Uncertainty quantification and design-of-experiment in absorption-based aqueous film parameter measurements using Bayesian inference

Diode laser-based multi-wavelength near-infrared (NIR) absorption in aqueous films is a promising diagnostic for making temporally resolved, simultaneous measurements of film thickness, temperature, and concentration of a solute. Our previous work in aqueous urea solutions aimed at determining simultaneously two of these system parameters, while the third one must be fixed or specified by additional measurements. The current work presents a simultaneous NIR absorption-based multi-parameter measurement of thickness, temperature, and solute concentration coupled with the Bayesian methodology that is used to infer probability densities for the obtained data. The Bayesian analysis is based on a temperature- and concentration-dependent spectral database generated with a Fourier transform infrared spectrometer in the range $5500–8000{\mathrm{cm}}^{-1}$ for water with variable temperature and urea concentration. The concept was first validated with measurements using a calibration cell. Probability densities in the measured parameters were quantified using a Markov chain Monte Carlo algorithm, which were used to derive credibility intervals. As a practical demonstration, the temporal variation of film thickness, urea concentration, and liquid temperature were recorded during evaporation of a liquid film deposited on a transparent heated quartz plate.