# Gas diffusion in nanoporous thin films

## TL;DR

This paper investigates gas diffusion in nanoporous thin films using various mathematical methods to solve the diffusion equation under different boundary conditions, including adsorption effects and steady-state analysis.

## Contribution

It provides a comprehensive review of solution techniques for diffusion problems in nanopores, including complex boundary conditions and adsorption phenomena.

## Key findings

- Different solution methods are compared and applied to specific boundary conditions.
- The effects of surface adsorption on diffusion profiles are analyzed.
- Steady-state recovery processes are characterized for various scenarios.

## Abstract

We analyze the Fick's diffusion of a gas inside porous nanomaterials through the one-dimensional diffusion equation in nanopores for various cases of boundary conditions for homogeneous and non-homogeneous problems. We study the diffusion problems, starting without adsorption of the gas inside the pores, to more complex situations with surface adsorption in the pore walls and at the pore tips. Different methods of solution are reviewed depending on the problem, such as similarity transformation, Laplace transform, separation of variables, Danckwerts method and the Green's functions technique. The recovery step when the diffusion process stops and reached the steady-state is presented as well for the different problems.