Measurement of Mass Diffusivity Using Interferometry through Sensitivity Analysis Yogesh M. Nimdeo, † Yogesh M. Joshi,* ,† and K. Muralidhar ‡ † Department of Chemical Engineering and ‡ Department of Mechanical Engineering, Indian Institute of Technology Kanpur Kanpur 208016, India ABSTRACT: 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. 1. INTRODUCTION The diffusion of species in a mixture is a stochastic process and is known to redistribute matter at a microscopic level. On a macroscopic scale, it follows the gradient diffusion model and is, in principle, completely characterized by Fick’s law leading to a diffusion coefficient, namely, mass diffusivity. The knowledge of mass diffusivity is essential for material characterization, optimal design of unit operations, 1,2 and mathematical modeling of various chemical and other engineering processes. 3,4 Although an order-of-magnitude determination of a mass diffusivity can be readily obtained using various techniques, improved values of the property, specifically as a function of solute concentration and temperature, require specialized tools. The mass diffusivity of a solute in a solvent, namely a binary system, can be predicted theoretically or determined from empirical correlations. 5,6 On the other hand, experimental methods such as quasi-steady-state diffusion through a porous diaphragm, 7 Wiener’s method, 8 light beam deflection techniques, 9,10 decaying pulse technique, 11 and interferometry 12−16 have also been used to experimentally determine the mass diffusivity. Out of these, optical techniques are of special importance owing to their inertia-free and nonintrusive nature. In this work we present the measurement of mass diffusivity using a Mach−Zehnder interferometer. In particular, we examine two data analysis techniques in the context of interferograms formed in a mass transfer process. We analyze their advantages and disadvantages from a point of view of rigor and possible errors in experimental determination of mass diffusivity. We aid the interferometric determination of mass diffusivity by locating the most sensitive region of space and time, which leads to greater confidence in the parameter measurement procedure. In an interferometric experiment, diffusion is allowed to progress in time in a reference configuration, such as a rectangular cavity. The binary system is required to be transparent and nonabsorbing. Owing to a gradient in density, properties such as phase and path length of the light beam get altered, which leads to the formation of fringes. The data thus recorded is highly resolved in space and time. Fringes represent the concentration field in the spatiotemporal domain from which diffusivity can be obtained experimentally. In the literature, various interferometric techniques have been employed to measure mass diffusivity. Guo et al. 17 used phase shifting interferometry to determine the diffusion coefficient of NaCl solution in water as a function of salt concentration. The concentration field was obtained by counting the number of fringes. Torres et al. 18 employed a phase shifting technique to determine the mass diffusivity of 10 mg/mL solution of NaCl and 400 mg/mL solution of sucrose in water using a small (3 mm × 20 mm × 45 mm) diffusion cell. Interestingly, usage of a small cavity facilitated the formation of fewer fringes and the experimental determination of mass diffusivity within a short period of 10−13 min with an uncertainty of 5%. Riquelme et al. 14 carried out interferometric measurement of the diffusion coefficient by using electronic Received: June 30, 2014 Revised: November 7, 2014 Accepted: November 10, 2014 Published: November 10, 2014 Article pubs.acs.org/IECR © 2014 American Chemical Society 19338 dx.doi.org/10.1021/ie502601h | Ind. Eng. Chem. Res. 2014, 53, 19338−19350