The optimal diffusion experiment

Diffusion experiments are time-consuming and expensive. Therefore, diffusion experiments should be designed such that they allow for efficient measurements while still leading to high accuracy of the diffusion coefficients. Numerous experimental setups have been designed in the past centuries incorporating a variety of geometries. The accuracy of experimentally determined diffusion coefficients depends on the geometry of the experimental setup as well as on the analytical techniques used to determine concentrations of the diffusion species. Whereas analytical techniques and their accuracy are subject of continuous improvement, geometries are genuine features of a setup. Therefore, optimal geometries for diffusion experiments can be identified once and for all. In this work, we identify optimal geometries to measure diffusion coefficients. For this purpose, we analyze the influence of the geometry of an experimental setup on the accuracy of the determined Fick diffusion coefficients. We consider both already existing and theoretically conceivable geometries. The analysis is based on the method of model-based optimal experimental design. 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. (C) 2016 Elsevier Ltd. All rights reserved.