New experimental method to measure pure and cross diffusion coefficients of transparent ternary mixtures using Mach–Zehnder interferometry Amirhossein Ahadi, M. Ziad Saghir n Department of Mechanical & Industrial Engineering, EPH-322, 87 Gerrard St. East, Ryerson University, Toronto, Ontario, Canada M5B 2K3 article info Article history: Received 19 December 2013 Received in revised form 9 February 2014 Accepted 22 March 2014 Available online 12 April 2014 Keywords: Mach–Zehnder Interferometry Ternary mixture Diffusion coefficient measurement Image processing Space experiment abstract In this study, a Mach–Zehnder interferometer that is equipped with two lasers of different wavelengths was used to conduct high resolution measurements of concentration profiles of a ternary mixture inside a diffusion cell. Windowed Fourier transform along with an advanced unwrapping procedure was employed to extract the phase image from fringe images. Then the phase difference was obtained for a spatial resolution of 1920  1240. According to the measured refractive index profile, concentration contours of two components (out of three) were measured. Consequently, the concentration profile of the third components was calculated. Previously, the analytical solution for binary mixtures was used to estimate only the pure diffusion coefficients. In this study, for the first time, the refractive indices measured by two lasers along with the analytical solution for the ternary system, based on Fick's law, and an evolutionary algorithm (EA) known as a genetic algorithm (GA) were employed to measure the pure and cross diffusion coefficients of a transparent ternary mixture simultaneously. The optimization method to estimate diffusion coefficients was tested against various objective functions, and the best approach was that which was proposed herein. In order to validate the proposed measurement method, the experimental results of the Selectable Optical Diagnostics Instrument-Diffusion Coefficients in Mixtures (SODI-DCMIX1 project) on board the International Space Station (ISS) were analyzed using this technique and the obtained results were compared with previous techniques. & 2014 Elsevier Ltd. All rights reserved. 1. Introduction Diffusion phenomena play a vital role in many applications of mechanical and chemical engineering, oil discovery, oil reservoir simulation, in pollution control, and biological systems [1–3]. Scientists in these fields require accurate measurements of the diffusion coefficients of the components in mixtures in order to properly design new products such as drugs or to accurately simulate the mass transfer in multi-component phenomena such as species transport in oil reservoirs [4]. The diffusion coefficient of a component in a mixture can be predicted theoretically or estimated from various correlations [1]. In addition to that, these coefficients might also be determined experimentally. Optical methods are the most popular among the wide variety of techni- ques for this measurement. The most important advantages of optical methods, which have been utilized for measurement of the diffusion coefficients, are their non-intrusiveness and high sensitivity [5–7]. As these methods are contactless, their measurements do not disturb the process under research; consequently, more accurate measure- ment results [8,9]. Optical methods suggest the qualitative and the quantitative data. The phenomenological theories are developed based on the information that was obtained by the optical method [10–12]. The principle limitations of the optical methods are that first the media should be transparent and have small dimensions relatively [1,10,13]. For instance, for nano-fluids with the initial mass fraction of nanoparticle is high, these methods cannot be used and various correlations along with numerical simulation methods are alternative options [11]. The key principle of the new optical method is based on the concentration profile in a diffusion phenomenon, which induces a gradient in the refractive index inside the fluid domain [1,10,13]. Interferometry is conceivably the most broadly used optical measurement method, and it includes various methods such as digital interferometry [9,14], electronic speckle pattern interfero- metry [15–17], and holographic interferometry [18–20]. Even though all these methods rely on the change of the refractive index, each method includes the application of specific instru- mentation, with various experimental uncertainties [21]. A com- parison of these techniques has been published elsewhere [1,22]. Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/optlaseng Optics and Lasers in Engineering http://dx.doi.org/10.1016/j.optlaseng.2014.03.009 0143-8166/& 2014 Elsevier Ltd. All rights reserved. n Corresponding author. Tel.: þ1 416 979 5000x6418; fax: þ1 416 979 5265. E-mail address: zsaghir@ryerson.ca (M.Z. Saghir). Optics and Lasers in Engineering 59 (2014) 72–81