Measurement of Mass Diffusivity Using Interferometry through Sensitivity Analysis

Mass diffusion of a solute in a solvent is realized in many applications. The extraction of transport properties from optical images has not received sufficient attention, though refractive index techniques for determination of the mass diffusion coefficient of a solute in a binary system have been discussed in the literature. The issue becomes important in experiments involving slow diffusion during which concentration gradients in parts of the domain are large. Accordingly, refractive index gradients are also large and higher order effects influence image formation. This weakness can be addressed by carrying out sensitivity analysis, wherein only that part of the data is analyzed which is highly sensitive to the experimental determination of diffusivity. In the context of interferometry, the present study reports fringe patterns obtained for the diffusion of NaCl and sucrose in deionized water at 25 °C. A Mach–Zehnder configuration of the interferometer has been employed. In an experiment, a layer of solution is placed in a temperature-controlled cavity with fresh water above. The diffusion of the solute into water leads to the formation of time-dependent fringe patterns. The images obtained are analyzed using two different techniques that work with the right combination of fringes. Data analysis is carried out in that region of space and time which is most sensitive to mass diffusivity. The two approaches rely on working with distinguishable fringes in the field of view and their displacement in time. Both of these methods are found to be effective in predicting the mass diffusion coefficient, in fair agreement with the literature. The present work signifies the importance of sensitivity analysis while obtaining reliable values of mass diffusivity using interferometry.