Effective diffusion in the region between two surfaces

TL;DR

This paper derives a formula for effective diffusion in a region between two surfaces by projecting 3D diffusion onto 2D, accounting for finite stabilization rates with reflective boundaries.

Contribution

It introduces a new formula for effective diffusion operators considering finite transversal stabilization, extending previous models.

Findings

Derived a projection-based diffusion formula for bounded regions

Accounts for finite transversal stabilization rate

Provides a mathematical tool for modeling diffusion between surfaces

Abstract

The purpose of this paper is to provide a formula for the effective diffusion operator obtained by projecting the 3-dimensional diffusion equation onto a 2-dimensional plane, assuming reflective boundary conditions at two surfaces in 3-dimensional space. The formula provided corresponds to the case of finite transversal stabilization rate.