  In this note, we demonstrated for the first time that one can derive an
expression for the effective diffusion coefficient, equal to the Lifson-Jackson
formula, using a subsequent homogenization of the 1D
reaction-diffusion-advection equation. The latter has been derived by applying
asymptotic perturbation analysis to the underlying 3D reaction-diffusion
equation with spatially dependent no-flux boundary conditions and incorporates
the effects of boundary interactions on the reactants via a boundary-induced
advection term [S. Martens et al, Phys. Rev. E 91, 022902 (2015)].
