Reaction Enhanced Diffusion in Spherical Membranes

TL;DR

This paper investigates how reversible reactions influence diffusion in spherical membranes, demonstrating enhanced fluxes through approximate solutions applicable to biological and solid surfaces with complex geometries.

Contribution

It introduces approximate analytical solutions for reaction-diffusion equations in spherical geometries, highlighting reaction-enhanced diffusion effects in biological and solid systems.

Findings

Reversible reactions can significantly increase diffusive fluxes.

Approximate solutions effectively model concentration profiles in spherical geometries.

Enhanced oxygen transfer demonstrated in biological membrane models.

Abstract

The reversible reactions like A+B <-> C in the many-component diffusive system affect the diffusive properties of the constituents. The effective conjugation of irreversible processes of different dimensionality takes place due to the stationarity in the system and can lead to essential increase of the resulting diffusive fluxes. The exact equations for the spatial concentration profiles of the components are difficult to treat analytically. We solve approximately the equations for the concentration profiles of the reaction-diffusion components in the spherical geometry in the application to the problem of the enhanced oxygen transfer through a biological membrane and to the mathematically similar problem of surface diffusion in a solid body. In the latter case the spherical geometry can be an adequate tool for describing the surface of a real solid body which can be modeled as a fractal object formed of sequences of spherical surfaces with different radii.