected spherical boundaries
• Fluctuations and correlations in chemical reaction kinetics and population dynamics
• Imperfect Diffusion-Controlled Reactions
• Shape-dependent guidance of active Janus particles by chemically patterned surfaces
• Reaction rate of a composite core-shell nanoreactor with multiple, spatially distributed embedded nano-catalysts
• Steady-state reaction rate of diffusion-controlled reactions in sheets

Cited by in corpus (7)

• First-passage times to anisotropic partially reactive targets
• An encounter-based approach to the escape problem
• Spectral properties of the Dirichlet-to-Neumann operator for spheroids
• Mean exit time in irregularly-shaped annular and composite disc domains
• Encounter-based approach to target search problems: a review
• Mean first-passage time to a small absorbing target in three-dimensional elongated domains
• Enhancing search efficiency through diffusive echo