Diffusion in complex geometries: an approach with biological applications
I. Pineda , L. Dagdug

Universidad Autonoma Metropolitana Unidad Iztapalapa, Av. San Rafael Atlixco No. 186, Col Vicentina C.P. 09340, Mexico, D.F.

Abstract: The diffusion equation has universal validity and satisfactorily describes the features of the mass transport in any geometry. However, actually this equation can not be analytically solved for a set of boundary conditions describing complex geometries, like interconnected spatial regions that are very common in the shapes of life. In this work we solved the diffusion equation in a geometry inspired by an ionic channel, and which consist of two chambers connected by a conical capillary. We used the Fick-Jacobs.s equation to model the diffusion inside the channel and a pair of propagators to describe the translocation and return fluxes across the capillary. Finally we joined the solutions in each chamber with the capillary using radiative boundary conditions.