Surface exchange reactions and diffusion in composite materials: A finite element approach

A two-dimensional square grain model has been applied to model oxygen exchange processes between a gas phase and a ceramic composite consisting of two randomly distributed phases of equal grain size (side length of squares). Both average diffusion profiles for thin films and the time dependence of the total amount of exchanged oxygen (relaxation curves) have been calculated numerically by means of the finite element method. The boundary conditions refer to an instantaneous change of the oxygen partial pressure in the surrounding gas phase, which gives rise to surface exchange reactions as well as to diffusion in the composite. Both local equilibrium at the interface between different phases (host phase and inclusions) and blocking heterophase boundaries have been taken into account. The numerical results are compared with the analytical solution for diffusion in a homogeneous medium introducing effective diffusion and surface exchange coefficients. When the relaxation time for effective medium diffusion is considerably shorter than that for the transport process from the host phase into the inclusions, relaxation curves with two separate time constants are predicted. Based on analytical approximations, relaxation times for various limiting cases are given.