Coupling of diffusion and reaction in a thin cylindrical tube: Methodological drawbacks of the Fick--Jacobs approach

Abstract

We investigate a problem, that describes coupling between diffusion and reaction inside a thin circular cylindrical tube. The asymptotic solution of the posed problem is derived by means of the boundary functions method. We perform comparison of this asymptotic solution against corresponding exact solution, which revealed serious methodological drawbacks of known Fick-Jacobs reduction approach. The results obtained may be used to study a wide range of reaction-diffusion problems, when the Fick-Jacobs method cannot be applied.