Model-free estimation of mass fluxes based on concentration profiles. I. Presentation of the method and of a sensitivity analysis

An approach to identify mass diffusion coefficients (D) is presented, and applied to the case of a slab. It was based on a numerical exploitation of the concentration profiles to estimate the mass fluxes. The effect of the quality of the experimental data (spatial resolution, Δz¯, temporal resolution, ΔFo, of the concentration profiles, sampling) on the bias and sensitivity of the method was studied thanks to the use of simulated data (Fo ∈ [0, 2]), to which could be added Gaussian noise. Estimated D value were compared with the true solution (the one used for generating the simulated concentration data). The errors on D are large at low Fo < 0.2. But for Fo > 0.2, D can be estimated with less than 1% of bias if ΔFo < 0.1 and Δz¯<0.2. Space resolution had a minor effect. Although rough, the numerical procedure adopted in this paper revealed especially suitable for modern techniques of concentration measurements exhibiting high-accuracy (<1%).