The optimal diffusion experiment

Open geometries, where components can diffuse out of the geometry, are identified to be most beneficial. The most commonly employed free diffusion experiments are shown to lead to high uncertainty. Replacing free diffusion experiments by experiments with open geometries can improve the accuracy of the Fick diffusion coefficients by up to two orders of magnitude. We show that the optimal geometries are robust with respect to uncertainties in the diffusion coefficient as well as with respect to uncertainties in measurement positions, measurement times and positions of the initial domain boundary.